Monte-Carlo-Simulation - RiskNET - The Risk Management Network

Get into Playing the Monte Carlo Simulation What makes the casino software of Monte Carlo Simulation so unique is that it's not a conventional game. It's not like all casinos or slots have games that replicate what the casino offers. This game offers something totally different.

Get into Playing the Monte Carlo Simulation What makes the casino software of Monte Carlo Simulation so unique is that it's not a conventional game. It's not like all casinos or slots have games that replicate what the casino offers. This game offers something totally different. submitted by MakhiCooke to HudSoft [link] [comments]

WELCOME TO CASINO DOTA: An Analysis of Luck in 7.23 Using Pseudo-Random Monte Carlo Simulations

UPDATE: Valve heard our prayers and have fixed the most significant issues outlined below. Now the difference between a "lucky" and "unlucky" team's ability to farm 3 items (the max per tier) is at least 30 creeps.

TL;DR: Even without accounting for the value of random drops, there is very significant variation in the number of creeps required to receive drops. These values are particularly impactful for the 3rd, 4th, and 5th drops, with differences ranging well into the hundreds of CS. You can follow along & reroll the simulation here.

I am sure you have all read the patch notes by now. I am sure you have thoughts about how neutrals drop items. I sure as fuck do. In addition to thoughts, here's some math.

Everyone is - correctly, as we shall see - worried about the balance problems introduced with the neutral drops mechanic. Clearly some drops are better than others, the non-worriers argue, but on average both teams will get approximately the same number of drops from the jungle (between 3-5). Whether, how, and the extent to which certain drop items are superior to others is at least partially a matter of debate. But the role that luck plays in the number of items each team gets is quantifiable and significant.

First, note that most of the threads discussing probabilities of drops assume true random distributions. Each creep has a certain chance to drop an item, which is independent from every other creep. In reality (and the patch notes) the distributions in Dota 2 are pseudorandom; each creep killed that does not drop an item increases the likelihood that the next creep will. My analysis takes PRNG into account*. The difference between pseudo and true RNG can be seen in the Charting sheet here.

Second, let us define "luck". Luck is the difference in outcomes between two identical sets of inputs. In this case, to be "lucky" is to get an item drop after killing a small number of creeps, while "unluckiness" implies having to kill a larger number of creeps in order to get the same number of items.

More specifically, I define "lucky" as requiring a number of creep-kills in the bottom quartile (25th percentile) and "unlucky" as requiring a number of creep-kills in the top quartile (75+percentile). By this definition, 1 in 16 1 in 8 games will be played between a lucky and an unlucky team or about 6.5% 13%**. I define "very lucky" and "very unlucky" as requiring creep-kills in the top and bottom decile (10th percentile and 90+ percentile). About 1% 2% of games will take place between a very lucky and very unlucky team.

To examine the role of luck, I created a 5000 entry Monte Carlo simulation using realistic Dota2 PRNG. You can copy and rerun the simulation here. Results are represented in two tables. The first shows the number of creep-kills required to get each level of drop, broken down by percentile. Each line of this table assumes that you have just received the previous drop number. The second table shows the cumulative totals found in the simulation; that is, the total number of creeps needed to get a certain number of drops.

Looking at the second table, one can see there is significant variation between the 25th and 75th percentile values, especially with larger numbers of items. For instance, a lucky team will only need less than 240 CS to get 5 items, whereas an unlucky team will need more than 370. That is a difference of at least 130 CS! What this means is that a lucky team will frequently have at least one additional item over an unlucky team, even if both teams kill an equivalent number of jungle creeps. Considering how powerful the drop items can be, especially at Tier 3+, this is functionally IceFrog randomly giving a player a 2k+ gold boost. Crazy!

When looking at very lucky versus very unlucky teams, the situation is even more dire (har har). To receive 5 items, a very unlucky team will have to kill at least 250 more creeps to receive the same number of drops as a very lucky team. In fact, a very lucky team will accumulate 5 items with the same number of CS that will net a very unlucky team three items.

Taken together, this suggests to me that the implementation of item drops is broken without even taking into account the wildly varying power levels of the abilities, the completely broken item/hero interactions (looking at you, Imp Claw and Kunkka), or the fact that random items make it impossible to forecast and counter your opponents' item builds. Two teams farming jungle at exactly the same speed will experience wildly different returns based on nothing more than luck. Especially with Tier 3 items, that can be equivalent to a gold swing in the thousands which can be decisive at higher levels of play.

OSFrog pls fix.


*If you are interested in the Python script I used to calculate the pseudorandom constant for each nominal likelihood, it is included in the PRNG tab of the Google Sheet.
**Note here that these tables apply to each new tier-timing. It is possible that one team is lucky in the 5-15min window but unlucky in the 25-35min window. The results stand regardless.
submitted by saladinsaladout to TrueDoTA2 [link] [comments]

User "Casino" game analysis using Monte Carlo simulation

User
tl;dr: you're going to lose in the long run, and the long run doesn't take too long at all.
Instead of doing life skills (in game and IRL) I ran some Monte Carlo simulations (code) of the user home "casino" games that are advertised in world chat.
How the game is played:
Trade onyx bet to host, host creates 4 random groups of players using the /randomgroup [number] command. If you're in a group under the host, you win 2x your bet! If you're in the same group or above, you lose 100% of your bet.
I simulated players betting 150 times, 1/5 bankroll (Kelly citerion) and a starting bankroll of 10K Onyx.
40 player's bankrolls (each on a line of a different color)
After I did the simulations I found beserker10 made a good post about the casino odds, check it out! The 40% oods are laid out there and I hope the plot makes it clear that those odds are a losing proposition.
Be safe out there! ~ RiskWizard
submitted by UpstairsTeacher to MapleStory2 [link] [comments]

Has anyone else noticed this absolute travesty?

There is an exotic weapon in D2 with the perk 'Break the Bank' and that weapon isn't the one named 'Monte Carlo'.
Furthermore, the weapon in question is themed after burglary (and gambit/the taken) rather than gambling, thus failing to use the phrase 'break the bank' correctly.
(I joke, but seriously; that was such a missed opportunity).
submitted by Flintlockman to DestinyTheGame [link] [comments]

Ultimate Gambling Guide for GTA Online - odds, probabilities, and optimal strategies

Since the Diamond Casino update, I have seen a large number of 12-year-olds posting Blackjack memes on this sub. As a parent, this has me very worried.
On top of that, I have seen some of the most trustworthy GTA Youtubers giving flawed gambling advice, which can have damaging impact on their gullible audiences.
So that's why I decided to write this up, to educate everyone on the subject, so there will be no more misunderstandings.
(2020 Update down at the bottom.)
If you're one of those Youtubers that wants to use this information in a video, feel free to do so. The more people (especially kids) that become educated about gambling, the better.
But then also please go back and review your own work, and delete or edit the videos that are giving out the wrong advice, like where you're saying you have "a good strategy for making money with roulette", or some other nonsense that I've heard this week. Delete that please.
Before I get into the individual games, I need to discuss a few concepts first, that will make understanding the rest a lot easier.

Expected return and variance
A game like Roulette or Slots has a fixed expected return on your bets. This is a percentage that you have no way of influencing. Say you are flipping a coin against a friend, and you both put up $1. The winner gets the pot. Since the odds are even at 50%, in the long run, you will expect to break even. Your expected return is 100% of your bet.
But imagine if you would play this coin flipping game in a casino against the house. On the "house rules" listed at the table they would probably say that you would only get 95 cents back for every win, while you are forfeiting a dollar on every loss. Would you still play?
Sounds stupid to do so, but still, everybody does it. Every bet they place on Roulette, every coin they put into a Slot machine, is based on the same concept.
Those few cents they take on every bet are their profit margin, and has paid for all the Vegas lights, the Mirage volcanoes, and the Bellagio fountains. Make no mistake - casino gambling games are not designed to make you lose, because sure, you can get lucky on a single night, but they are designed to make them win. That's the beauty of it. They can both exist at the same time.
Too many people that don't see how this works, are just destined for disaster. Just because you went on a lucky streak and won 8 games out of 10, does not mean that flipping coins is a profitable game, or that choosing tails is a winning strategy. Always be aware of the house edge, your true chances of winning, and just realize that you got lucky. There is no such thing as a strategy in flipping a coin that will give you a higher expected return, so it's just pure gambling, just like Slots and Roulette.
Most casino games are made in such a way, that your expected return is a little under 100%. This means that from every dollar bet at the tables, the casino expects to keep a few cents. For individual players, results may vary. Some will win, most will lose. But for the house, it doesn't matter. They take millions of bets each day, so for them, the expected average works out a lot sooner. In short: the house always wins.
When looking at the house edge, we're talking about the expected long-term result, based on the game's house rules. But for a player, it can take literally tens of thousands of hands or spins before you also reach this average number. Until that time, you can experience huge upswings and downswings, that are the result of nothing but short-term luck, which is called variance.
Some games and some bets have a much higher variance than others, which means your actual results will differ enormously from what you're expected to be at.
Take for example betting on red/black at the Roulette table. This is a low-variance proposition, because it has a high percentage chance of occurring, and a low payout.
Contrast this with betting single numbers in Roulette, which only win once every 38 spins on average. This bet has a much higher variance, meaning you can easily hit a dry spell, and not hit anything for 200 bets in a row, or you can see a single number hit three times in five consecutive spins. This is not a freak occurrence in high-variance bets.
Even though the expected return in both these bets is exactly the same, there's a huge difference in variance, causing massive differences in short-term results, which can go both ways. You need to be aware of this, before you decide what types of bets you are comfortable with placing.

Gamblers' Fallacy
Another thing to realize, is that each individual game, hand, or spin, is completely independent from the one(s) before it, and after it.
Gamblers tend to believe, that the chance of a certain outcome is increased, based on previous results.
The most famous example comes from the Casino de Monte Carlo, where the Roulette wheel managed to land on black 26 times in a row. Gamblers lost many millions during that streak, all frantically betting on red, believing that the odds were in favor of the wheel coming out on red, after producing so many blacks. This is not true. Each round is completely independent, and the odds are exactly the same.
You will hear people say things like a Blackjack table being "hot" or "cold", which is completely superstitious, and should be ignored. The exception was when Blackjack was being dealt from a shoe. It made card counting possible. But with the introduction of shuffle machines, and continuous shuffling like is being used in GTA, this no longer exists.
This is also why "chasing your losses" is a very bad idea. After being on a losing streak for some time, many gamblers believe that now it's their turn to start winning. So they will often increase their bet size, believing that when their predicted winning streak comes around, they will win back their losses, and more.
The reality of it, more often than not, is that people will indeed start playing higher and higher limits, until they are completely broke. Nobody is ever "due for a win". There is never a guarantee that you're about to start winning. In fact, the opposite is more likely to be true. You are, after all, in a casino.

Betting systems
Some people like to think that they have a fool-proof betting system, like the Martingale system. Simply increase or even double your bet when you lose, and keep doing that until you win. In theory, this system will always win. So that's why table limits were introduced, and where the system fails.
If you start at the Roulette table, playing red/black, with a small 750 chip wager, and just double your bet every time you lose, you only have to lose 6 times in a row, before you will be betting the table limit of 48,000, just to get that 750 chip profit.
Sure, you can go on all evening without this happening, winning 750 chips each time, but this losing streak only has to happen once, and you're bust. Any betting system like this is ill-advised, because you are hugely increasing your so-called "risk of ruin", and that's what we were trying to avoid.
And even if your starting bet is only 100 chips, after only nine straight losses, and nine doubled bets, you are betting the table limit at 50,000 chips. If you lose that bet, you're 100,000 chips in the hole, with no way to recover that with your 100 chip base wager.
So don't believe anyone that says this is the perfect system to always win in the casino. Sooner or later they will understand why they were wrong, when they're asking you for a loan.

Set your limits BEFORE you start playing
One final point before we get into the games, a general tip for people that head out to play: money management.
Just like in real life, before you go to the casino, decide on a maximum amount that you are WILLING TO LOSE.
Bet small enough, so that amount can last you through the entire evening, and you will not be tempted to run to the ATM to continue playing.
Considering GTA money, some people will be comfortable losing 1% of their GTA bank balance, some people will be comfortable with gambling away 5% of their total GTA savings. It's up to you what you can handle. Decide for yourself where it will start to hurt, and don't cross that line.
But whatever number you decide on, as soon as you lost that amount, get up and walk away. Don't chase your losses, stick to your limits, and accept that this has not been your day. There is always another game tomorrow. Always agree with yourself on a simple stop-loss rule, how much you would want to lose at most, and simply stop playing when you get there.
Same goes for winning. You can decide on a number, how much profit you would like to take away from the casino. You can go on a hot streak and be up half a million in a short period of time, but if you would continue to play longer, looking for more, chances are that you're going to lose it all back.
Most people are happy with doubling their daily casino budget, for example. Others are looking for 10 bets profit in Blackjack. Whatever you choose, when you hit that number, you can stop playing and bank your profits, or you can continue playing if you're still enjoying the games, but then only just play minimum bet sizes. Then you're just playing for fun, not for money. You've already made your profit, so simply keep it in your pocket, and don't risk losing it again.
Either way, decide on what your money management strategy will be, and STICK TO IT.

