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Monte Carlo methods – Why it's a bad idea to go to the casino

431 points by whereistimbo 7y ago

roenxi 7y ago
I have a pet peeve about Monte Carlo methods; although it might be more fairly characterised as a rookie mistake I saw once. MCM are not strong if the tail variance isn't an important feature of what is being modeled. I've seen simulations where the modeler starts with an analytic model - from which they could trivially calculate the mean and variance of a KPI - then used a MCM simulation to find out essentially what the mean and variance of the KPI. So I get that this code is just for illustrative, educational purposes. That is fine. Well done Christof, thanks for the contribution to education. But if anyone is actually using MCM to simulate well known probability distributions they should really put the effort in to learning how to work with well known probability distributions. I feel pretty confident that simulating the Bernoulli in a professional setting is a mistake, because I've seen it done and it was a mistake. For amateurs who aren't confident with math then they can use MCM if they like; but statistics is dangerous and they should be aware that they are using the wrong tool for the job and it is a tell they will get other things wrong. You get a lot of insight from a good analytic model. If there is some interesting tail issue (eg, maybe after 3 heads there is guaranteed to be a tails and your insurance contract pays out on a tails) then sure, use MCM. Great tool if you have the right problem.
- Retric 7y ago
  While I generally agree with what your saying, I think the MCM can be a great way to validate more accurate approaches. The primary advantage for validation is you can get a reasonably accurate answer with minimal effort.
- petermcneeley 7y ago
  Really dependents on your philosophy. Would you rather do error propagation using this method http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm or would you rather perturbate your variables and resolve mean and variance. My philosophy drives me towards the computational approach over the analytical mathematical approach.
  - deleted 7y ago
    [deleted]
  - roenxi 7y ago
    Are you sure there is even a philosophical difference there? I'm still going to use a program to do the heavy lifting of calculating the errors. I'm happy to argue that there is no philosophical difference; if both approaches are feasible and take comparable amount of time to implement then one gets the exact answer to the question at hand and the other is a poor man's shortcut for people who aren't confident in their maths skills. The calculations should be arriving at the same numbers in the end, and implementing a simulation vs. an error propagation tree isn't going to favour the simulation for simple scenarios. MCM is great for when doing usual error propagation is infeasible. It is sloppy when the error propagation could be done with a one or two analytic formula. Simulation isn't appropriate for problems that are easy analytically. For example, in practice, most of the examples in the article are not suitable problems for breaking out MCM (and although the author probably knows that, maybe not everyone on HN does). The Pi one might be a standard application, but even there Pi in particular is not a great choice for a showcase because Pi has some very nice analytic approximations.
    - alexgmcm 7y ago
      I think the value is in checking assumptions - if the analytical approach assumes a normal distribution and then you do MCM and get a vastly different result then it is probably worth checking the assumptions made by the analytical model.
      - roenxi 7y ago
        That is an inappropriate way of checking your assumptions. Assuming a normal is assuming a model (a model is a simplification of a situation by only considering the relative parts). Writing a simulation is also assuming a model, although the process is a lot less formal than traditional statistical regression. If a modeler has assumed two different models of a situation and are getting vastly different results then that is evidence something is wrong, but it is also evidence that the modeler is out of their depth. It is not appropriate to fit two different models and then claim that the differences are delivering insight. The differences are revealing big gaps in the modelers understanding of key influences, rendering both models highly suspect. They should not be creating models, they should be putting more time into understanding the thing they are modeling. There are times when a modeler would have two different models, but they should certainly not be surprised that they give different results. Indeed, they should be assuming two different models because they are going to give completely different results. There will probably be other edge cases, but in my experience they are rarer than people just making mistakes about where MCM is appropriate.
- klipt 7y ago
  Well yeah MC is usually meant for problems that are otherwise intractable, e.g. sampling complex Bayesian posteriors, or solving stochastic differential equations. Using it for an answer you could easily get analytically isn't very useful outside of education/fun.
- arsenide 7y ago
  If there is an analytic model, using Monte Carlo methods is extremely useful to validate the theoretical result. If both agree, it is unlikely that there is a mistake in the theoretical result: which is valuable information. For something as straightforward as Bernoulli, where you plug values into a formula and are done, there is no reason to use MCM. However, I am in agreement that in more complicated cases (e.g. a probability distribution is based on some result of one Markov or Markov-like calculation — or possibly multiple), and the theory is slightly or much more complicated then there is a lot of value in Monte Carlo methods.
- bathyspheric 7y ago
  Can I ask if I understand your use of `tail` in tail variance? Do you mean tail as in extremes of a distribution, or tails, as in losses. I'm very interested in using MC techniques to model extremes of a distribution, like 1-in-1000 year events from a Weibull distribution, but my (naive) algorithms spend a lot of time in the fat belly of the curve rather than out in the tails, but perhaps (probably) I'm holding it wrong. Is there a way to constrain the MC sampling to the tails of a distribution?
  - salty_biscuits 7y ago
    You want to look up about importance sampling. There are lots of ways to do it, the two most common are via scaling or translation.
  - roenxi 7y ago
    I meant tail as in the extremes of the distribution. My point was more that once you've assumed that your events follow a Weibull distribution then the opportunities for MCM to add more insight are limited if the task at hand is to predict what the distribution and its parameters are. Obviously if you simulate a Weibull distribution you will get results in line with the info box on the Wikipedia page for the Weibull distribution, and you need to effectively assume parameters to simulate. Simulating a distribution just creates a very error-prone calculator the obscures the assumptions. I've seen people do exactly that thinking it was somehow helping - it is surprisingly easy to accidentally simulate a normal distribution, for example, because if you add a whole bunch of uncorrelated random things together (with identical distributions) then the result is normally distributed. You don't need a simulation to tell you that, and it is easier to mull over without simulation. If I were using simulation it is because I think that something fishy happens in extreme events (eg, maybe stock returns all starting to become highly correlated in a liquidity crisis, destroying i.i.d assumptions). Or as other commenters mentioned because the thing being simulated has a distribution that is not analytically tractable. But there has to be some phenomena in there that is more complicated than standard distributions or a steady state Markov model, because they are more productive models when they work. > Is there a way to constrain the MC sampling to the tails of a distribution? You could sample 100 numbers at a time and drop out the middle 95? The question is maybe not well posed.
- emarsden 7y ago
  I agree. Here's a Python notebook that illustrates this problem on a classical gambling problem, the Saint Petersburg paradox. The notebook explains why stochastic simulation methods such as Monte Carlo are not suitable for situations where a very unlikely event has a significant impact on the output of interest in your simulations. https://risk-engineering.org/notebook/saint-petersburg.html https://risk-engineering.org/notebook/saint-petersburg.html
- DarkWiiPlayer 7y ago
  I once was in a situation where I had to hammer in a nail with a screwdriver (grabbing it by the front, hitting with the grip). The feeling I had back then is one I all too often experience again in programming. This example isn't so much different; MCM = screw driver, problem = nail and learning proper statistics = driving to the hardware store and buying a hammer. The only aspect where the comparison is somewhat lacking, is that the costs of having a hammer (both aquisition and storage) are minimal compared to in-depth knowledge about statistics.
Proven 7y ago
It’s not a bad idea. It’s this stupid clickbait title which assumes that the value of entertainment and other intangible outcomes doesn’t offset tangible outcomes. If that were the case buying most devices would be a bad idea. Junk submission.
blunte 7y ago
If you want to really know why you shouldn't gamble (for profit... gambling for fun, with discipline, can be satisfying), read this quintessential book: Scarne’s Complete Guide to Gambling What you will probably take away from this book is that the house wins when you win. And the reason they win is that they don't pay actual odds. Take the roulette wheel as a simple example. There are 37 (or 38 in the case of 0 and 00 wheels) slots. If you bet on a single number, they pay 36:1. TFA mentioned doubling down when you lose. That's known as the Martingale Strategy. As banks and real estate lenders discovered in 2007, regardless of your model, there will be some condition where the near-impossible will happen. If you want to use the roulette wheel again as an example, and even if you want to ignore the green 0/00 slots, you have half black and half red. You can simply play one color and double your bet if you lose... until you finally win it all back. The problem there is that while it's true that for millions of spins, about half should land black and half should land red... but in short periods it is possible for there to be 10 or 15 or 20 or more spins of the same color. We can all do exponential growth, so it's easy to see how doubling down will empty your wallet eventually. But just to be sure that strategy won't work, most casinos will set a table limit. That limit will be designed to prevent you from doubling your bet too many times (5-7ish times? depends on the place). Of course, if you discuss in advance with the casino, you may be able to set a personal table limit based on your initial bet. So you can bet 1 million on the first spin in order to set your table limit to 1 million. But that's truly a gamble. There is one element you can control when gambling: that is when you increase or decrease your bets, and ultimately when you stop playing. Yes, you can count cards in blackjack; but that's generally frowned upon (where "frowned" means you will be escorted out and told to never return -- and they are very serious). Even levels of indirection of counting such as employed by the fascinating experience of the MIT crews of yore (https://en.wikipedia.org/wiki/MIT_Blackjack_Team https://en.wikipedia.org/wiki/MIT_Blackjack_Team) have become obvious. So the short of it is, unless you only play a little, bet big, and get lucky for your limited period (and then stop so you don't get banned), you will otherwise lose more than you win. Now for my personal opinion :). Casinos used to be a fun place. Now they are so optimized and commercial that they are like Walmart. Yes you can go, but you'd probably rather not. For modern thrills, we now have crypto exchanges with 50:1 or more leverage.
- 7y ago
deleted 7y ago
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55555 7y ago
It's more complicated (worse) than this. That the house has a small edge only tells a small part of the story. When people go to vegas for a weekend, they might have a number in their head they are willing to gamble. If they dont, then that number is their bank account balance. Then they start flipping coins, and often they keep doing this until they go bust. They rarely cash out when up but they always lose when they go bust. They scale the bets as their bankroll grows. Essentially they are flipping coins for infinite time and just waiting to get a bunch of tails in a row, which is inevitable. The behavioral factors are bigger than the house edge. The idea that people are rational is also absurd. Some people are driving to the slots _because_ they are depressed. Or they are there for fun but they lose a bunch of hands in a row and tilt and now they're betting everything on a longshot to win it all back and win some because they dont want to self-identify as a 'loser'. You can only spend so much money on drugs and sex. Gambling is the only vice where you can lose billions. And these days, all you have to do is pull out your phone to place a trade or a bet.
- RomanBob 7y ago
  This is a common misconception about why casinos win. That 'casinos have infinite bankroll so they cannot lose' isn't actually an argument because casinos have limited bankroll. If they would allow me to play a +EV game I can crush them even if they had infinite bankroll by varying my betsize. The 'random walk' argument only works for fixed bet size.
  - eric_h 7y ago
    > If they would allow me to play a +EV game If a business offered a positive EV gambling game, it wouldn't be called a casino and would only last as long as the venture capital lasted.
    - ojbyrne 7y ago
      Actually there are still +EV video poker games in Vegas. http://www.slotsmamma.com/blog/how-do-you-find-full-pay-deuces-wild/ http://www.slotsmamma.com/blog/how-do-you-find-full-pay-deuc... There are a few catches though. Mostly if you play perfectly (which is not simple) the most you can expect to make is less than eight dollars an hour.
wavefunction 7y ago
Blackjack has been a source of success for me though I'm unconventional in my betting strategy which seems to enrage the other players even when I break the dealer consistently.
- phkahler 7y ago
  Dont they kick you out if you're consistently winning?
  - forbiddenvoid 7y ago
    Not necessarily. Casinos will kick you out for a particular set of behaviors. Just winning isn't enough. Playing a minimum bet for a long time, then suddenly increasing to the max near the last half of a shoe is a good way to get a casino to ask you to stop playing blackjack.
  - GVIrish 7y ago
    Only if you're winning a lot of money. They don't care that a small fish wins a few hundred dollars every now and then.
- listenallyall 7y ago