Casino games in GTA Online
Now, I'm going to dive into the games that you can find at the Diamond casino, ordered from worst to best.

6) Slots
Generally the rule is this: the less strategy a game has, the worse it is for the player. And with slots, this is definitely the case.
The only influence you have, is choosing what type of machine you're going to play. Basically, there are two types of slot machines:
-high frequency, low payout slots
-low frequency, high payout slots
In the first type, there is no huge (progressive) jackpot on offer, just your average selection of prizes that don't go up to crazy amounts.
This will result in a player having many more spins resulting in a win. The amounts that you win on the bigger prizes, will be smaller, but they do come around more often. This type of slot machine has a lower variance, which means that your money should last you longer, winning many smaller prizes along the way to keep you going.
The second type of slot machine lures you in with the temptation of a huge jackpot prize. Even though the long-term expected return on these machines is the same as the previous type, the prize distribution is hugely different. The large jackpot prize weighs heavily on the scale of expected return, but the chance of it hitting is extremely small. This results in a much higher variance on this type of machine. Usually your money will go down very fast, because the smaller prizes are less rewarding than on the other type of machine.
At the Diamond, the info screen says the player return at slots is set at 98.7%. This means that, on average, for every maximum bet of 2,500 chips, you expect to lose 32.5 chips.
This might not seem like a lot, but the danger of slots is that the game is extremely fast. You can spin about once every 6 seconds, which would result in an expected LOSS of about 20,000 chips per hour of playing.
But again, in this long-term expected number, the large jackpot awards are also factored in, and as long as you don't hit those big prizes, you'll see your money go down a lot faster.
In any case, thank heavens the max bet is only set at 2,500, or else we would see more players go bankrupt at alarming rates.
Optimal strategy for slots:
There is none. Because after betting, you have no more influence over the outcome. The only choices you have, is what type of machine you want to play at, and how much money you are going to risk. And those are all personal preference. As long as you stick to your loss limits, as discussed above, there's no harm in having a go every once in a while, hoping to get a lucky hit. Just realize that you don't have a high chance of scoring a big win, so as soon as you do, get up and walk away.

5) Roulette
Roulette is also a game where you have no influence over the outcome. There is zero skill involved. You place your bet, and that's it.
In traditional French roulette, a table has only the single-zero, but of course, for American casinos that wasn't enough of a house edge, so they simply doubled their profits by adding a second zero. The house edge was increased from 1/37 to 1/19, which is huge.
This makes playing on a double-zero roulette table by definition a sucker's play.
The payouts scale evenly, which means that a bet on a single number, and a bet on half of the numbers, and everything in between, yields the same expected return. The only difference, again, being the variance that you are willing to subject yourself to.
The player return for double-zero Roulette for all bets is 94.74%.
Except for the 5-number bet, which can only be made by placing a bet on the two top rows that contain 0, 00, 1, 2 and 3. The expected return on this bet is lower: 92.1%. This is because it only pays out 6-1. Why? Well, the number 36 isn't divisible by 5, so the greedy people that came up with double-zero Roulette had to round it off someway, and as expected, it wasn't going to be in the players' favor.Just remember that that 5-number bet is the worst bet at the table, and should be avoided. All other possible bets have the same expected return.
So it really doesn't matter how you spread your bets, if you bet only one chip, or if you litter the entire table with a bucketload of chips. Each chip you put out there, has the same expected return, so there is no strategy that will improve your long-term results.
Assuming that you're betting the maximum table amount of 50,000 chips, you will be looking at an expected loss of about 2,630 chips per spin. Considering that a round takes about 45 seconds to complete, your expected LOSS at the GTA Roulette tables will be around 200,000 chips per hour of playing.
Optimal strategy for double-zero roulette:
Stay away. Stay far away.

4) Three Card Poker
With Three Card Poker, we come across the first game where there is actually some strategy involved. You get to look at your cards, and then decide if you want to fold, and surrender your ante, or double your bet.
Additionally, you can choose to place a side bet on "Pair Plus", which offers progressive payouts.
There are some websites out there that ran all the numbers with computer simulations, and even though I would like to quote the source here, these websites are understandably littered to the max with online casino ads, so that's why I have decided against doing that.
Optimal strategy for Three Card Poker:
For this game you only have to remember one strategy rule: Always bet on any high card queen-six-four or better, and fold any high card queen-six-three or lower. That's it. Just don't forget to double check if you're not folding a straight or a flush, and you'll be fine.
This strategy will result in an expected return of 96.63%.
The Pair Plus sidebet, with the payout table that is used at the Diamond casino, gives you an expected return of 97.68%, which is actually a bit better than the main ante bet.
So by playing both wagers, you're reducing your expected losses per bet, but since you're betting more, you're also increasing your expected loss per hour.
My advice would obviously be to not play this game at all, but if you do, put as much of your bet as possible on the Pair Plus, while making our Ante bet as small as you can.
To be able to compare it to the other games at the Diamond, let's stay on that 50,000 maximum wager, meaning making your ante bet 35,000, and your pair plus bet 15,000, if the table would allow it.
This results in an expected loss of about 1,525 chips per hand, and with a round taking about 45 seconds, this adds up to an expected LOSS of around 120,000 chips per hour of playing. In comparison, if you would only play the ante bet for 50,000 per hand, you expect to lose 1,685 chips per hand, which means an expected LOSS of about 135,000 chips per hour. So the more out of that 50,000 wager you can put on the "Pair Plus" sidebet, the better.
Even though it may be fun to try out this game for a bit, since there's only one simple strategy rule to follow, you'll soon find yourself robotically grinding down your bankroll until it has vaporized. You're not missing out on anything if you skip these tables, there is no real challenge.
Just like with Roulette and Slots, if you want to try it out nonetheless, you can just bet the minimum amounts and only play for fun, so it won't matter if you win or lose.

3) Blackjack
Blackjack is the most complicated game by far. Simply because the player has to make a series of decisions, which will largely decide the outcome. Luckily, there is such a thing as an optimal strategy, which will be outlined below.
However, the strategy is also dependent on the house rules. These not only affect your expected return, but in some places also your decisions.
Here are the house rules at the Diamond casino:
-The game uses 4 standard decks, and a continuous shuffle.
-Blackjack pays 3 to 2, dealer checks for early blackjack.
-No insurance offered, no surrender.
-Dealer stands on soft 17.
-Double down on any two cards.
-Player can split only once, but doubling after split is allowed.
-Seven-Card Charlie.
Under these rules, and following the "basic strategy" chart, your expected return at Blackjack is a shade under 99.6%, which is extremely good for a casino game, that's why Blackjack should be your table game of choice.
But it comes at a price: you are going to have to memorize the relatively complicated strategy chart, or at least stick it to your monitor until you have it in your head. But in case you ever stumble into a real-life casino, you won't regret having this table memorized, so I would definitely advise you to work on that.
The strategy chart might look complicated at first, but you will be able to notice certain patterns. Your decisions are mainly based on the dealer's upcard, which is basically divided into a weak card (2 to 6), and a strong card (7 to ace).
When a dealer shows a strong card, you will be hitting more often with the risk of going bust, but when a dealer shows a weak card, you're not taking that risk, and you will be standing more, but also doubling and splitting more. You want to increase your bets when the odds are in your favor, and get out cheap when they're not.
But it also helps to take some time to think about why a certain advice is given. For example, why does it say that you always have to split two eights, even against an ace. Well, that's because two eights equals 16, which is the worst total you can have. It's better to split them up, and give yourself a chance of finding a 17, 18 or 19 with the next card. Once you see the logic in that, you'll have one less thing to memorize.
The playing advice in the basic strategy chart is a result of computer simulations that ran all possible outcomes against each other, and produced the most profitable decision for each situation. So you can't go wrong following it.
Optimal strategy for Blackjack with Seven-Card Charlie
The added house rule of Seven-Card Charlie, adds a small advantage for the player, and it does influence a few strategy decisions. For example, you might have a 14 with 6 cards, against the dealer's 5 upcard.
Normally this would be an automatic stand, but if you're only one card away from the Seven-Card Charlie, meaning an instant win for the player, regardless of the dealer's hand, it turns it into a hit.
Here's the most optimal strategy chart to follow for the Diamond Casino house rules: https://prnt.sc/olct6g
You'll see that two fives are missing from the chart, and that's because you never split them. You treat them as a regular 10. You also never split tens. Just stand on 20.
If you follow this strategy religiously, even with a maximum wager of 50,000 chips, you only expect to lose about 215 chips per hand, and with rounds taking about 30 seconds, that amounts to an expected LOSS of 26,000 chips per hour, which is only half a bet. A small price to pay for an hour of entertainment.
But since the expected return is so extremely close to 100%, you will see more positive short-term results than with other games. But obviously it can also swing the other way. Again, this is supposed to be the game where your money lasts you the longest, but always set your loss and win limits before you sit down. That rule simply always applies.

Still, even with optimal strategies applied, all these games are expected to lose you money in the long run. So betting any kind of large amounts is not advised. If you simply want to enjoy playing these games, there's nothing wrong with betting a minimal amount. Playing these games for a longer period of time will already cost you money anyway, since your daily property fees will still be charged while you're playing in the GTA casino. As long as you can play for fun, there's nothing wrong, but when you see yourself betting insane chunks of your entire bank balance to try to recoup some unfortunate losses, you're doing it wrong.
As the commercials in Britain all correctly say: when the fun stops, stop.

2) Virtual Horse Racing
Now onto the good stuff. I ran some numbers, and I believe Rockstar has made a mistake with the horse racing game. Because as it stands, and if I read the numbers correctly, this game is actually profitable for the player. You can actually make money with this, at least, until Rockstar figures out their mistake and patches it.
If anyone wants to jump into the math and double check this to make sure, please do so. I will add any corrections to this post. This is one of those "to good to be true" things, so I keep thinking that I might have overlooked something. So please verify it if you can.
The setup is this. There is a pool of 100 horses, each with their own attached payout. These are divided into 3 groups, ranked by their odds. From each group, 2 horses are randomly selected to provide a pool of six runners for you to bet on.
Now it's not an actual race you're looking at. You are looking at a raffle. This is important to realize.
Each horse gets awarded a certain number of raffle tickets. The favorites get awarded more tickets than the underdogs, and therefore, have a higher chance of winning.
If this distribution works like it does in the real-life casinos, then the raffle tickets are awarded according to the betting odds.
Example 1: imagine a race with 3 runners, all have 2/1 odds, representing a 33.3% chance of winning. (Because 2/1 means 2 AGAINST 1, so 3 total.) In this case, each horse gets one third of the raffle tickets, giving them an equal chance to win.
Example 2: imagine a race with 3 runners, one has 1/1 odds (or EVENS), representing a 50% chance of winning, and the other two horses are marked up as 3/1, with a 25% chance of winning. The favorite gets half the tickets, the other two get a quarter of the tickets each.
A ticket is drawn, and you'll have a winner.
It doesn't matter in this game which horse you bet on, because the expected return is always the same: 100% or break-even, for the above examples.
Now, what happens if the percentages don't exactly add up to 100%?
They must add up to 100%, because there will always be a winner. And only one winner.
So when this is the case, the actual winning chances of the horses are adjusted to meet the 100% requirement, using their payout odds to determine the scale.
So, if the represented percentages add up to more than 100%, the actual winning chances of the runners will be DECREASED, resulting in all bets becoming losing propositions for the players.
Example: In a 6-horse race, all runners are listed at 4/1, representing a 20% chance. Only with six runners that amounts to 120%. So all chances are scaled down by 1/6th, to end up at 100%.
This means your horse's chances are reduced from 20% to 16.67%, turning it into a losing bet: 5 times you will lose your bet, and 1 time you will win, but only get 4 bets back in this instance, instead of 5. A losing bet in the long run.
This is the type of odds that you find in regular casinos, with fields as large as 15 runners to bet on, where the assumed winning chances always add up to more than 100%, therefore are decreased for all runners, resulting in a house edge.