  You've never broken the dealer. Dealer has specific rules in blackjack of when to hit or stand that are completely independent of your cards, betting amount or strategy, emotional attitude, or how good or bad your breath smells.
- scarejunba 7y ago
  More likely it's just numbers, right? If 1024 people flip coins ten times in a row, it's expected that one of them gets 10 heads. But he's not a genius, right? Of course you should always back yourself. So more power to you if you're winning in this way. At least you get to keep playing :)
  - stordoff 7y ago
    Derren Brown had an interesting example of this on UK TV a few years ago. It's nothing new, but showing it this way demonstrates how you can get drawn in: > The System, a Channel 4 special in which Brown shared his "100 percent guaranteed" method for winning on the horses, was first shown on 1 February 2008. > The show was based around the idea that a system could be developed to "guarantee a winner" of horse races. Cameras followed a member of the public, Khadisha, as Brown anonymously sent her correct predictions of five races in a row, before encouraging her to place as much money as she could on the sixth race. > After Brown had placed a bet of £4,000 of Khadisha's money on a horse in the final race, he explained how "The System" worked. He had started by contacting 7,776 people and split them into six groups, giving each group a different horse. As each race had taken place 5⁄6 of the people had lost and were dropped from the system. Brown had a different person backing each horse in each race, and one individual, Khadisha, won five times in a row. https://en.wikipedia.org/wiki/List_of_Derren_Brown_shows#Derren_Brown:_The_System_(2008) https://en.wikipedia.org/wiki/List_of_Derren_Brown_shows#Der...
lanrh1836 7y ago
Blackjack on the strip has become a boiling frog of sorts. Everytime I go back the rules are tweaked a little more in the house’s favor. 3:2 payouts for Blackjack were gone years ago, but more recently no even money for Blackjack if dealer shows an Ace, only split once for two Aces...not worth it at that point.
- SmellyGeekBoy 7y ago
  In the handful of times I've been into casinos here in the UK I've always just stuck to the Blackjack table (I used to play it with my grandma for buttons when I was a kid). Every time I've walked away with more money than I started with. My biggest profit was over £500. The one and only time I was convinced to give roulette a try I lost everything pretty quickly (I mean the small pot I'd set aside for gambling - I'm not stupid enough to keep withdrawing money and bet more than I can afford). Seems blackjack can be pretty lucrative if you're willing to walk away at the right moment. I seriously doubt it would work as any kind of long term strategy, however. Of course you also have to have the discipline to spend the rest of the night drinking beer and watching your friends get poorer and poorer.
- dehrmann 7y ago
  Pointing out the obvious: it's more expensive to run a modern resort casino than a Fremont St casino in the 50's, even in inflation-adjusted dollars.
listenallyall 7y ago
This article should be down-voted, the only reason it isn't is due to the clickbaity nature of discussing casino games. It's a terrible initial introduction to Monte Carlo simulations, he doesn't even discuss the possibility of seeing the distributions of the results of the games he proposes, which is essentially the most valuable reason to perform a Monte Carlo simulation.
- screaminghawk 7y ago
  If you read it instead as an advertisement for easylang.online it's a pretty nice introduction for the language
  - listenallyall 7y ago
    ...and if the headline was "Learn to Program in easylang.online" it never would have sniffed the front page of HN
    - chkas 7y ago
      https://news.ycombinator.com/item?id=19299760 https://news.ycombinator.com/item?id=19299760
      - listenallyall 7y ago
        another clickbaity headline, confirming my point
    - chkas 7y ago
      I do not understand your criticism. The main content is Monte Carlo simulation at Roulette and that you lose in roulette games. The headline says just that. "easylang.online" is in this case just a means to transport this content. It would be much harder to do that in JavaScript and the examples would also be less comprehensible.
jaimex2 7y ago
If you go to a casino play poker with other humans. Nothing else is worth your time.
- soVeryTired 7y ago
  Even poker in a casino probably isn't worth it unless your opponents are obviously drunk or bad players. After the rake and the dealer tip, there's a good chance your edge is zero or negative.
  - AlexandrB 7y ago
    I read parent as saying that playing poker with others is the most entertaining way to spend your time at the casino, since he didn't mention money.
oldandtired 7y ago
When I was 8, I spent 6 months in hospital and that was over 50 years ago. Not much to do, so my parents made sure I had lots of puzzle books of all kinds as well as story books. One of those books had a chapter on gambing, which I found interesting, it was written for children. It made the claim that as long as the "bank" had a significant value greater than your own (by at least 10 times), you could not win against them even if the odds were 50:50. As the decades have gone by, I followed this up with other research and basically, gambling is a mugs games if you are not the bank. Yes, you can at times win and come out ahead. But on the whole, you will lose. My father's advice has always been: "Son, treat it as entertaiment and spend only what you can afford to lose like every other form of entertainment. If you think you can win, you be the fool and will lose more than you can afford." I have also found that gambling institutions are so depressing a venue to be in.
kai101 7y ago
I have similar simulation 10 years back written in C, no fancy description but understand how casino works. Similar conclusion, once u win enough, you leave; once you lose enough, you leave. Never bring your whole bank account to a casino, or the figures will be move closer to 0.
WalterBright 7y ago
Investing: Return on Investment > 0 Gambling: Return on Investment < 0 For the casinos, it's an investment, for the customers, it's gambling.
- denormalfloat 7y ago
  Perhaps we could combine the two? Make a slot machine that pays out in penny-stocks, rather than chips.
  - WalterBright 7y ago
    We call them "online brokers" :-)
blt 7y ago
The subtitle made me expect something about a failure mode of MC methods in some popular application...
slewis 7y ago
Great article showing how easy it is to experiment with probability using Monte Carlo methods. You don’t need any fancy libraries or deep mathematical knowledge. Of course you should always try to have a deeper understanding if you want to make serious conclusions. But I felt this article got the concept across really concisely! Nice work.
TazeTSchnitzel 7y ago
The language they're using seems to pretty much be BASIC with slightly different syntax, it even lacks user-defined parameters for functions just like BASIC does.
- chkas 7y ago
  There are user defined functions with parameters and locals.
  - TazeTSchnitzel 7y ago
    Why have subroutines then?
    - deleted 7y ago
      [deleted]
    - chkas 7y ago
      Subroutines have a global namespace - this is easier to understand. Functions with parameters and local variables allow longer and recursive programs.
arsenide 7y ago
I work on Monte Carlo simulations professionally for casino slot games. I wish that more depth was presented here: what percentage of the time do you get favorable vs unfavorable outcomes with each strategy? For further depth, use different types of players (with different exiting conditions). Perhaps I should write such a blog post at some time..
- paulkon 7y ago
  Please do, I'd love to read more about this!
- dang 7y ago
  That post would probably be of interest to a lot of HN readers. If you want, we can look over a draft if you send it to hn@ycombinator.com. Sometimes we can make suggestions that improve an article's appeal to this crowd. Same offer goes for anyone else who's putting a lot of work into a post they hope will interest HN.
  - arsenide 7y ago
    Thanks dang. I may very well take you up on this offer.
TBurette 7y ago
A while ago I wrote a similar interactive article to prove that the martingale betting technique at the roulette doesn't work : [1]. The martingale is when you bet 1, double the bet each time you lose, start again at 1 when you win. The aim was to create a single page anybody could link to that proves without a doubt the abysmal odds of making money off the roulette with the martingale technique. Instead of pre-written probabilities, charts and 'obscure complicated math' that people could easily dismiss. I wanted to give people the ability to run simulations of playing at the casino in the browser. The idea being that people would end up building the probabilities/charts themselves through simulations. It is running Monte Carlo simulations inside the webpage and outputs the result as charts dynamically using js and D3. What it does is it repeatedly simulates going to a casino with a certain starting amount of money and an objective of how much you want to win. It then plays the roulette using the martingale technique until you got your target winnings or you lost your money. Unfortunately I don't think I wrote the article really well and the 'generate yourself the charts proving it doesn't work' doesn't come across really well. I should have put a 'run' button instead of needing a page refresh for a start. [1] http://thomasburette.com/martingale/ http://thomasburette.com/martingale/
- eric_h 7y ago
  All of that is completely invalidated by that one time I hit 13 on the roulette table at two different casinos and quit gambling up $1500 ;)
  - tapland 7y ago
    Just a few varied anecdotes from working as a dealer and croupier for a few years: I once saw 13 be hit 4 times in a row (and once more within my 45 min rotation at the nearby table). Don't think I've personally seen any other 4 number streaks. A lof of people won a lot of money during the two last ones. I've only played a few slot games online and visited a real casino as a guest once, where I bought chips for $150 and left with $5400. The goal was losing it all and at the end I was putting $1500 on the table at a time, and dipped below $500 just a few minutes before making the $5400 and leaving. One of the best nights I had while working was a regular from the poker room coming to my Black Jack table trying to win back the $15k he was down. Had the 'chef' (senior position at the casino floor, poker equivalent would be 'brush') there talking to him since he wasn't doing well. He managed to win it back which was a great relief.
deleted 7y ago
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spaceflunky 7y ago
It's (relatively) easy to show the math on why casino games are impossible to win, but what about sports betting? Does the house always have the advantage? Perhaps it's slightly better for the gamer? FWIW I was looking a betting website recently [0] and they were offering DOUBLE your initial deposit for signing-up, up to $1000. So to reiterate, they are willing to give up to $1000 for FREE just for creating an account. All I can imagine is that they would only do this if the numbers are vastly not in your favor. [0] I'm not going to post the name of said website.
- OscarCunningham 7y ago
  >Does the house always have the advantage? The mathematics doesn't really matter because if you find a systematic way of winning then they just ban you.
  - SmellyGeekBoy 7y ago
    So... yes?
- listenallyall 7y ago
  >> just for creating an account No, for creating an account, funding it AND making a significant amount of wagers. The details vary by site, but there are always restrictions in the fine print -- either you only "earn" the bonus a few percent at a time, or you aren't allowed to withdraw until you've made enough bets, or some similar restriction. I'd guess that some or all of the "free" $1000 is inaccessible until you've made a 10x rollover, or $10,000 in wagers.
- Gustomaximus 7y ago
  You have to bet the bonus money at least once. I did this. Bet the bonus on some super low odds trots race to place that was as good odds as anything to get my money back and then bet the other half on a 36:1 long shot that Bernie would win the nomination. I got my money back with the low odds Trotter, otherwise I would have bet the balance on another low odds event. Obviously didn't win the long shot. Not sure why I did it as I don't normally gamble but generally curious and though it was a fun way to risk a small amount to potentially win a "free" holiday.
nurettin 7y ago
I made an effort to download previous draws form my local lotto website [1] And parsed them and applied a montecarlo method to see: 1. If I could find an optimal way of playing the game to maximize my profits. 2. If I could find a bias towards certain numbers. The result was: 1. I found a way with 1/3 chance of winning big and paying back all expenses you played for the past 20 years. It is a significant investment and everyone will think you are crazy, but you have a very high chance of early retirement. 2. I found no obvious difference between the frequency of numbers. The idea is to spread your betting numbers as far apart as possible in order to follow the normal distribution. If you reduce the overall gap between your numbers, your chances of winning is significantly reduced. [1] http://www.millipiyango.gov.tr/sonuclar/_cs_superloto.php http://www.millipiyango.gov.tr/sonuclar/_cs_superloto.php
- kaoD 7y ago
  If you found no difference on number frequency, it's the uniform distribution, not normal (a.k.a. gaussian) distribution. AFAIK uniform distribution means any number is equally likely to be drawn, regardless of distance to your other picks. Just to check if I got that right: does that mean that playing 333333 and 666666 in a 6 digits lottery had a higher chance of winning that picking 333333 and 333334? If so, why? And, since playing more numbers will reduce the overall gap. Does that mean the optimal strategy is playing a single number? Did you test your method via simulation? I can't see how it works with my little knowledge of statistics. Can someone chime in?
  - nurettin 7y ago
    Yes, I meant uniform distribution. My method was to give it a higher chance to have a lower gap between the numbers to see if it would make a difference within a montecarlo simulation and it did. So if you have say 16 slots and you need to choose four numbers, according to my simulation, highest likelyhood of winning is to spread out your numbers like [3 6 9 12] or [4 7 10 13] and lowest likelyhood of winning is to spread like [1 2 3 4] [2 3 4 5] all the time. Not exactly sure why.
    - 7y ago
trymas 7y ago
I am even more impressed by the `easylang`[0] itself, which was used to create the demo. [0] https://easylang.online/ide/ https://easylang.online/ide/
paulcarroty 7y ago
It's absolutely obviously for people who know the basics of Probability theory. Not sure if modern high schools covers it now. But it's only a part of the problem. Second part - money and gaming easily can be addictive like drugs.
- doomjunky 7y ago
  Everything that makes your brain feel good, can be addictive. Not the drugs are addictive, feeling good is.