But in GTA Online's Inside Track, there are other scenarios, because of the small field, and the way that they are put together.
In some cases, the represented percentages when added up, are LESS than 100%, meaning that the actual winning chances of all runners, are INCREASED.
This creates profitable bets for the players, because in the long run, you're expecting to win more money than you lose. This is a gambler's dream, pure and simple.
So, according to the in-game information, the three groups of horses are divided as follows:
-Favorites: EVENS to 5-1
-Outsiders: 6-1 to 15-1
-Underdogs: 16-1 to 30-1

Let's take the two most extreme examples to show what's happening.
The worst possible field to bet on: two runners at EVENS, two runners at 6-1, and two runners at 16-1.
EVENS represents a 50% chance, 6-1 is 14.29%, and 16-1 is 5.88%. Add those up and you land on a total of 140.34%.
This means that the actual winning chances of the horses are decreased by 28.75% (to get that 140% down to 100%), which makes betting on this field extremely unwise.
A horse at EVENS will only come in as a winner 35.63% of the time, instead of 50%,
a horse at 6-1 will only win 10.18% of the time,
and an underdog at 16-1 will only win 4.19% of the time.

The expected return on a bet on any of the horses in this field is only 71.26%, so a maximum bet of 10,000 chips on any of these horses holds an expected LOSS of 2,875 chips.
These returns are the same, because the winning chances are scaled equally, according to the payout numbers. So it really doesn't matter which horse you bet on, in the long run, you expect the same results.
But as explained before, it does influence variance, and therefore your short-term result, which can swing both ways.

But now, the best possible field to bet on: two runners at 5-1, two runners at 15-1, and two runners at 30-1.
Odds at 5-1 represents a winning chance of 16.67%, 15-1 odds means 6.25% chance, and 30-1 odds means a 3.23% chance of winning. Add these six horses together, and you only get 52.285%.
This means that, to get from 52% to 100%, the actual winning chances of these horses will be almost doubled! Multiplied by 1.91 to be exact.
So the 5-1 favorites will now win 31.88% of the time, instead of 16.67%,
the 15-1 runners will win 11.95% of the time,
and the underdogs at 30-1 odds will still win 6.17% of the time.
When betting on this field, the expected return on your bet is 191.25%!
This means that a max bet of 10,000 chips will result in an expected PROFIT of 9,125 chips.
This is printing money, if there ever was such a thing.
Optimal strategy for Virtual Horse racing
So all you have to do, is only bet high on the games where you have an expected positive return, and bet the absolute minimum on the games where your expected return is negative. Or back out of the racing game to refresh the field.
If you don't have a way to quickly add up all the percentages, and until somebody shows up here with a neatly formatted table, just use a few general rules of thumb:
-Always bet the maximum on a race with favorites at 2/1 and 3/1 or higher in it.
-Simply skip all races with two favorites at EVENS in it, and at EVENS and 2/1. Or bet the minimum, if you can't skip or refresh the field.
-To decide if you should play races with other favorite combinations EVENS and 3/1, EVENS and 4/1, EVENS and 5/1, or two favorites at 2/1, the payouts on the other four runners determine whether or not it's profitable to play them. The results of betting on these fields vary from an expected 1,330 chip loss (worst-case) to an expected 1,680 chip win (best-case), with a max bet of 10,000 chips.
But if you're not looking for another strategy chart, you might just want to skip these borderline cases, and just cherry pick the best ones, which are easy to recognize, and with which you can never go wrong.
It's difficult to put a number on an expected win-rate, because it all depends on which fields you get presented with, but it's not unreasonable to state that you can maintain a steady win-rate of around 200,000 chips per hour, with about 50 seconds per race.
Remember, you're not trying to win every race. You're trying to win the most money per hour. So don't sweat it when you bet on a 4/1 favorite, and lose a couple of races in a row. It will still be more profitable in the long run. You have the math on your side.
To reduce negative variance, always bet on the favorite, when betting on profitable fields. We're not gambling anymore, we're grinding out a steady profit. We want to keep the swings to a minimum.
I contacted Rockstar support to verify if this is indeed how it works, but the only reply I got after 6 weeks is that they were "looking into it".
User u/Garsant made a useful Excel-worksheet, available for you to download, where you can quickly type in the payouts on the horses, to see if it produces a profitable bet or not. You can find it in his post here: https://www.reddit.com/gtaonline/comments/ekp8na/gta_online_inside_track_odd_calculato

1) Wheel of Fortune
The number one profitable casino game in GTA Online is obviously the Wheel of Fortune, because it costs you nothing to play.
Unfortunately, you only get one free spin per day, but it holds great value, so make sure you do it.
With a chance to win a super car, vehicle discounts, expensive mystery prizes (which also can be vehicles), and a lot of cash and chips, the expected return on a single spin is around $100,000 in value.
So don't forget your daily spin, it's definitely worth your time.

2020 Update:
As of the Diamond Casino Heist update, the Inside Track horse racing is confirmed to still be as profitable as outlined above.The only thing that seems to be changed, is that you can't refresh the field anymore by backing out of the screen. This does affect your hourly rate in a negative way, but does not change the fact that this game has a huge positive expected return, and should be your go-to when you're trying to take money from the house, without having Lester's nagging voice in your ear. That should also be worth something.

And with that, I conclude my 5,000 word essay on gambling in GTA. Questions, comments, feel free to add your input to this guide.

Cliffs:
-Gambling games should only be played for fun, not for big money. You should expect to lose in the long run. The house always wins.
-A casino game doesn't have a memory, and betting systems don't work.
-Set your limits before you start, how much you are willing to lose or win, and then walk away when you get there.
-Don't play slots, roulette, or three card poker.
-Only play blackjack following a basic strategy chart (https://prnt.sc/olct6g).
-Inside Track betting can be played profitably, if you only bet on fields WITHOUT a heavy favorite.
-Wheel of Fortune is always your best bet, because it's a free bet.
submitted by enderpiet to gtaonline [link] [comments]

Ultimate Gambling Guide for GTA Online - odds, probabilities, and optimal strategies