  - TremendousJudge 7y ago
    Yes, that's what psychological addiction is. Make no mistake though, chemical addiction is very real. Alcohol withdrawals can be fatal
learnstats2 7y ago
My experience of going to high-end casinos, mostly in London, is that: - Many players were plainly cheating in some way, by marking cards and sometimes colluding with the dealer, but the casino didn't appear to mind because they were cheating in an ineffective way and still losing money to the house edge. - (Related: you would just be banned if you won an amount of money that showed you were beating the house edge: see also the Phil Ivey lawsuit) - Some players were gambling large sums of money generally on games with a small house edge, and looked bored like they were there to do a job. I assume from their behaviour they were laundering money.
- matwood 7y ago
  European casinos I have found to be boring compared to American casinos. A craps game in an American casino can get raucous in a good, exciting way. Even more so at a 'cheap' American casino. Contrast this when I was at the Monte Carlo casino in Monaco where they somehow sucked the fun out of craps.
  - learnstats2 7y ago
    Las Vegas-type casinos are definitely selling entertainment. European casinos seem to be selling something else.
arisAlexis 7y ago
I am very surprised that this is something that needs to be said in a hacker news site? Would there be community members here that don't understand basic arithmetic and stats?
dalore 7y ago
This actually taught me that the losing strategies win more often then we thought. I got positive 2 our 4 times for the single 13 choice. And for the strategy to double your bet to cover your loss actually worked for me! Day 1: $10870 Day 2: $12980 Day 3: $10630 Day 4: $8190 Day 5: $7560 Day 6: $9100 Day 7: $9090 Day 8: $10130 Day 9: $12080 Day 10: $12870 Day 11: $12910 Day 12: $14110 Day 13: $15450 Day 14: $15030 Day 15: $15500 Day 16: $14230 Day 17: $13700 Day 18: $11190 Day 19: $12250 Day 20: $14190 Day 21: $16070 Day 22: $12880 Day 23: $12820 Day 24: $11480 Day 25: $12470 Day 26: $14920 Day 27: $9940 Day 28: $10240 Day 29: $9020 Day 30: $10740 Day 31: $12600 Day 32: $14880 Day 33: $17220 Day 34: $15700 Day 35: $17920 Day 36: $18150 Day 37: $14080 Day 38: $16150 Day 39: $18140 Day 40: $19960 Day 41: $20000 -------------
raubtier 7y ago
One strategy not mentioned is to double on win, not on loss. That way you only play with money you've won. Then you set a rule when to stop gambling, for example after 8 wins. This strategy works if there's enough span between min- and max bet. It was a strategy that worked till the 60s when the casinos killed it by closing the min-max gap. I proved it by simulating a million times.
refrigerator 7y ago
For people interested in applying Monte Carlo methods, here are some tools that make it easy: - Causal: https://causal.app https://causal.app (I'm working on this, web app) - Guesstimate: https://getguesstimate.com https://getguesstimate.com (no longer in development but very cool, web app) - Palisade @RISK: https://palisade.com/risk https://palisade.com/risk (Excel plugin) - GoldSim: https://goldsim.com https://goldsim.com (very technical, desktop app)
joyjoyjoy 7y ago
How about the lottery? If the Megamillions jackpot is, lets say 500 MM, your changes are not higher to win it, but more is paid out in that drawing than paid in.
stibba 7y ago
From personal experience: this is absolutely true. There is this csgo gambling scene on the internet. It's basically betting with real money but masked as a value of weapon skins. I have made some idiotic decisions in the past regarding these websites and I still regret it a ton. The problem really is that these websites also allow people of any age to gamble with their weapon skins (aka money), and it's fairly easy to buy new skins with actual money. What's interesting though is that it's easy to observe a ton of gamblers for a long time. And since there is usually also a chat, interacting is also possible. These sites usually have 14 numbers for roulette where 1-7 is red and 8-14 is black, 0 is green which gives 14x your bet. Red and black give you 2x. If you observe enough gamblers long enough (which I did), you see the same pattern over and over and over again. It goes like this: 1. Gambler starts out with a random amount of money (could be high or low). 2. Gambler wins big (usually like 1-3 times on green) 3. Gambler feels lucky and gives out money to 'passive' beggars* in the chat. ( Sometimes I would feel bad for the gamblers and hint them in the chat that they should cash out, no one ever listened ) 4. Gambler continues and might win some more, or lose some but not all. 5. Gambler has been betting for such a long time that he/she is back at where he/she started. ( Beggars keep begging but gambler says he is down so doesn't give out money right now ) 6. Gambler suddenly wins big on green again (or went all in) and feels like a king again. 7. Now Gambler cashes out (by buying a skin) the money with which they started and continues with what his/her leftovers. 8. Gambler loses the leftover money on the website. 9. Gambler deposits the skin that was previously withdrawn again. 10. Gambler loses everything now and the beggars focus on a different big gambler. 11. Gambler usually comes back within a week or month and loses more money. 12. The cycle continues. * People, usually kids, that lost their (usually small amount of) money earlier and our now cheering for some big gamblers so these gamblers might send them money on the website. I personally also lost a (for me) quite big amount of money on these sites over a decent period of time. Later, I was able to sort of stop my addiction and I made a bot which predicted random results (red/black/green) in the chat. It got me like 30 dollars of tips from people that had probably used the bot but the website changed some things so my bot stopped working and I have been too lazy to fix it. Last thing: I also kept some stats of the roulette because I had to know the timing of the roulette so my bot wouldn't predict if it was already rolling. I added an extra feature for myself so I could see how many times red/black and green were rolled and how many times my bot got the predictions right. Obviously this always ended up in a big loss for my bot (in terms of predictions, I did not bet money with my bot) in the long term.
IngoBlechschmid 7y ago
The Python examples are delightful! If you input them at https://www.speicherleck.de/iblech/zufall-im-browser/index.en.html https://www.speicherleck.de/iblech/zufall-im-browser/index.e... (with slight modifications), then you get continuously-updated histograms of the results.
potatote 7y ago
I do not have a lot of background on statistics. Hoping someone here could explain why in Roulette game, although the apparent chances of getting number between 0-18 (inclusive) and 19-36 (inclusive) are the same, we lose money if we keep playing more and more numbers of games.
- obenn 7y ago
  The 0 does not count as a lower number. There at 18 numbers in both the groups 1-18 and 19-36. Each of these give a 18/37 chance of winning, which is lower than 50% and therefore loses in the long run when the money is being doubled on a win.
  - potatote 7y ago
    Ah...I see. I am not much of a gambler either, so this is a very useful piece to know why Roulette gambling, in the long run, turns negative for the gambler. Thank you.
mateo411 7y ago
The American roulette wheel has 38 slots, which include a zero and a double zero. The French roulette wheel has 37 slots. The house edge on the french wheel is half of what it is on the American wheel.