This is not mine, the creator of this is u/enderpiet

Since the Diamond Casino update, I have seen a large number of 12-year-olds posting Blackjack memes on this sub. As a parent, this has me very worried.
On top of that, I have seen some of the most trustworthy GTA Youtubers giving flawed gambling advice, which can have damaging impact on their gullible audiences.
So that's why I decided to write this up, to educate everyone on the subject, so there will be no more misunderstandings.
(2020 Update down at the bottom.)
If you're one of those Youtubers that wants to use this information in a video, feel free to do so. The more people (especially kids) that become educated about gambling, the better.
But then also please go back and review your own work, and delete or edit the videos that are giving out the wrong advice, like where you're saying you have "a good strategy for making money with roulette", or some other nonsense that I've heard this week. Delete that please.
Before I get into the individual games, I need to discuss a few concepts first, that will make understanding the rest a lot easier.
Expected return and variance
A game like Roulette or Slots has a fixed expected return on your bets. This is a percentage that you have no way of influencing. Say you are flipping a coin against a friend, and you both put up $1. The winner gets the pot. Since the odds are even at 50%, in the long run, you will expect to break even. Your expected return is 100% of your bet.
But imagine if you would play this coin flipping game in a casino against the house. On the "house rules" listed at the table they would probably say that you would only get 95 cents back for every win, while you are forfeiting a dollar on every loss. Would you still play?
Sounds stupid to do so, but still, everybody does it. Every bet they place on Roulette, every coin they put into a Slot machine, is based on the same concept.
Those few cents they take on every bet are their profit margin, and has paid for all the Vegas lights, the Mirage volcanoes, and the Bellagio fountains. Make no mistake - casino gambling games are not designed to make you lose, because sure, you can get lucky on a single night, but they are designed to make them win. That's the beauty of it. They can both exist at the same time.
Too many people that don't see how this works, are just destined for disaster. Just because you went on a lucky streak and won 8 games out of 10, does not mean that flipping coins is a profitable game, or that choosing tails is a winning strategy. Always be aware of the house edge, your true chances of winning, and just realize that you got lucky. There is no such thing as a strategy in flipping a coin that will give you a higher expected return, so it's just pure gambling, just like Slots and Roulette.
Most casino games are made in such a way, that your expected return is a little under 100%. This means that from every dollar bet at the tables, the casino expects to keep a few cents. For individual players, results may vary. Some will win, most will lose. But for the house, it doesn't matter. They take millions of bets each day, so for them, the expected average works out a lot sooner. In short: the house always wins.
When looking at the house edge, we're talking about the expected long-term result, based on the game's house rules. But for a player, it can take literally tens of thousands of hands or spins before you also reach this average number. Until that time, you can experience huge upswings and downswings, that are the result of nothing but short-term luck, which is called variance.
Some games and some bets have a much higher variance than others, which means your actual results will differ enormously from what you're expected to be at.
Take for example betting on red/black at the Roulette table. This is a low-variance proposition, because it has a high percentage chance of occurring, and a low payout.
Contrast this with betting single numbers in Roulette, which only win once every 38 spins on average. This bet has a much higher variance, meaning you can easily hit a dry spell, and not hit anything for 200 bets in a row, or you can see a single number hit three times in five consecutive spins. This is not a freak occurrence in high-variance bets.
Even though the expected return in both these bets is exactly the same, there's a huge difference in variance, causing massive differences in short-term results, which can go both ways. You need to be aware of this, before you decide what types of bets you are comfortable with placing.
Gamblers' Fallacy
Another thing to realize, is that each individual game, hand, or spin, is completely independent from the one(s) before it, and after it.
Gamblers tend to believe, that the chance of a certain outcome is increased, based on previous results.
The most famous example comes from the Casino de Monte Carlo, where the Roulette wheel managed to land on black 26 times in a row. Gamblers lost many millions during that streak, all frantically betting on red, believing that the odds were in favor of the wheel coming out on red, after producing so many blacks. This is not true. Each round is completely independent, and the odds are exactly the same.
You will hear people say things like a Blackjack table being "hot" or "cold", which is completely superstitious, and should be ignored. The exception was when Blackjack was being dealt from a shoe. It made card counting possible. But with the introduction of shuffle machines, and continuous shuffling like is being used in GTA, this no longer exists.
This is also why "chasing your losses" is a very bad idea. After being on a losing streak for some time, many gamblers believe that now it's their turn to start winning. So they will often increase their bet size, believing that when their predicted winning streak comes around, they will win back their losses, and more.
The reality of it, more often than not, is that people will indeed start playing higher and higher limits, until they are completely broke. Nobody is ever "due for a win". There is never a guarantee that you're about to start winning. In fact, the opposite is more likely to be true. You are, after all, in a casino.
Betting systems
Some people like to think that they have a fool-proof betting system, like the Martingale system. Simply increase or even double your bet when you lose, and keep doing that until you win. In theory, this system will always win. So that's why table limits were introduced, and where the system fails.
If you start at the Roulette table, playing red/black, with a small 750 chip wager, and just double your bet every time you lose, you only have to lose 6 times in a row, before you will be betting the table limit of 48,000, just to get that 750 chip profit.
Sure, you can go on all evening without this happening, winning 750 chips each time, but this losing streak only has to happen once, and you're bust. Any betting system like this is ill-advised, because you are hugely increasing your so-called "risk of ruin", and that's what we were trying to avoid.
And even if your starting bet is only 100 chips, after only nine straight losses, and nine doubled bets, you are betting the table limit at 50,000 chips. If you lose that bet, you're 100,000 chips in the hole, with no way to recover that with your 100 chip base wager.
So don't believe anyone that says this is the perfect system to always win in the casino. Sooner or later they will understand why they were wrong, when they're asking you for a loan.
Set your limits BEFORE you start playing
One final point before we get into the games, a general tip for people that head out to play: money management.
Just like in real life, before you go to the casino, decide on a maximum amount that you are WILLING TO LOSE.
Bet small enough, so that amount can last you through the entire evening, and you will not be tempted to run to the ATM to continue playing.
Considering GTA money, some people will be comfortable losing 1% of their GTA bank balance, some people will be comfortable with gambling away 5% of their total GTA savings. It's up to you what you can handle. Decide for yourself where it will start to hurt, and don't cross that line.
But whatever number you decide on, as soon as you lost that amount, get up and walk away. Don't chase your losses, stick to your limits, and accept that this has not been your day. There is always another game tomorrow. Always agree with yourself on a simple stop-loss rule, how much you would want to lose at most, and simply stop playing when you get there.
Same goes for winning. You can decide on a number, how much profit you would like to take away from the casino. You can go on a hot streak and be up half a million in a short period of time, but if you would continue to play longer, looking for more, chances are that you're going to lose it all back.
Most people are happy with doubling their daily casino budget, for example. Others are looking for 10 bets profit in Blackjack. Whatever you choose, when you hit that number, you can stop playing and bank your profits, or you can continue playing if you're still enjoying the games, but then only just play minimum bet sizes. Then you're just playing for fun, not for money. You've already made your profit, so simply keep it in your pocket, and don't risk losing it again.
Either way, decide on what your money management strategy will be, and STICK TO IT.
Casino games in GTA Online
Now, I'm going to dive into the games that you can find at the Diamond casino, ordered from worst to best.
6) Slots
Generally the rule is this: the less strategy a game has, the worse it is for the player. And with slots, this is definitely the case.
The only influence you have, is choosing what type of machine you're going to play. Basically, there are two types of slot machines:
-high frequency, low payout slots
-low frequency, high payout slots
In the first type, there is no huge (progressive) jackpot on offer, just your average selection of prizes that don't go up to crazy amounts.
This will result in a player having many more spins resulting in a win. The amounts that you win on the bigger prizes, will be smaller, but they do come around more often. This type of slot machine has a lower variance, which means that your money should last you longer, winning many smaller prizes along the way to keep you going.
The second type of slot machine lures you in with the temptation of a huge jackpot prize. Even though the long-term expected return on these machines is the same as the previous type, the prize distribution is hugely different. The large jackpot prize weighs heavily on the scale of expected return, but the chance of it hitting is extremely small. This results in a much higher variance on this type of machine. Usually your money will go down very fast, because the smaller prizes are less rewarding than on the other type of machine.
At the Diamond, the info screen says the player return at slots is set at 98.7%. This means that, on average, for every maximum bet of 2,500 chips, you expect to lose 32.5 chips.
This might not seem like a lot, but the danger of slots is that the game is extremely fast. You can spin about once every 6 seconds, which would result in an expected LOSS of about 20,000 chips per hour of playing.
But again, in this long-term expected number, the large jackpot awards are also factored in, and as long as you don't hit those big prizes, you'll see your money go down a lot faster.
In any case, thank heavens the max bet is only set at 2,500, or else we would see more players go bankrupt at alarming rates.
Optimal strategy for slots:
There is none. Because after betting, you have no more influence over the outcome. The only choices you have, is what type of machine you want to play at, and how much money you are going to risk. And those are all personal preference. As long as you stick to your loss limits, as discussed above, there's no harm in having a go every once in a while, hoping to get a lucky hit. Just realize that you don't have a high chance of scoring a big win, so as soon as you do, get up and walk away.
5) Roulette
Roulette is also a game where you have no influence over the outcome. There is zero skill involved. You place your bet, and that's it.
In traditional French roulette, a table has only the single-zero, but of course, for American casinos that wasn't enough of a house edge, so they simply doubled their profits by adding a second zero. The house edge was increased from 1/37 to 1/19, which is huge.
This makes playing on a double-zero roulette table by definition a sucker's play.
The payouts scale evenly, which means that a bet on a single number, and a bet on half of the numbers, and everything in between, yields the same expected return. The only difference, again, being the variance that you are willing to subject yourself to.
The player return for double-zero Roulette for all bets is 94.74%.
Except for the 5-number bet, which can only be made by placing a bet on the two top rows that contain 0, 00, 1, 2 and 3. The expected return on this bet is lower: 92.1%. This is because it only pays out 6-1. Why? Well, the number 36 isn't divisible by 5, so the greedy people that came up with double-zero Roulette had to round it off someway, and as expected, it wasn't going to be in the players' favor.Just remember that that 5-number bet is the worst bet at the table, and should be avoided. All other possible bets have the same expected return.
So it really doesn't matter how you spread your bets, if you bet only one chip, or if you litter the entire table with a bucketload of chips. Each chip you put out there, has the same expected return, so there is no strategy that will improve your long-term results.
Assuming that you're betting the maximum table amount of 50,000 chips, you will be looking at an expected loss of about 2,630 chips per spin. Considering that a round takes about 45 seconds to complete, your expected LOSS at the GTA Roulette tables will be around 200,000 chips per hour of playing.
Optimal strategy for double-zero roulette:
Stay away. Stay far away.
4) Three Card Poker
With Three Card Poker, we come across the first game where there is actually some strategy involved. You get to look at your cards, and then decide if you want to fold, and surrender your ante, or double your bet.
Additionally, you can choose to place a side bet on "Pair Plus", which offers progressive payouts.
There are some websites out there that ran all the numbers with computer simulations, and even though I would like to quote the source here, these websites are understandably littered to the max with online casino ads, so that's why I have decided against doing that.
Optimal strategy for Three Card Poker:
For this game you only have to remember one strategy rule: Always bet on any high card queen-six-four or better, and fold any high card queen-six-three or lower. That's it. Just don't forget to double check if you're not folding a straight or a flush, and you'll be fine.
This strategy will result in an expected return of 96.63%.
The Pair Plus sidebet, with the payout table that is used at the Diamond casino, gives you an expected return of 97.68%, which is actually a bit better than the main ante bet.
So by playing both wagers, you're reducing your expected losses per bet, but since you're betting more, you're also increasing your expected loss per hour.
My advice would obviously be to not play this game at all, but if you do, put as much of your bet as possible on the Pair Plus, while making our Ante bet as small as you can.
To be able to compare it to the other games at the Diamond, let's stay on that 50,000 maximum wager, meaning making your ante bet 35,000, and your pair plus bet 15,000, if the table would allow it.
This results in an expected loss of about 1,525 chips per hand, and with a round taking about 45 seconds, this adds up to an expected LOSS of around 120,000 chips per hour of playing. In comparison, if you would only play the ante bet for 50,000 per hand, you expect to lose 1,685 chips per hand, which means an expected LOSS of about 135,000 chips per hour. So the more out of that 50,000 wager you can put on the "Pair Plus" sidebet, the better.
Even though it may be fun to try out this game for a bit, since there's only one simple strategy rule to follow, you'll soon find yourself robotically grinding down your bankroll until it has vaporized. You're not missing out on anything if you skip these tables, there is no real challenge.
Just like with Roulette and Slots, if you want to try it out nonetheless, you can just bet the minimum amounts and only play for fun, so it won't matter if you win or lose.
3) Blackjack
Blackjack is the most complicated game by far. Simply because the player has to make a series of decisions, which will largely decide the outcome. Luckily, there is such a thing as an optimal strategy, which will be outlined below.
However, the strategy is also dependent on the house rules. These not only affect your expected return, but in some places also your decisions.
Here are the house rules at the Diamond casino:
-The game uses 4 standard decks, and a continuous shuffle.
-Blackjack pays 3 to 2, dealer checks for early blackjack.
-No insurance offered, no surrender.
-Dealer stands on soft 17.
-Double down on any two cards.
-Player can split only once, but doubling after split is allowed.
-Seven-Card Charlie.
Under these rules, and following the "basic strategy" chart, your expected return at Blackjack is a shade under 99.6%, which is extremely good for a casino game, that's why Blackjack should be your table game of choice.
But it comes at a price: you are going to have to memorize the relatively complicated strategy chart, or at least stick it to your monitor until you have it in your head. But in case you ever stumble into a real-life casino, you won't regret having this table memorized, so I would definitely advise you to work on that.
The strategy chart might look complicated at first, but you will be able to notice certain patterns. Your decisions are mainly based on the dealer's upcard, which is basically divided into a weak card (2 to 6), and a strong card (7 to ace).
When a dealer shows a strong card, you will be hitting more often with the risk of going bust, but when a dealer shows a weak card, you're not taking that risk, and you will be standing more, but also doubling and splitting more. You want to increase your bets when the odds are in your favor, and get out cheap when they're not.
But it also helps to take some time to think about why a certain advice is given. For example, why does it say that you always have to split two eights, even against an ace. Well, that's because two eights equals 16, which is the worst total you can have. It's better to split them up, and give yourself a chance of finding a 17, 18 or 19 with the next card. Once you see the logic in that, you'll have one less thing to memorize.
The playing advice in the basic strategy chart is a result of computer simulations that ran all possible outcomes against each other, and produced the most profitable decision for each situation. So you can't go wrong following it.
Optimal strategy for Blackjack with Seven-Card Charlie
The added house rule of Seven-Card Charlie, adds a small advantage for the player, and it does influence a few strategy decisions. For example, you might have a 14 with 6 cards, against the dealer's 5 upcard.
Normally this would be an automatic stand, but if you're only one card away from the Seven-Card Charlie, meaning an instant win for the player, regardless of the dealer's hand, it turns it into a hit.
Here's the most optimal strategy chart to follow for the Diamond Casino house rules:https://prnt.sc/olct6g
You'll see that two fives are missing from the chart, and that's because you never split them. You treat them as a regular 10. You also never split tens. Just stand on 20.
If you follow this strategy religiously, even with a maximum wager of 50,000 chips, you only expect to lose about 215 chips per hand, and with rounds taking about 30 seconds, that amounts to an expected LOSS of 26,000 chips per hour, which is only half a bet. A small price to pay for an hour of entertainment.
But since the expected return is so extremely close to 100%, you will see more positive short-term results than with other games. But obviously it can also swing the other way. Again, this is supposed to be the game where your money lasts you the longest, but always set your loss and win limits before you sit down. That rule simply always applies.
Still, even with optimal strategies applied, all these games are expected to lose you money in the long run. So betting any kind of large amounts is not advised. If you simply want to enjoy playing these games, there's nothing wrong with betting a minimal amount. Playing these games for a longer period of time will already cost you money anyway, since your daily property fees will still be charged while you're playing in the GTA casino. As long as you can play for fun, there's nothing wrong, but when you see yourself betting insane chunks of your entire bank balance to try to recoup some unfortunate losses, you're doing it wrong.
As the commercials in Britain all correctly say: when the fun stops, stop.
2) Virtual Horse Racing
Now onto the good stuff. I ran some numbers, and I believe Rockstar has made a mistake with the horse racing game. Because as it stands, and if I read the numbers correctly, this game is actually profitable for the player. You can actually make money with this, at least, until Rockstar figures out their mistake and patches it.
If anyone wants to jump into the math and double check this to make sure, please do so. I will add any corrections to this post. This is one of those "to good to be true" things, so I keep thinking that I might have overlooked something. So please verify it if you can.
The setup is this. There is a pool of 100 horses, each with their own attached payout. These are divided into 3 groups, ranked by their odds. From each group, 2 horses are randomly selected to provide a pool of six runners for you to bet on.
Now it's not an actual race you're looking at. You are looking at a raffle. This is important to realize.
Each horse gets awarded a certain number of raffle tickets. The favorites get awarded more tickets than the underdogs, and therefore, have a higher chance of winning.
If this distribution works like it does in the real-life casinos, then the raffle tickets are awarded according to the betting odds.
Example 1: imagine a race with 3 runners, all have 2/1 odds, representing a 33.3% chance of winning. (Because 2/1 means 2 AGAINST 1, so 3 total.) In this case, each horse gets one third of the raffle tickets, giving them an equal chance to win.
Example 2: imagine a race with 3 runners, one has 1/1 odds (or EVENS), representing a 50% chance of winning, and the other two horses are marked up as 3/1, with a 25% chance of winning. The favorite gets half the tickets, the other two get a quarter of the tickets each.
A ticket is drawn, and you'll have a winner.
It doesn't matter in this game which horse you bet on, because the expected return is always the same: 100% or break-even, for the above examples.
Now, what happens if the percentages don't exactly add up to 100%?
They must add up to 100%, because there will always be a winner. And only one winner.
So when this is the case, the actual winning chances of the horses are adjusted to meet the 100% requirement, using their payout odds to determine the scale.
So, if the represented percentages add up to more than 100%, the actual winning chances of the runners will be DECREASED, resulting in all bets becoming losing propositions for the players.
Example: In a 6-horse race, all runners are listed at 4/1, representing a 20% chance. Only with six runners that amounts to 120%. So all chances are scaled down by 1/6th, to end up at 100%.
This means your horse's chances are reduced from 20% to 16.67%, turning it into a losing bet: 5 times you will lose your bet, and 1 time you will win, but only get 4 bets back in this instance, instead of 5. A losing bet in the long run.
This is the type of odds that you find in regular casinos, with fields as large as 15 runners to bet on, where the assumed winning chances always add up to more than 100%, therefore are decreased for all runners, resulting in a house edge.
But in GTA Online's Inside Track, there are other scenarios, because of the small field, and the way that they are put together.
In some cases, the represented percentages when added up, are LESS than 100%, meaning that the actual winning chances of all runners, are INCREASED.
This creates profitable bets for the players, because in the long run, you're expecting to win more money than you lose. This is a gambler's dream, pure and simple.
So, according to the in-game information, the three groups of horses are divided as follows:
-Favorites: EVENS to 5-1
-Outsiders: 6-1 to 15-1
-Underdogs: 16-1 to 30-1
Let's take the two most extreme examples to show what's happening.
The worst possible field to bet on: two runners at EVENS, two runners at 6-1, and two runners at 16-1.
EVENS represents a 50% chance, 6-1 is 14.29%, and 16-1 is 5.88%. Add those up and you land on a total of 140.34%.
This means that the actual winning chances of the horses are decreased by 28.75% (to get that 140% down to 100%), which makes betting on this field extremely unwise.
A horse at EVENS will only come in as a winner 35.63% of the time, instead of 50%,
a horse at 6-1 will only win 10.18% of the time,
and an underdog at 16-1 will only win 4.19% of the time.
The expected return on a bet on any of the horses in this field is only 71.26%, so a maximum bet of 10,000 chips on any of these horses holds an expected LOSS of 2,875 chips.
These returns are the same, because the winning chances are scaled equally, according to the payout numbers. So it really doesn't matter which horse you bet on, in the long run, you expect the same results.
But as explained before, it does influence variance, and therefore your short-term result, which can swing both ways.
But now, the best possible field to bet on: two runners at 5-1, two runners at 15-1, and two runners at 30-1.
Odds at 5-1 represents a winning chance of 16.67%, 15-1 odds means 6.25% chance, and 30-1 odds means a 3.23% chance of winning. Add these six horses together, and you only get 52.285%.
This means that, to get from 52% to 100%, the actual winning chances of these horses will be almost doubled! Multiplied by 1.91 to be exact.
So the 5-1 favorites will now win 31.88% of the time, instead of 16.67%,
the 15-1 runners will win 11.95% of the time,
and the underdogs at 30-1 odds will still win 6.17% of the time.
When betting on this field, the expected return on your bet is 191.25%!
This means that a max bet of 10,000 chips will result in an expected PROFIT of 9,125 chips.
This is printing money, if there ever was such a thing.
Optimal strategy for Virtual Horse racing
So all you have to do, is only bet high on the games where you have an expected positive return, and bet the absolute minimum on the games where your expected return is negative. Or back out of the racing game to refresh the field.
If you don't have a way to quickly add up all the percentages, and until somebody shows up here with a neatly formatted table, just use a few general rules of thumb:
-Always bet the maximum on a race with favorites at 2/1 and 3/1 or higher in it.
-Simply skip all races with two favorites at EVENS in it, and at EVENS and 2/1. Or bet the minimum, if you can't skip or refresh the field.
-To decide if you should play races with other favorite combinations EVENS and 3/1, EVENS and 4/1, EVENS and 5/1, or two favorites at 2/1, the payouts on the other four runners determine whether or not it's profitable to play them. The results of betting on these fields vary from an expected 1,330 chip loss (worst-case) to an expected 1,680 chip win (best-case), with a max bet of 10,000 chips.
But if you're not looking for another strategy chart, you might just want to skip these borderline cases, and just cherry pick the best ones, which are easy to recognize, and with which you can never go wrong.
It's difficult to put a number on an expected win-rate, because it all depends on which fields you get presented with, but it's not unreasonable to state that you can maintain a steady win-rate of around 200,000 chips per hour, with about 50 seconds per race.
Remember, you're not trying to win every race. You're trying to win the most money per hour. So don't sweat it when you bet on a 4/1 favorite, and lose a couple of races in a row. It will still be more profitable in the long run. You have the math on your side.
To reduce negative variance, always bet on the favorite, when betting on profitable fields. We're not gambling anymore, we're grinding out a steady profit. We want to keep the swings to a minimum.
I contacted Rockstar support to verify if this is indeed how it works, but the only reply I got after 6 weeks is that they were "looking into it".
User u/Garsant made a useful Excel-worksheet, available for you to download, where you can quickly type in the payouts on the horses, to see if it produces a profitable bet or not. You can find it in his post here: https://www.reddit.com/gtaonline/comments/ekp8na/gta_online_inside_track_odd_calculato
1) Wheel of Fortune
The number one profitable casino game in GTA Online is obviously the Wheel of Fortune, because it costs you nothing to play.
Unfortunately, you only get one free spin per day, but it holds great value, so make sure you do it.
With a chance to win a super car, vehicle discounts, expensive mystery prizes (which also can be vehicles), and a lot of cash and chips, the expected return on a single spin is around $100,000 in value.
So don't forget your daily spin, it's definitely worth your time.
2020 Update:
As of the Diamond Casino Heist update, the Inside Track horse racing is confirmed to still be as profitable as outlined above.The only thing that seems to be changed, is that you can't refresh the field anymore by backing out of the screen. This does affect your hourly rate in a negative way, but does not change the fact that this game has a huge positive expected return, and should be your go-to when you're trying to take money from the house, without having Lester's nagging voice in your ear. That should also be worth something.
And with that, I conclude my 5,000 word essay on gambling in GTA. Questions, comments, feel free to add your input to this guide.
Cliffs:
-Gambling games should only be played for fun, not for big money. You should expect to lose in the long run. The house always wins.
-A casino game doesn't have a memory, and betting systems don't work.
-Set your limits before you start, how much you are willing to lose or win, and then walk away when you get there.
-Don't play slots, roulette, or three card poker.
-Only play blackjack following a basic strategy chart (https://prnt.sc/olct6g).
-Inside Track betting can be played profitably, if you only bet on fields WITHOUT a heavy favorite.
-Wheel of Fortune is always your best bet, because it's a free bet.
submitted by sircore to gtaonline [link] [comments]