431 points by whereistimbo 7y ago

I have a pet peeve about Monte Carlo methods; although it might be more fairly characterised as a rookie mistake I saw once. MCM are not strong if the tail variance isn't an important feature of what is being modeled. I've seen simulations where the modeler starts with an analytic model - from which they could trivially calculate the mean and variance of a KPI - then used a MCM simulation to find out essentially what the mean and variance of the KPI. So I get that this code is just for illustrative, educational purposes. That is fine. Well done Christof, thanks for the contribution to education. But if anyone is actually using MCM to simulate well known probability distributions they should really put the effort in to learning how to work with well known probability distributions. I feel pretty confident that simulating the Bernoulli in a professional setting is a mistake, because I've seen it done and it was a mistake. For amateurs who aren't confident with math then they can use MCM if they like; but statistics is dangerous and they should be aware that they are using the wrong tool for the job and it is a tell they will get other things wrong. You get a lot of insight from a good analytic model. If there is some interesting tail issue (eg, maybe after 3 heads there is guaranteed to be a tails and your insurance contract pays out on a tails) then sure, use MCM. Great tool if you have the right problem.

Retric 7y ago
While I generally agree with what your saying, I think the MCM can be a great way to validate more accurate approaches. The primary advantage for validation is you can get a reasonably accurate answer with minimal effort.
petermcneeley 7y ago
Really dependents on your philosophy. Would you rather do error propagation using this method http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm or would you rather perturbate your variables and resolve mean and variance. My philosophy drives me towards the computational approach over the analytical mathematical approach.
- deleted 7y ago
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- roenxi 7y ago
  Are you sure there is even a philosophical difference there? I'm still going to use a program to do the heavy lifting of calculating the errors. I'm happy to argue that there is no philosophical difference; if both approaches are feasible and take comparable amount of time to implement then one gets the exact answer to the question at hand and the other is a poor man's shortcut for people who aren't confident in their maths skills. The calculations should be arriving at the same numbers in the end, and implementing a simulation vs. an error propagation tree isn't going to favour the simulation for simple scenarios. MCM is great for when doing usual error propagation is infeasible. It is sloppy when the error propagation could be done with a one or two analytic formula. Simulation isn't appropriate for problems that are easy analytically. For example, in practice, most of the examples in the article are not suitable problems for breaking out MCM (and although the author probably knows that, maybe not everyone on HN does). The Pi one might be a standard application, but even there Pi in particular is not a great choice for a showcase because Pi has some very nice analytic approximations.
  - alexgmcm 7y ago
    I think the value is in checking assumptions - if the analytical approach assumes a normal distribution and then you do MCM and get a vastly different result then it is probably worth checking the assumptions made by the analytical model.
    - roenxi 7y ago
      That is an inappropriate way of checking your assumptions. Assuming a normal is assuming a model (a model is a simplification of a situation by only considering the relative parts). Writing a simulation is also assuming a model, although the process is a lot less formal than traditional statistical regression. If a modeler has assumed two different models of a situation and are getting vastly different results then that is evidence something is wrong, but it is also evidence that the modeler is out of their depth. It is not appropriate to fit two different models and then claim that the differences are delivering insight. The differences are revealing big gaps in the modelers understanding of key influences, rendering both models highly suspect. They should not be creating models, they should be putting more time into understanding the thing they are modeling. There are times when a modeler would have two different models, but they should certainly not be surprised that they give different results. Indeed, they should be assuming two different models because they are going to give completely different results. There will probably be other edge cases, but in my experience they are rarer than people just making mistakes about where MCM is appropriate.
klipt 7y ago
Well yeah MC is usually meant for problems that are otherwise intractable, e.g. sampling complex Bayesian posteriors, or solving stochastic differential equations. Using it for an answer you could easily get analytically isn't very useful outside of education/fun.
arsenide 7y ago
If there is an analytic model, using Monte Carlo methods is extremely useful to validate the theoretical result. If both agree, it is unlikely that there is a mistake in the theoretical result: which is valuable information. For something as straightforward as Bernoulli, where you plug values into a formula and are done, there is no reason to use MCM. However, I am in agreement that in more complicated cases (e.g. a probability distribution is based on some result of one Markov or Markov-like calculation — or possibly multiple), and the theory is slightly or much more complicated then there is a lot of value in Monte Carlo methods.
bathyspheric 7y ago
Can I ask if I understand your use of `tail` in tail variance? Do you mean tail as in extremes of a distribution, or tails, as in losses. I'm very interested in using MC techniques to model extremes of a distribution, like 1-in-1000 year events from a Weibull distribution, but my (naive) algorithms spend a lot of time in the fat belly of the curve rather than out in the tails, but perhaps (probably) I'm holding it wrong. Is there a way to constrain the MC sampling to the tails of a distribution?
- salty_biscuits 7y ago
  You want to look up about importance sampling. There are lots of ways to do it, the two most common are via scaling or translation.
- roenxi 7y ago
  I meant tail as in the extremes of the distribution. My point was more that once you've assumed that your events follow a Weibull distribution then the opportunities for MCM to add more insight are limited if the task at hand is to predict what the distribution and its parameters are. Obviously if you simulate a Weibull distribution you will get results in line with the info box on the Wikipedia page for the Weibull distribution, and you need to effectively assume parameters to simulate. Simulating a distribution just creates a very error-prone calculator the obscures the assumptions. I've seen people do exactly that thinking it was somehow helping - it is surprisingly easy to accidentally simulate a normal distribution, for example, because if you add a whole bunch of uncorrelated random things together (with identical distributions) then the result is normally distributed. You don't need a simulation to tell you that, and it is easier to mull over without simulation. If I were using simulation it is because I think that something fishy happens in extreme events (eg, maybe stock returns all starting to become highly correlated in a liquidity crisis, destroying i.i.d assumptions). Or as other commenters mentioned because the thing being simulated has a distribution that is not analytically tractable. But there has to be some phenomena in there that is more complicated than standard distributions or a steady state Markov model, because they are more productive models when they work. > Is there a way to constrain the MC sampling to the tails of a distribution? You could sample 100 numbers at a time and drop out the middle 95? The question is maybe not well posed.
emarsden 7y ago
I agree. Here's a Python notebook that illustrates this problem on a classical gambling problem, the Saint Petersburg paradox. The notebook explains why stochastic simulation methods such as Monte Carlo are not suitable for situations where a very unlikely event has a significant impact on the output of interest in your simulations. https://risk-engineering.org/notebook/saint-petersburg.html https://risk-engineering.org/notebook/saint-petersburg.html
DarkWiiPlayer 7y ago
I once was in a situation where I had to hammer in a nail with a screwdriver (grabbing it by the front, hitting with the grip). The feeling I had back then is one I all too often experience again in programming. This example isn't so much different; MCM = screw driver, problem = nail and learning proper statistics = driving to the hardware store and buying a hammer. The only aspect where the comparison is somewhat lacking, is that the costs of having a hammer (both aquisition and storage) are minimal compared to in-depth knowledge about statistics.

Proven 7y ago

It’s not a bad idea. It’s this stupid clickbait title which assumes that the value of entertainment and other intangible outcomes doesn’t offset tangible outcomes. If that were the case buying most devices would be a bad idea. Junk submission.

blunte 7y ago

If you want to really know why you shouldn't gamble (for profit... gambling for fun, with discipline, can be satisfying), read this quintessential book: Scarne’s Complete Guide to Gambling What you will probably take away from this book is that the house wins when you win. And the reason they win is that they don't pay actual odds. Take the roulette wheel as a simple example. There are 37 (or 38 in the case of 0 and 00 wheels) slots. If you bet on a single number, they pay 36:1. TFA mentioned doubling down when you lose. That's known as the Martingale Strategy. As banks and real estate lenders discovered in 2007, regardless of your model, there will be some condition where the near-impossible will happen. If you want to use the roulette wheel again as an example, and even if you want to ignore the green 0/00 slots, you have half black and half red. You can simply play one color and double your bet if you lose... until you finally win it all back. The problem there is that while it's true that for millions of spins, about half should land black and half should land red... but in short periods it is possible for there to be 10 or 15 or 20 or more spins of the same color. We can all do exponential growth, so it's easy to see how doubling down will empty your wallet eventually. But just to be sure that strategy won't work, most casinos will set a table limit. That limit will be designed to prevent you from doubling your bet too many times (5-7ish times? depends on the place). Of course, if you discuss in advance with the casino, you may be able to set a personal table limit based on your initial bet. So you can bet 1 million on the first spin in order to set your table limit to 1 million. But that's truly a gamble. There is one element you can control when gambling: that is when you increase or decrease your bets, and ultimately when you stop playing. Yes, you can count cards in blackjack; but that's generally frowned upon (where "frowned" means you will be escorted out and told to never return -- and they are very serious). Even levels of indirection of counting such as employed by the fascinating experience of the MIT crews of yore (https://en.wikipedia.org/wiki/MIT_Blackjack_Team https://en.wikipedia.org/wiki/MIT_Blackjack_Team) have become obvious. So the short of it is, unless you only play a little, bet big, and get lucky for your limited period (and then stop so you don't get banned), you will otherwise lose more than you win. Now for my personal opinion :). Casinos used to be a fun place. Now they are so optimized and commercial that they are like Walmart. Yes you can go, but you'd probably rather not. For modern thrills, we now have crypto exchanges with 50:1 or more leverage.