Deathrolling! Is it a fair game or a scam?

Hey guys! We all know that people love using math and statistics to scam people (carnivals, casinos etc.).

So I was curious about death rolling. Is there a hidden way to increase your chances of winning? Are chronic death rollers desperate gamblers in need of help? Or are they gaming the system and hustling people (beyond the ones that simply don't pay out when they lose) and making mad money?

I'm no mathmetician, but I am a programmer. I'd be hard pressed to find any formulae that explain with any accuracy the chances to win a deathrolling game. So I wrote a program and hit it with millions of games to figure this out via the Monte Carlo method.

Now as a reminder, let's go over the rules of the game. You wager an amount of gold, let's say 10. Then each player takes turns rolling. The first roll is 10 times the amount of gold wagered, so in our 10 gold deathroll game, the first roll is out of 100. Each subsequent roll uses the results of the last roll as the top-end. For instance, if the first player rolled a 72, the second player then rolls 1-72. The game continues alternating rolls like this until a player rolls a 1. The player who rolls a 1 loses.

My questions are:
1) Can you give yourself an advantage by deciding who rolls first?
2) Can you give yourself an advantage by choosing a specific number to roll with?

The answers are slightly complicated. Let's look at some of the results of my simulations.

When rolling with a top end of 1:
Player 2 won 1000000 games
Player 1 won 0 games

This makes sense because the first player who rolls a 1 loses and the player who rolls first always rolls a 1. No one would ever play a death roll game like this, but its results are interesting none-the-less and provide a bit of insight on the rest of the results.

When rolling with a top end of 2:
Player 2 won 666278 games
Player 1 won 333722 games

Well now, that's something! Thinking it through logically it also makes sense. If you're flipping a coin, the person who goes first has a 50/50 chance of just losing on their first flip. But "winning" the first flip doesn't win the game, it's just player 2's turn now. So essentially player 2 has the advantage by giving player 1 the opportunity to lose first. But, again, a deathroll game out of 2 just isn't practical or realistic. But it also provides insight as to whether or not you can give yourself an advantage. Is there something to rolling second?

Let's skip a head and look at the next few top-end rolls:

When rolling with a top end of 3:
Player 2 won 583518 games
Player 1 won 416482 games

When rolling with a top end of 4:
Player 2 won 549326 games
Player 1 won 450674 games

When rolling with a top end of 5:
Player 2 won 533834 games
Player 1 won 466166 games

When rolling with a top end of 10:
Player 2 won 508707 games
Player 1 won 491293 games

Hmm, the higher we go the closer to 50/50 we get. We're only at 10 which is a single gold wagered and we're already at only a 50.9% chance to win by going second. It seems there's only a benefit to going second, and that benefit becomes negigible very quickly. Let's skip to a standard 10 gold deathroll game and see the chances of winning when starting the roll out of 100:

When rolling with a top end of 100:
Player 2 won 500002 games
Player 1 won 499998 games

So any benefit to going second is all but gone at this point.

In conclusion the answer is a technical yes, but only if going second and starting death rolls with unrealistically low wagers. I ran simulations with rolls starting from 1 to 100 and it looks like around 30 is when it's pretty much a 50/50 chance regardless of who goes first. 36 was the first set of deathroll games where player 1 won more games than player 2.

So if you're going to deathroll then always roll second for a negligible advantage. If anyone tries any bullshit to change the rules to start the roll with a low number then call them out on it. Starting the roll at 10 times the amount wagered is actually a great rule that keeps the game more or less fair.
submitted by Geryth04 to classicwow [link] [comments]

Horse Betting Calc

So I have recently gotten back into GTA online after a long break and stumbled upon horse racing and was making 200-300k every night I played just by spending an hour in the casino. This lead me to look into the math because it seemed really really easy to beat the house and wanted to make it easy for my friends to also do the same.
So I wanted to make a spreadsheet and it turned out that I really liked u/wully616 's that he put together, but I wanted to make it a little more in depth and easier to understand for my friends. I want to credit Wully here because all the groundwork was constructed by him or her.
So what did I do to this already good spreadsheet?
I added in the adjusted odds based on the difference in percentage points of the current horses. If the percentage is less than 100%, then the actual odds of each horse goes up based on a calculation of that percentage difference and their original odds. If the total percentage is over 100%, then the actual odds of each horse goes down based on that same type of calculation. I found that recalculating the adjusted odds 6 times was enough to normalize any odd set given so that is why that calculation is ran so many times even though in some cases it only takes once or twice to equal up to 100%.
Something else I also did was remove the part about horse one being evens and giving less profit since my sheet is only focused on making good bets and that is most certainly one of the best bets you can make.
Hopefully everyone enjoys the sheet and finds it helpful. You will have to make a copy to plug in different odds and play around with the sheet.
Here is my version of the sheet: My Spreadsheet
Here is the original post by u/wully616 that lead to the inspiration.
submitted by BucFanJKE to gtaonline [link] [comments]

does Montercarlo simulation works on roulette?

Hi, I don't know if this is the correct subreddit for this question, please let me know. In class we talk about Montercarlo simulation and reviewed the classic example to calculate pi, but i was wondering if it is possible to apply a montecarlo simulation for a roulette and how correct it is. Will it be able to replicate the same results as i go to the cassino? Thanks everyone.
submitted by rockcamus to statistics [link] [comments]

Know the odds - gambling

Posting this only because i saw the Floobius gambling rort being advertised in Arugal weekly It's probably not a good idea to bet on this, the odds in this case are particularly stacked.
If you play either game you will lose (it is a casino) and it's not even close.

rules of the game:
You can bet on two outcomes (oveunder) or (sevens).
Keep in mind here that you have already paid your bet to the house so the amount you "win" is not actually the same as the payout.

Results

EV = (Amount won per bet * probability of winning) – (Amount lost per bet * probability of losing)
EV is the expected value of a bet or how much you can expect to win per 1g bet. + you are paid, - you are paying.
EV(sevens) = 3*(1/6) - 1*(5/6) | approx -33s per bet. EV(unders) = 1*(15/36) - 1*(21/36) | approx -18s per bet. 

Monte Carlo Simulation

Just as a quick sanity check. Law of large numbers should net us a result that is close to the true expected value.
Snippet if anyone wants to check for themselves
import numpy as np n= 100000 bet = 1 def event(): r1 = np.random.randint(low=1,high=7) r2 = np.random.randint(low=1,high=7) return r1 + r2 outcomes = [event() for x in range(0,n)] sevens = sum([3*bet if (x==7) else -1*bet for x in outcomes]) unders = sum([1*bet if (x<7) else -1*bet for x in outcomes]) ev_sevens = (sevens/n) ev_unders = (unders/n) 
submitted by Mituapple to Arugal [link] [comments]

Monte Carlo Simulation – Explanation, Examples, and Uses

Monte Carlo is a method that works based on computerized math. It accounts for all the possibilities, positive or negative, about a decision. The person applying this method gets to see all the possible outcomes of an action. The scientists involved in the making of the atom bomb used this method for the first time. It got the name Monte Carlo from the renowned town of casinos, Monaco.
https://androclue.com/monte-carlo-simulation/
submitted by abhi_aswal to u/abhi_aswal [link] [comments]

Resume Help - Please Any Helpful Tips or Formats!