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55555 7y ago

It's more complicated (worse) than this. That the house has a small edge only tells a small part of the story. When people go to vegas for a weekend, they might have a number in their head they are willing to gamble. If they dont, then that number is their bank account balance. Then they start flipping coins, and often they keep doing this until they go bust. They rarely cash out when up but they always lose when they go bust. They scale the bets as their bankroll grows. Essentially they are flipping coins for infinite time and just waiting to get a bunch of tails in a row, which is inevitable. The behavioral factors are bigger than the house edge. The idea that people are rational is also absurd. Some people are driving to the slots _because_ they are depressed. Or they are there for fun but they lose a bunch of hands in a row and tilt and now they're betting everything on a longshot to win it all back and win some because they dont want to self-identify as a 'loser'. You can only spend so much money on drugs and sex. Gambling is the only vice where you can lose billions. And these days, all you have to do is pull out your phone to place a trade or a bet.

RomanBob 7y ago
This is a common misconception about why casinos win. That 'casinos have infinite bankroll so they cannot lose' isn't actually an argument because casinos have limited bankroll. If they would allow me to play a +EV game I can crush them even if they had infinite bankroll by varying my betsize. The 'random walk' argument only works for fixed bet size.
- eric_h 7y ago
  > If they would allow me to play a +EV game If a business offered a positive EV gambling game, it wouldn't be called a casino and would only last as long as the venture capital lasted.
  - ojbyrne 7y ago
    Actually there are still +EV video poker games in Vegas. http://www.slotsmamma.com/blog/how-do-you-find-full-pay-deuces-wild/ http://www.slotsmamma.com/blog/how-do-you-find-full-pay-deuc... There are a few catches though. Mostly if you play perfectly (which is not simple) the most you can expect to make is less than eight dollars an hour.

wavefunction 7y ago

Blackjack has been a source of success for me though I'm unconventional in my betting strategy which seems to enrage the other players even when I break the dealer consistently.

phkahler 7y ago
Dont they kick you out if you're consistently winning?
- forbiddenvoid 7y ago
  Not necessarily. Casinos will kick you out for a particular set of behaviors. Just winning isn't enough. Playing a minimum bet for a long time, then suddenly increasing to the max near the last half of a shoe is a good way to get a casino to ask you to stop playing blackjack.
- GVIrish 7y ago
  Only if you're winning a lot of money. They don't care that a small fish wins a few hundred dollars every now and then.
listenallyall 7y ago
You've never broken the dealer. Dealer has specific rules in blackjack of when to hit or stand that are completely independent of your cards, betting amount or strategy, emotional attitude, or how good or bad your breath smells.
scarejunba 7y ago
More likely it's just numbers, right? If 1024 people flip coins ten times in a row, it's expected that one of them gets 10 heads. But he's not a genius, right? Of course you should always back yourself. So more power to you if you're winning in this way. At least you get to keep playing :)
- stordoff 7y ago
  Derren Brown had an interesting example of this on UK TV a few years ago. It's nothing new, but showing it this way demonstrates how you can get drawn in: > The System, a Channel 4 special in which Brown shared his "100 percent guaranteed" method for winning on the horses, was first shown on 1 February 2008. > The show was based around the idea that a system could be developed to "guarantee a winner" of horse races. Cameras followed a member of the public, Khadisha, as Brown anonymously sent her correct predictions of five races in a row, before encouraging her to place as much money as she could on the sixth race. > After Brown had placed a bet of £4,000 of Khadisha's money on a horse in the final race, he explained how "The System" worked. He had started by contacting 7,776 people and split them into six groups, giving each group a different horse. As each race had taken place 5⁄6 of the people had lost and were dropped from the system. Brown had a different person backing each horse in each race, and one individual, Khadisha, won five times in a row. https://en.wikipedia.org/wiki/List_of_Derren_Brown_shows#Derren_Brown:_The_System_(2008) https://en.wikipedia.org/wiki/List_of_Derren_Brown_shows#Der...

lanrh1836 7y ago

Blackjack on the strip has become a boiling frog of sorts. Everytime I go back the rules are tweaked a little more in the house’s favor. 3:2 payouts for Blackjack were gone years ago, but more recently no even money for Blackjack if dealer shows an Ace, only split once for two Aces...not worth it at that point.

SmellyGeekBoy 7y ago
In the handful of times I've been into casinos here in the UK I've always just stuck to the Blackjack table (I used to play it with my grandma for buttons when I was a kid). Every time I've walked away with more money than I started with. My biggest profit was over £500. The one and only time I was convinced to give roulette a try I lost everything pretty quickly (I mean the small pot I'd set aside for gambling - I'm not stupid enough to keep withdrawing money and bet more than I can afford). Seems blackjack can be pretty lucrative if you're willing to walk away at the right moment. I seriously doubt it would work as any kind of long term strategy, however. Of course you also have to have the discipline to spend the rest of the night drinking beer and watching your friends get poorer and poorer.
dehrmann 7y ago
Pointing out the obvious: it's more expensive to run a modern resort casino than a Fremont St casino in the 50's, even in inflation-adjusted dollars.

listenallyall 7y ago

This article should be down-voted, the only reason it isn't is due to the clickbaity nature of discussing casino games. It's a terrible initial introduction to Monte Carlo simulations, he doesn't even discuss the possibility of seeing the distributions of the results of the games he proposes, which is essentially the most valuable reason to perform a Monte Carlo simulation.

screaminghawk 7y ago
If you read it instead as an advertisement for easylang.online it's a pretty nice introduction for the language
- listenallyall 7y ago
  ...and if the headline was "Learn to Program in easylang.online" it never would have sniffed the front page of HN
  - chkas 7y ago
    https://news.ycombinator.com/item?id=19299760 https://news.ycombinator.com/item?id=19299760
    - listenallyall 7y ago
      another clickbaity headline, confirming my point
  - chkas 7y ago
    I do not understand your criticism. The main content is Monte Carlo simulation at Roulette and that you lose in roulette games. The headline says just that. "easylang.online" is in this case just a means to transport this content. It would be much harder to do that in JavaScript and the examples would also be less comprehensible.

jaimex2 7y ago

If you go to a casino play poker with other humans. Nothing else is worth your time.

soVeryTired 7y ago
Even poker in a casino probably isn't worth it unless your opponents are obviously drunk or bad players. After the rake and the dealer tip, there's a good chance your edge is zero or negative.
- AlexandrB 7y ago
  I read parent as saying that playing poker with others is the most entertaining way to spend your time at the casino, since he didn't mention money.

oldandtired 7y ago

When I was 8, I spent 6 months in hospital and that was over 50 years ago. Not much to do, so my parents made sure I had lots of puzzle books of all kinds as well as story books. One of those books had a chapter on gambing, which I found interesting, it was written for children. It made the claim that as long as the "bank" had a significant value greater than your own (by at least 10 times), you could not win against them even if the odds were 50:50. As the decades have gone by, I followed this up with other research and basically, gambling is a mugs games if you are not the bank. Yes, you can at times win and come out ahead. But on the whole, you will lose. My father's advice has always been: "Son, treat it as entertaiment and spend only what you can afford to lose like every other form of entertainment. If you think you can win, you be the fool and will lose more than you can afford." I have also found that gambling institutions are so depressing a venue to be in.

kai101 7y ago

I have similar simulation 10 years back written in C, no fancy description but understand how casino works. Similar conclusion, once u win enough, you leave; once you lose enough, you leave. Never bring your whole bank account to a casino, or the figures will be move closer to 0.