I am trying to make a transition into the Data Science field. At my current position, I designed Time Series forecasting (both with ARIMA and FBProphet) along with Linear Regression models for our marketing team, but we haven't gotten much traction. The casino business is a little more on the traditional side, and they can afford to be since they are always making money.
After I finished my Master's in Business Analytics, I've been trying to figure out what steps I can do to get my foot in the door. I am not entirely sure, so I figured reaching out to reddit might prove helpful. Any insights into what I can improve upon would be greatly appreciated.
Another project I was thinking of doing was asking other data scientist about projects that they are working on and see if it excites me or if I can ask more questions.
Please see below:
Experience BUSINESS ANALYST | PARX CASINO| JAN. 2019 TO PRESENT
· Gathered requirements and developed project plans for Slot Asset Management Systems to improve data integrity in Parx Slot Master Database. · Planned and developed interfaces using Tableau that simplified overall management decisions and offered ease-of-use. · Provided comprehensive analysis and recommend solutions to address complex business problems and issues using data from internal and external sources and applied advanced analytical methods to assess factors impacting growth and profitability. · Coached, developed and motivated team members, providing coaching and mentoring on SQL, Python, and Machine Learning techniques.
BUSINESS ANALYST - INTERN | PARX CASINO | JUN. 2018 TO JAN. 2019
· Created a Linear Program in Excel that would utilize the average rate of bills inserted into a machine to find the optimal times to empty machines prior to reaching the full marker. · Coordinated with Slots Department for data cleaning and variable selection to ensure Slot Data was meaningful and analyzable. · Reconciled Pennsylvania Gaming Control Board Program ID and Paytable to Parx Slot Master by creating a program in Python that would join the relevant data on the states data to ensure standardization. · Ran and coordinated Monte Carlo simulations on casino marketing events, uncovering probable financial risks and impacts on Parx's Marketing Budgeting.
SALES ASSOCIATE | COLOR INC | SEP. 2015 TO JUL. 2018
· Worked with sales team to collaboratively reach targets, consistently meeting or exceeding personal quotas averaging over $2,000 in daily sales. · Trained and developed new sales team associates in products, selling techniques and company procedures. · Liaised with customers and recommended specific products and specials, aligning with individual needs, requirements and specifications earning a customer satisfaction rating over 90% Education M.S. BUSINESS ANALYTICS | 2018 | FOX SCHOOL OF BUSINESS, TEMPLE UNIVERSITY
submitted by littlemattjag to DataScienceJobs [link] [comments]

[HELP][Python vs Rust] Monte-Carlo-Simulation of Craps

Edit: The problem is solved (the indicatif library was the bottleneck, it couldn't keep up with the amount of iterations)
I updated the code with multithreading version for anyone who is intrested on an implementation in rust.
On my PC it performs about 90 Million iterations per second! (about 10 seconds for 1 billion simulations vs 7 minutes for 100 Million)
--------
I will hold in several weeks a presentation about the Monte Carlo Simulation in school and one of my examples will be Craps. My math teacher also teaches me computer science (simple stuff like Java, Ceasar, Vigenere or Internet Infrastructure...), so he wants to see some code from me. Instead of just writing some simple python code, I decided to rewrite it in rust to improve speed, but for some reason the code I wrote in rust is 2 times slower, than the python code (8min vs 17min)!
I think it has something to do with the random number generation, but I tried multiple different ways to generate the random dice throws and also changed from ThreadRng to SmallRng. The rust code has been compiled with cargo run --release and on python the script has been run with python craps.py.
import tqdm # pip install tqdm import random def roll() -> int: return random.choice([1, 2, 3, 4, 5, 6]) + random.choice([1, 2, 3, 4, 5, 6]) # true = gewonnen # false = verloren def craps() -> bool: erster_wurf = roll() # natural if erster_wurf in [7, 11]: return True # craps elif erster_wurf in [2, 3, 12]: return False else: # jede weitere Runde while True: wurf = roll() if wurf == erster_wurf: return True elif wurf == 7: return False total = 100_000_000 gewonnen = 0 for _ in tqdm.tqdm(range(total)): if craps() == True: gewonnen += 1 print("Wahrscheinlichkeit: {:5.3f}%".format((gewonnen/total)*100)) 
It uses the rand crate.
use rand::rngs::{ SmallRng }; use rand::{ self, FromEntropy, Rng }; use rand::seq::SliceRandom; use std::time::{ Instant, Duration }; use std::thread; fn roll(rng: &mut R) -> usize { ( [1, 2, 3, 4, 5, 6] .choose(rng.into()) .unwrap() + [1, 2, 3, 4, 5, 6] .choose(rng.into()) .unwrap() ) as usize } fn craps(rng: &mut R) -> bool { let erster_wurf = roll(rng); if erster_wurf == 7 || erster_wurf == 11 { return true; } else if erster_wurf == 2 || erster_wurf == 3 || erster_wurf == 12 { return false; } else { loop { let wurf = roll(rng); if wurf == erster_wurf { return true; } else if wurf == 7 { return false; } } } } fn craps_mt(total: usize, thread_number: usize) -> f64 { let mut threads = vec![]; for _ in 0..thread_number { let number = total / thread_number; // TODO funktioniert nur wenn die Anzahl der Threads Basis 10 ist! let handle = thread::spawn(move || { let mut rng = SmallRng::from_entropy(); let mut gewonnen = 0; for _ in 0..number { if craps(&mut rng) { gewonnen += 1; } } gewonnen }); threads.push(handle); } let gewonnen: usize = threads.into_iter().map(|t| t.join().unwrap()).sum(); gewonnen as f64 / total as f64 * 100.0 } fn craps_st(total: usize) -> f64 { let mut rng = SmallRng::from_entropy(); let mut gewonnen = 0; for _ in 0..total { if craps(&mut rng) { gewonnen += 1; } } gewonnen as f64 / total as f64 * 100.0 } fn main() { let mut rng = SmallRng::from_entropy(); let total = 100_000_000; let start = Instant::now(); let result = craps_mt(total, 100); println!("{:5.7}", result); println!("iterations per second: {:?}", total as f64 / to_float_seconds(start.elapsed())); println!("total time: {:?}", start.elapsed()); } fn to_float_seconds(val: Duration) -> f64 { val.as_secs() as f64 + (val.subsec_nanos() as f64 * 0.000_000_001) } 

Note: I don't need ultra precise time measurements, so I am just comparing the elapsed times of the progress bars.

Thanks for the help :)
submitted by Luroalive to rust [link] [comments]

Literary Destiny: Primary Weapons!

Hey all, 30,000 words later, I've finished the rough draft of my thesis, so I get to reward myself with this!
It is an attempt to catch all the literary references in Destiny's flavor texts–I did armor last week, you can find that post here!
Obviously, since I'm not a writer in Destiny, nor do I know any of the writers, this will not 100% complete–but I read a lot, so maybe it'll be close!
Without more ado about nothing, here's the primary weapons! They're organized by class, and then roughly in descending order of rarity.

Auto Rifles

Fabian Strategy: Wait for enemy to make a mistake. Die. Stand by for Ghost Resurrection. Repeat as necessary.
Interestingly, despite its name being the an actual military strategy, the use of Fabian Strategy really doesn't seem in line with that strategy. The actual strategy is one of attrition, guerrilla warfare, and light skirmishes, as opposed to the frontline fighting the gun espouses. The strategy itself was named after Quintus Fabius Maximus Verrucosus Cunctator (can't make this stuff up), a Roman dictator who pioneered it against Hannibal, a legendary Carthaginian commander. Fun fact, his cognomen–or honorary last name–Verrucosus, means 'warty', a reference to a wart on his upper lip.
((GENESIS CHAIN~)): ~if(input(SIVA)) // echo Shirazi // output(death) // ask(not in vain)~
I think this is a reference to James 4:3:
3You ask and do not receive, because you ask wrongly, in order to spend what you get on your pleasures.
New Revised Standard Version. 'Ask not in vain', as it were. I'm not 100% about this one simply because it's not a great fit, but 'ask not in vain' is a pretty iconic phrase.
Monte Carlo: There will always be paths to tread and methods to try. Roll with it.
Uhh, so this is a reference to the Monte Carlo method, which, according to Wikipedia, is, "a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results." If someone with relevant expertise could explain this better, I'll edit it in, but for now, I'll take a whack at it: as a part of risk analysis, Monte Carlo methods allow you to simulate a large number of possible outcomes, so you can better make decisions under uncertainty. Of course, it is also a reference to the Monte Carlo principality in Monaco, particularly its opera-house-cum-casino, from which the RNG of the Monte Carlo method takes its name.
Abyss Defiant: We will not go quietly.
A reference to Welsh poet Dylan Thomas' "Do not go gentle into that good night", all of which is fabulous, but I will quote just a short stanza here:
Do not go gentle into that good night, Old age should burn and rave at close of day; Rage, rage against the dying of the light. 
As Guardians, we're pretty conditioned against the 'dying of the light', so this one definitely feels like a good fit.
Arminius-D: Unleash a torrent on your enemies with the Häkke Arminius-D.
The name is of Arminus (german, Hermann), a legendary German commander who lived in both the BCE and CE, and gave the Romans their greatest defeat at the Battle of Teutonberg, in 9CE. Arguably one of the most important battles in history, it likely stopped Roman advancement past the Rhine permanently–which is likely the "torrent" referenced in the flavor text.
Zarinaea-D: You provide the will, and the Häkke Zarinaea-D provides the way.
A Sacae woman, who also fought in battles. Wife of the Parthian (ayyyyy, see pulse rifles, below) King Marmares. Her story is related in Ctesias' history of the Persian empire, Persica.
Paleocontact JPK-43: An auto rifle, modified by Dead Orbit's superb technicians and specialists.
Paleocontact is the idea that aliens rendezvoused with early humans and influenced civilization. It is generally considered a pseudo-historic theory at best, and falls under "Ancient astronauts". No idea about the "JPK-43" part, unfortunately.
Questing Beast: You'll never catch it. But that's not the point.
A reference to Arthurian legend, the Questing Beast is a vicious monster, and a, "... subject of quests undertaken by famous knights such as King Pellinore, Sir Palamedes, and Sir Percival". Its description was quite ferocious:
The strange creature has the head and neck of a snake, the body of a leopard, the haunches of a lion, and the feet of a hart.[1] Its name comes from the great noise that it emits from its belly, a barking like "thirty couple hounds questing". 'Glatisant' is related to the French word glapissant, 'yelping' or 'barking', especially of small dogs or foxes.
More contemporary incarnations can be found in The Magicians series by Lev Grossman, and possibly South Park? Unsurprisingly, it also makes an appearance in the Merlin TV series. Thanks to Phoenity1 for pointing that one out!
Zero-Day Dilemma: There's no defense against it.
A reference to zero-day vulnerabilities, which are computer vulnerabilities found and exploited before the developers can come up with a solution or workaround–thus the 'zero-day' moniker.
For The People: I stand against the state of nature.
A reference to Thomas Hobbes' "natural condition of mankind", from Leviathan. A 'state of nature' was the theoretical idea of man's existence before society. A really interesting exploration of that idea is Ḥayy ibn Yaqẓān, a philosophical work by Ibn Tufail–Arabic, أبو بكر محمد بن عبد الملك بن محمد بن طفيل القيسي الأندلسي– which tells the story of a young man raised entirely in nature by animals, who only comes into contact with society later on in his life.
Izudabar-D: Millenia will pass, and still your name will ring out.
"Izdubar" was the initial translation of the name Gilgamesh, who of course is the protagonist of the Epic of Gilgamesh a fabulous (and surprisingly short!) ancient Mesopotamian epic poem, which is considered the first example of the genre.
Bronzed Miyamoto-D: An aggressive Häkke auto rifle, earned through glory in the Crucible.
A reference to the later-era (1600s) Japanese swordsman and strategist, Miyamoto Musashi–Japanese, 宮本 武蔵–and likely not the co-founder of Nintendo! In his later years, he wrote The Book of Five Rings, a treatise on strategy, tactics and philosophy.
Galahad-E: This extraordinary multirole rifle boasts a smartmatter frame, the key to remarkable capabilities.
More Arthurian legend! Sir Galahad is the illegitimate son of Lancelot and Elaine of Corbenic, ironically renowned for his purity and gallantry. He appeared quite late in the Medieval Arthurian legends, but became much more common in the later narratives, like Le Morte d'Arthur. Ultimately, he is considered to be the only night of Arthur's table worthy to see the Holy Grail and ascend to Heaven.
Shingen-E: The exemplary Shingen-E is built to pop skulls.
One of my old favorites (still sad I sharded it, though :( alas for small vaults), it likely references another 16th century feudal Japanese lord, Takeda Shingen–Japanese, 武田 信玄. A commander of "exceptional military prestige" during the Sengoku period, his alleged death by sniper was depicted by Kurosawa in the movie Kagemusha. It will be the 444th anniversary of his death on May 13th!
Longespée-A: When all around you is chaos, the dependable Longespée-A won't fail you.
A reference to William Longespée (literally, 'long sword' ( ͡° ͜ʖ ͡°)), 3rd Earl of Salisbury. Renowned for being friggin' huge and having a friggin' huge sword. Go figure. He died in 1226, and was buried in Salisbury Cathedral. Five hundred and fifty years later, his tomb was opened, and a well-preserved rat was found inside his skull. I guess you could say it was skulking around? He got ratted out, though!
SUROS TYR-14: Stable. Dependable. Rapid-fire. SUROS.
Reminding me of how much I hate Suros' flavor text style, I'm not 100% sure about this one, because most of the 'cheap' Suros weapons have three-letter acronyms at the end of their name, so this might be coincidence. But, Týr is an ancient Germanic/Norse god, either the son of Odin, by the Prose Edda, or Hymar, by the Poetic Edda. Associated with war and might. Had his hand bit off by Fenrir, and is therefore known also known as 'The Leavings of the Wolf' which is an honorific, rather than a dig at him. His name is also where we get 'Tuesday' (Týr's-day)!
Cydonia-AR3: The City can't rely on a steady supply of programmable matter, so the multirole AR3 uses it only sparingly.
A region of Mars, but also a surname of Athena. That region of Mars was also where we found 'the Face of Mars', a rock formation whose shadows made it look like a face. Pretty neat.

Pulse Rifles

Herja-D: Devastate your foes with the deadly precision of the Häkke Herja-D.
More from the Prose Edda! This is a Valkyrie (demigoddesses of war, they would ride into battles and pick the worthy dead to come with them to Valhalla) specifically named in one of the two Nafnaþulur lists. Etymologically, it is also related to the Old Norse herja and Old High German herjón, both of which mean 'destruction' or 'devastation'.
Apple of Discord: "For the Fairest."
Huge shout-out to G3vanB, I'll put their analysis here:
Eris, godess of strife, supposedly throws one:
An apple of discord is a reference to the Golden Apple of Discord (Greek: μῆλον τῆς Ἔριδος) which, according to Greek mythology, the goddess Eris (Gr. Ἔρις, "Strife") tossed in the midst of the feast of the gods at the wedding of Peleus and Thetis as a prize of beauty, thus sparking a vanity-fueled dispute among Hera, Athena, and Aphrodite that eventually led to the Trojan War.
https://en.wikipedia.org/wiki/Apple_of_Discord
The Apple was inscribed with ΤΗΙ ΚΑΛΛΙΣΤΗΙ The translation is the Gun's flavour text.
Interesting to note the Goddess of Strife's name ...
Hawksaw: A northwesterly wind is blowing.
Perhaps one of the more well-known references to our dear Bard, this is from Hamlet, Act 2, Scene 2, Line 351:
HAMLET I am but mad north-north-west. When the wind is southerly, I know a hawk from a handsaw. 
We're all mad, mad I tell you! Thanks to pocsaclypse for pointing that one out!
Parthian Shot: Who's got the last laugh now?
A military tactic turned literary term, a Parthian shot is an insult or retort delivered as the speaker was leaving. It eventually evolved into the much more well-known 'parting shot' in a delightful little bit of linguistic movement. It comes from a strategy developed by the Parthians, ancient Iranian peoples, where they would ride their horses away from the enemy while firing their bows at said enemy. Of course, it was also before the development of stirrups, so this was a technique that required a truly sublime mastery of equestrian skill. Imagine shooting a bow, while riding a horse, that you're only controlling with the muscles in your legs. Insane.
Smite of Merain (Adept): Barrel etching: "He parted them like a sea, which closed upon him again."
It's not exact, but any references to any parting of any seas are of course biblical in nature–Exodus, 14:21-15:19. Just taking the most similar quote I can find:
26 Then the LORD said to Moses, "Stretch out your hand over the sea, so that the water may come back upon the Egyptians, upon their chariots and chari- ot drivers."
14:26, NRSV. As usual, that particular act of God is followed with a great deal of praise.
The Messenger: From deep within the shadows it came—a messenger borne on black wings.
The personification of death often includes a pair of black wings. Crows and Ravens (and many other members of the Corvus family), often thought of as battlefield scavengers, are black. This feels like it should be a specific reference, but honestly it's more a trope than anything.
Hopscotch Pilgrim: It's a long road. Enjoy it.
In a seriously impressive bit of detective work, JohnnyFlack found that this is actually referencing:
Oh oh i found this while reading about the origins of hopscotch...
"In Cuba and in Puerto Rico it is called "La Peregrina" (meaning "Pilgrim Girl") and the squares represent the 9 rings the pilgrim traveler has to pass in order to reach Heaven from Purgatory according to Dante's Inferno."
Here's the Wikipedia article!
Moriaen-D: You are a child of many peoples, a protector of all cultures.
More Arthurian literature. This is a 13th century romance, called Moriaen, whose story of the titular hero follows him as he first attempts to find his father, and meets with famous knights of the round table, like Lancelot and Gawain. Once his father Aglovale is found, they return to his mother and take back her rightful lands. He is Moorish after his mother, but obviously is also a part of the Arthurian tradition. Thus the 'child of many cultures'.
Lump Distribution: This nimble rifle's on-board tactical systems keep a scrupulous tally of combat stats.
Besides looking totally neat, the gun refers to a Lump-Sum Distribution, which is, "... the distribution or payment within a single tax year of a plan participant's entire balance from all of the employer's qualified plans of one kind (for example, pension, profit-sharing, or stock bonus plans)." Thanks for that, IRS.
Painted Apollo MSc: A highly accurate Nadir firearm, earned through glory in the Crucible.
Our first Nadir gun! Apollo is the Greek god of, among other things, music, poetry, art, oracles, archery, plague, medicine, sun, light and knowledge. Wicked important, very well known. Has a sister, Artemis.
Painted Neptune MSc: A high velocity Nadir firearm, earned through glory in the Crucible.
I'm sensing a naming trend, though perhaps not a consistent! Neptune is the Roman god of the sea and freshwater, and is the counterpart to the Greek Poseidon.
Hotspur-A: Piezopolymer paneling makes the Häkke Hotspur-A a balanced war machine.
Hey! This is interesting. The green Häkke weapons are named after English noblemen! This one is after Henry 'Hotspur' Percy. Led a bunch of rebellions against Henry IV and was eventually killed at the Battle of Shrewsbury by an arrow to the face. Get rekt kiddo. He also featured as a character in Shakespeare's Henry IV, part I.

Scout Rifles

Fate of All Fools: *"The wise man knows his fate. The fool merely finds it."
I orignally thought this was a reference to Matthew, but turns out it's not–check out the story below!
A really excellent explanation of this from Voroxpete, which makes much more sense:
The Fate of All Fools - This one is actually a reference to a videogame... Specifically, Marathon, the series that Bungie created back in 1994, and from which many, many elements of both Halo and Destiny are derived. Rather apropo, given that the weapon was originally gifted to a long time fan who was recovering from brain cancer.
The specific reference is to this scene from Marathon 2:
Tycho's ship has been destroyed. The crater where it annihilated itself on Lh'owon's inner moon is still glowing. There were no survivors. With a focused message laser I burned his epitaph into the surface near the crash site, in letters three hundred meters high: "Fatum Iustum Stultorum."
The speaker in that scene is Durandal, an incredibly powerful rampant AI (wow, gee, its almost like Bungie have some kind of fixation on powerful rogue AIs or something). Tycho is another very powerful AI, acting under the control of an alien empire and sent to destroy or capture Durandal.
The phrase in latin at the end is a little bit wonky (hiring experts to get your dead languages right wasn't exactly a thing in nineties video game design), but it's more or less agreed that the intended translation is something like "The just fate of the foolish"...
Or "The fate of all fools."
Cocytus SR4: The Omolon Cocytus SR4 will drown your enemy in a river of pain.
Thanks to scapulargolem for this:
The 'Cocytus' is referencing the black river surrounding Dis/Hades (The underworld) in Classical mythology. It's mentioned many times in Virgil's Aeneid book 6. It's flavour text reflects this.
Incidentally, in some versions of the tale, the Cocytus Styx was supposedly the river Achilles was submerged in to make him invulnerable. He was held by his ankle, thus making his ankle his only weak spot–his Achilles heel (thanks to thyrandomninja for that clarification!).
And some additional context from Owasippe_Ninja! Thanks!
Awesome. Also, in Dante's Inferno, Cocytus is the frozen lake of the Ninth circle of hell, encasing not only Lucifer himself, but those who betray a bond of trust with others like benefactors, countrymen, and family. The ice is formed by the tears of the Old Man of Crete, which are described as being frozen sorrow and pain, and the frozen winds blown up by the wings of Lucifer. The worst betrayers (who aren't being devoured in the three heads of Lucifer) are fully encased in the ice in a the region called Judecca, named supposedly for Judas Iscariot (although there's more to Judecca than just Judas, check out its use in medieval city planning and general attitudes of Italian Christians of the time to Jews). So seems to fit the flavor text of "drowning enemies in a river of pain."
Additional small bit from another stealthy person, thyrandomninja:
is not just a reference to a literal river, but the Cocytus is also the river of lamentation, or mournful woe. It not only drowns the enemy in front of you by shooting them, but their friends and family are drowned in mourning as well.
Tuonela SR4: Hell will freeze over before the Omolon Tuonela SR4 will fail you.
Ahahah funny joke, Bungo. In Finnish mythology, Tuonela is the equivalent of Hades. In Finnish Christianity, it is the word used for 'Hell' in translations of the Bible. In terms of a literary reference, though, Tuonela is featured in the Kalevela, a Finnish national epic. The protagonist (roughly speaking), Väinämöinen, travels there to seek the knowledge of the dead. It, uhh, went okay.
The Hero Formula: It's just so satisfying!
Okay, this is referencing one of two things: either Heron's formula, alternately spelled Hero's formula; or the Hero's journey, which, frankly, makes slightly more sense? The first is a mathematical formula that gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, where A=√(s-(s-a)(s-b)(s-c)). It's satisfying, I guess? Math isn't really my thing. The second refers to the 'monomyth' or the "common template of a broad category of tales that involve a hero who goes on an adventure, and in a decisive crisis wins a victory, and then comes home changed or transformed". The idea was originally put forward by Jason Joseph Campbell in his 1949 book on the subject, The Hero With a Thousand Faces.
Lethe Noblesse: Do not forget. Never forgive.
Many thanks to Johnny_Dirtbird for this one:
Good job. One other that I had in mind is the Queen's scout rifle, Lethe Noblesse. The flavor text is "Do not forget. Never forgive." From dictionary.com - Lethe is "a river in Hades whose water caused forgetfulness of the past in those who drank of it." Noblesse is a French word that means nobility. I know it from the phrase 'Noblesse Oblige' - nobility obligates. Putting the words together, my guess would be something like 'forgetfulness of nobility.'
High Road Soldier: The survival of civilization depends on our willingness to choose conscience over expedience.
Per S0rrowS0ng and JohnnyFlack, this is likely a reference to the common idiom (I mean, it bascially defines the concept in the flavor text) 'take the high road'. It could also be a winking reference to the chorus 'The Bonnie Bonnie Banks o' Loch Lomond':
O ye'll tak' the high road, and I'll tak' the low road, And I'll be in Scottland a'fore ye, But me and my true love will never meet again, On the bonnie, bonnie banks o' Loch Lomond. 
Zero Point LOTP: This much fun should be outlawed.
thyrandomninja has a great and funny explanation:
I'll do what I can to explain. Every object has "energy levels", whether it be an electron, a molecule, a snooker ball, or a planet. The DIFFERENCE between these energy levels is imperceptible to us because we exist on the macroscopic scale (i.e. we're too big to see tiny differences), so to us it looks continuous. On the microscopic level (e.g. electrons, these energy levels are relatively larger, and much more noticeable, which is what ultimately leads to all the "weird shit" in quantum mechanics, that doesn't show up in real life scenarios). Energy states are usually categorised as n=1, n=2, etc, where n is the number of that energy level. (Electrons NATURALLY tend to operate in n=1 through ~20 [give or take whatever - CERN like to add a few thousand/million/whatever n's in their accelerators :P ] territory, whereas a person is always on n = several fucking million) Zero Point Energy is the energy of an object at n=1. There is no n=0 (for reasons i won't get into here), and therefore no such thing as "having no energy". There is always SOME amount of energy in any given object, and you cannot get rid of it (that "some amount" is negligible compared to things we see in our lives, but that's not the point).
Relating to Life Of The Party, this is probably saying there's no such thing as a dead party. There is always SOME fun to be had, no matter what - the very idea a "life of the party" person would embody.
Alternatively, it could be a jab at the "life of the party" philosophy, by saying that "yeah, there's some fun, but it's negligible, and i'm going to go home", meaning the description takes on a more sarcastic approach.
The Scholar: You can't pull an all-nighter when the sun never sets.
Not really 'literature', but too relevant not to include ;)
Also, per goldenboot76:
Everyone probably knows this already, but the other reasoning behind the Scholar scout rifle's flavour text is the fact that Mercury's orbital period and rotational period are one and the same. As such, half of Mercury is in eternal sunlight, and the other is in eternal darkness.
Hence, the "You can't pull an all-nighter when the sun never sets.".
Thanks for that!
Lampad SR4: Let your enemies know: death will be their only companion.
The Lampads, or Lampedes, were spirits of the underworld in greek mythology. They accompanied Hecate and generally went around doing spooky stuff.
Orphne SR4: If death is the Darkness's way, let our Light defy their desire.
Orphne was a specific nymph of the Greek underworld. Also an alternate translation of Caliga, the goddess of Darkness.
Painted Abbadon SR5: A single-fire Omolon firearm, earned through glory in the Crucible.
Sharing its name with the exotic machine gun, Abbadon is either a "place of destruction" or an Angel of Death. Either way, not pleasant.
Just a quick clarification from westen81, thanks!
Abbadon is most usually associated with the angel of destruction (not necessarily death)..
Painted Sorg SR5: A powerful Omolon firearm, earned through glory in the Crucible.
In a large number of Germanic and Germanic-derived languages, 'sorg' means 'sorrow' or 'grieving'.
Primed Díyú SR5: A long range Omolon firearm, earned through glory in the Crucible.
Following a clear pattern here, 'Diyu' is the Chinese conception of Hell.
Silvered Kín SR5: A highly accurate Omolon firearm, earned through glory in the Crucible.
A Turkic word, it means, simply, 'pain'.
Bronzed Yamaduta SR5: An accurized Omolon Scout Rifle, earned through glory in the Crucible.
The Yamatuda are messengers of Death in the Hindu tradition.
Thanatos SR5: Where Death follows, new life will grow. Where new life grows... Death will follow.
Thanatos is the Greek personification of Death. He is the twin brother of Hypnos, the God of Sleep. Referenced in the Illiad:
... then send Death to carry him away, and Sleep who is painless ... 
The Iliad, 16.453-4. Richard Lattimore, translator.
Xibalba SR5: Tiled with picocircuitry, the Xibalba SR5 is fiendishly accurate and hungry to grow.
How many different conceptions of Hell can we find? This particular one refers to the Mayan realm of the dead. It shares its flavor text with the Acheron SR5. The Acheron is both a real river in Greece, but also another one of the five rivers of Hades. The Cocytus (discussed above) flows into it.
Naraka SR5: There will always be new hells to conquer.
hahah, no kidding about those 'new hells'. This specific hell is a particularly diverse amalgamate, finding its place in Hinduism, Jainism, Sikhism, and Buddhism. Modified to 'Neraka' in Indonesian and Malaysian, it also describes the Islamic concept of hell. Moreover, it also describes the servants and spirits of Hell when modified to 'Narakas'.
Garmr SR1: Death is hungry.
Garmr is a dog (or wolf) of the Underworld in Norse mythology. He is, "the blood-stained guardian of Hel's gate".
Shinigami SR1: Death comes for the City's foes. Let's not keep it waiting.
Shinigami–Japanese, 死神–are spirits or gods of death. They invite humans to death, and rule over the underworld. Fans of the anime Death Note will also remember their appearance in that series.

Hand Cannons

The Last Word: "Yours. Not mine." —Renegade Hunter Shin Malphur to Dredgen Yor
Many thanks to andreisse for this one!
I know it's based on a gun, and a speech... I'll try and find it.
The Last Word is likely based on a real-life counterpart called Revolver No. 5. It was a weapon devised in 1928 by Elmer Keith, a "firearms enthusiast" from Idaho renowned for his six-shot expertise. He wrote about this weapon in 1929, in an article titled "The Last Word".
http://destinydb.com/item/3164616405/the-last-word
Here's a link to a .pdf of the article.
Gaheris-D: Balanced and dependable, the Häkke Gaheris-D is a true warrior's weapon.
More Arthurian legends! Gaheris was the nephew of Arthur, and a knight of the round table. He is described as "... valiant, agile, handsome, reticent in speech, prone to excess when angered, and possessing a right arm longer than the left".
Judith-D: Headshots are strongly encouraged with the Häkke Judith-D.
So, there are a lot of things this could be, but most likely it is referencing Judith of Bethulia, an Israelite who beheaded the Assyrian general Holofernes. Headshots strongly encouraged, indeed! Incidentally, that poem is found in the same manuscript as Beowulf–the Nowell Codex.
Kumakatok HC4: When the Omolon Kumakatok HC4 comes knocking, even the Darkness locks its doors.
The kumakatok are three Philippine spirits, who walk from door to door, knocking and bringing bad omens. One is supposed to resemble a young woman, the other two old men–however, they obscure their faces with hoods. Seriously creepy.
The Devil You Know: Let's make a deal ...
A reference to the phrase, "Better the devil you know than the devil you don't", this is the only weapon I know of that actually completes the phrase in game. The Devil You Don't was widely acknowledged to be simply a worse version of TDYK, not only being an impact class lower, but also with worse base range. That's commitment to the joke right there.
Uffern HC4: Omolon's Uffern HC4 sentences the City's enemies to burn.
In what should be a surprise to nobody at this point, Uffern is the Celtic version of Hell. Unfortunately I can't source it beyond a three-word mention in the Wikipedia article on Hell.
A very helpful clarification by Rapstah–much appreciated!
"Uffern" is literally Welsh for "hell". "U" is a near-close central unrounded vowel, or even a short "i" sound in southern Welsh. The sound "f" is represented as "ff" in Welsh, so if you represent it as "yfern" it's clear that it's derived from Latin "infernus".
I wouldn't say it's the Celtic version of Hell, it's literally just what you would call the christian concept of Hell in Welsh.
Byronic Hero: Brood, baby, brood.
A type of anti-hero created and embodied by Lord Byron. Byronic Heroes are: "a man proud, moody, cynical, with defiance on his brow, and misery in his heart, a scorner of his kind, implacable in revenge, yet capable of deep and strong affection". Think Hamlet, with a touch of Han Solo.
Also possibly another more modern reference, per getedm8–thanks!
This may be a stretch, but with the Byronic Hero's flavor text, it could be a reference to Saturday Night Fever. More specifically, the song "Disco Inferno" where the main chorus sings "Burn, baby burn!"
Vortimer-D: Where you come from is not important. It's for what you do that you will be remembered.
Vortimer, or Saint Vortimer, was another English legend. He can be found in Geoffry of Monmouth's Historia Regum Britainniae–my copy of which I've misplaced, apologies–where he is a described as a Britonic king with a strong distaste for Saxons. Worked out well, he died though.
Rience-D: You will not suffer these invader kings to live.
Hey, wait, are you telling me Häkke named another one of their guns after an English legend?! Yes, yes I am: Rience was an English/Irish/Scottish/British king named in Arthurian legend. He is variously described as the king of North Wales, Ireland, and 'many Isles'. He had the habit of edging his robe with the beards of Kings he had conquered–by the time Arthur came along, he had eleven. Arthur's, of course, was to be the twelfth invader king that he would crush. Didn't work out so well. Gosh, I really hope that's not a predictor.
LOCK_ARETE: Her excellence lies in swiftness.
A confusing one, because arete-Greek, ἀρετή–is literally 'excellence', especially in regards to efficacy, but also in terms of bravery. Arete is also the wife of Alcinous of Scheria, described thus in the Odyssey:
... Alkínoös married her and hold her dear. No lady in the world, no other mistress of a man's household, is honored as our mistress is, and loved, by her own children, by Alkínoös, and by the people. When she walks the town they murmur and gaze, as though she were a goddess. No grace or wisdom fails in her; indeed just men quarrels come to her for equity ... 
The Odyssey, 7.70-8. Robert Fitzgerald, translator.
It wasn't originally my plan for these to go in descending order of references, but hey, that worked out nicely!
As I said in the beginning, I'm sure I've missed some, so don't hesitate to point them out.
Thanks so much for reading, Guardians, I really appreciate it!
submitted by XKCD_423 to DestinyTheGame [link] [comments]

Dice-based gambling game

So, I'm an ex-professional poker player and huge D&D nerd / DM, so naturally, one of the things I like to fill my worlds with is inventive games of chance. A similar game got a lot of attention recently so I figure there's a demand for this sort of thing; I had meant to share this a few months ago, but got busy and forgot.
My goals in creating this game were:
The third point led to the idea of using dice as a kind of casino chips, and I just kinda ran with that.
I call the game Athena's Hunt but that's completely arbitrary flavor. Reskin it as you please, of course.
Before playing, the character purchases dice. The idea is that these dice exist in-game, and it's the character purchasing them from an in-world casino. As such these dice have a monetary value, as a casino chip does. You can set this to whatever's appropriate, and can have variable-value dice, though for the game to retain its house edge, a player has to declare what value dice they're using before the house roll.
The players can buy d4's, d6's, d8's, and d12's. These dice all have the same value.
The game is then played as follows:
1) When a player commits to playing, the house rolls 1d20. The result is the house roll.
2) The player will then try to match that roll, first with their declared dice.
3) The declared dice are some combination of 1-3 d6's, d8's, and d12's (not d4's, which are special), and must include at least one d6.
4) The player rolls their declared dice. If they wish, they can then choose to roll a d4, called a stinger, and add the result to their total. The stinger counts as part of their bet but does not count toward calculating their multiplier.
5) If the player's roll (the declared dice plus the stinger, if the player rolled one) is equal to the house roll, the player wins. If the player's roll is within 1 of the house roll (above or below), the result is a push. With any other result, the player loses and forfeits their bet (including the stinger).
6) On a push, the player gets all their dice back.
7) On a win, the player gets all their dice back, and also wins from the house a sum that scales with how many declared dice they rolled:
1 Declared Die: Player wins 1 * their bet. 2 Declared Dice: Player wins 2 * their bet. 3 Declared Dice: Player wins 3 * their bet.
Stingers count as part of the bet but not toward calculating the multiple. So the max a player can win is 12 (when they had 3 declared dice and rolled a stinger).
Played as such, the house edge works out to exactly 3.472%, which is pleasantly in line with most modern casino games. This is if the player plays perfectly, which most won't. I've done the math on this, and verified it with a crude Monte Carlo simulation using an Excel macro. Over 30,000,000 plays with perfect play, the house won at about 3.4%.
I can share the math behind this (at least in part) if people want, but it's complicated as hell. To tease it, a house roll of 5 and 7-15 are favorable to the player, with a 12 being the player's best roll (if they declare 3d6).
The name "Athena's Hunt" is malleable (work to whatever end you want), but I phrase it as, Athena is hunting a stag that is a number of miles away that is equal to the house roll. The farther the stag is away, the harder it is to hit, but the greater the rewards are for hitting it. Feel free to ham it up as necessary.
Of course, with this being an in-universe dice game, DM's will have to have rules built in for players who want their characters to cheat. I haven't formalized anything for this yet, but imagine that sleight-of-hand and telekinesis will be popular, as might be weighted dice. Swapping out for more expensive dice after a favorable house roll might be a clever way to cheat (similar principle to card-counting in blackjack), and a sorcerer might subtle-spell-telekinesis their way to victory once or twice.
My games have been on hiatus over the holidays, so I haven't actually gotten a chance to play this in a live game yet, but I'm very happy with this one conceptually and want to see it played!
submitted by gdshaffe to DnD [link] [comments]

Science joke

What is the difference between a prisoner plotting revenge in his cell, a scientist doing physics simulation and a prostitute in famous casino?
Count of Monte Cristo, Count for Monte Carlo and Cunt of Monte Carlo
submitted by bebolaapi to Jokes [link] [comments]

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Les méthodes de Monte-Carlo - YouTube

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