WalterBright 7y ago

Investing: Return on Investment > 0 Gambling: Return on Investment < 0 For the casinos, it's an investment, for the customers, it's gambling.

denormalfloat 7y ago
Perhaps we could combine the two? Make a slot machine that pays out in penny-stocks, rather than chips.
- WalterBright 7y ago
  We call them "online brokers" :-)

blt 7y ago

The subtitle made me expect something about a failure mode of MC methods in some popular application...

slewis 7y ago

Great article showing how easy it is to experiment with probability using Monte Carlo methods. You don’t need any fancy libraries or deep mathematical knowledge. Of course you should always try to have a deeper understanding if you want to make serious conclusions. But I felt this article got the concept across really concisely! Nice work.

TazeTSchnitzel 7y ago

The language they're using seems to pretty much be BASIC with slightly different syntax, it even lacks user-defined parameters for functions just like BASIC does.

chkas 7y ago
There are user defined functions with parameters and locals.
- TazeTSchnitzel 7y ago
  Why have subroutines then?
  - deleted 7y ago
    [deleted]
  - chkas 7y ago
    Subroutines have a global namespace - this is easier to understand. Functions with parameters and local variables allow longer and recursive programs.

arsenide 7y ago

I work on Monte Carlo simulations professionally for casino slot games. I wish that more depth was presented here: what percentage of the time do you get favorable vs unfavorable outcomes with each strategy? For further depth, use different types of players (with different exiting conditions). Perhaps I should write such a blog post at some time..

paulkon 7y ago
Please do, I'd love to read more about this!
dang 7y ago
That post would probably be of interest to a lot of HN readers. If you want, we can look over a draft if you send it to hn@ycombinator.com. Sometimes we can make suggestions that improve an article's appeal to this crowd. Same offer goes for anyone else who's putting a lot of work into a post they hope will interest HN.
- arsenide 7y ago
  Thanks dang. I may very well take you up on this offer.

TBurette 7y ago

A while ago I wrote a similar interactive article to prove that the martingale betting technique at the roulette doesn't work : [1]. The martingale is when you bet 1, double the bet each time you lose, start again at 1 when you win. The aim was to create a single page anybody could link to that proves without a doubt the abysmal odds of making money off the roulette with the martingale technique. Instead of pre-written probabilities, charts and 'obscure complicated math' that people could easily dismiss. I wanted to give people the ability to run simulations of playing at the casino in the browser. The idea being that people would end up building the probabilities/charts themselves through simulations. It is running Monte Carlo simulations inside the webpage and outputs the result as charts dynamically using js and D3. What it does is it repeatedly simulates going to a casino with a certain starting amount of money and an objective of how much you want to win. It then plays the roulette using the martingale technique until you got your target winnings or you lost your money. Unfortunately I don't think I wrote the article really well and the 'generate yourself the charts proving it doesn't work' doesn't come across really well. I should have put a 'run' button instead of needing a page refresh for a start. [1] http://thomasburette.com/martingale/ http://thomasburette.com/martingale/

eric_h 7y ago
All of that is completely invalidated by that one time I hit 13 on the roulette table at two different casinos and quit gambling up $1500 ;)
- tapland 7y ago
  Just a few varied anecdotes from working as a dealer and croupier for a few years: I once saw 13 be hit 4 times in a row (and once more within my 45 min rotation at the nearby table). Don't think I've personally seen any other 4 number streaks. A lof of people won a lot of money during the two last ones. I've only played a few slot games online and visited a real casino as a guest once, where I bought chips for $150 and left with $5400. The goal was losing it all and at the end I was putting $1500 on the table at a time, and dipped below $500 just a few minutes before making the $5400 and leaving. One of the best nights I had while working was a regular from the poker room coming to my Black Jack table trying to win back the $15k he was down. Had the 'chef' (senior position at the casino floor, poker equivalent would be 'brush') there talking to him since he wasn't doing well. He managed to win it back which was a great relief.

deleted 7y ago

[deleted]

spaceflunky 7y ago

It's (relatively) easy to show the math on why casino games are impossible to win, but what about sports betting? Does the house always have the advantage? Perhaps it's slightly better for the gamer? FWIW I was looking a betting website recently [0] and they were offering DOUBLE your initial deposit for signing-up, up to $1000. So to reiterate, they are willing to give up to $1000 for FREE just for creating an account. All I can imagine is that they would only do this if the numbers are vastly not in your favor. [0] I'm not going to post the name of said website.

OscarCunningham 7y ago
>Does the house always have the advantage? The mathematics doesn't really matter because if you find a systematic way of winning then they just ban you.
- SmellyGeekBoy 7y ago
  So... yes?
listenallyall 7y ago
>> just for creating an account No, for creating an account, funding it AND making a significant amount of wagers. The details vary by site, but there are always restrictions in the fine print -- either you only "earn" the bonus a few percent at a time, or you aren't allowed to withdraw until you've made enough bets, or some similar restriction. I'd guess that some or all of the "free" $1000 is inaccessible until you've made a 10x rollover, or $10,000 in wagers.
Gustomaximus 7y ago
You have to bet the bonus money at least once. I did this. Bet the bonus on some super low odds trots race to place that was as good odds as anything to get my money back and then bet the other half on a 36:1 long shot that Bernie would win the nomination. I got my money back with the low odds Trotter, otherwise I would have bet the balance on another low odds event. Obviously didn't win the long shot. Not sure why I did it as I don't normally gamble but generally curious and though it was a fun way to risk a small amount to potentially win a "free" holiday.

nurettin 7y ago

I made an effort to download previous draws form my local lotto website [1] And parsed them and applied a montecarlo method to see: 1. If I could find an optimal way of playing the game to maximize my profits. 2. If I could find a bias towards certain numbers. The result was: 1. I found a way with 1/3 chance of winning big and paying back all expenses you played for the past 20 years. It is a significant investment and everyone will think you are crazy, but you have a very high chance of early retirement. 2. I found no obvious difference between the frequency of numbers. The idea is to spread your betting numbers as far apart as possible in order to follow the normal distribution. If you reduce the overall gap between your numbers, your chances of winning is significantly reduced. [1] http://www.millipiyango.gov.tr/sonuclar/_cs_superloto.php http://www.millipiyango.gov.tr/sonuclar/_cs_superloto.php

kaoD 7y ago
If you found no difference on number frequency, it's the uniform distribution, not normal (a.k.a. gaussian) distribution. AFAIK uniform distribution means any number is equally likely to be drawn, regardless of distance to your other picks. Just to check if I got that right: does that mean that playing 333333 and 666666 in a 6 digits lottery had a higher chance of winning that picking 333333 and 333334? If so, why? And, since playing more numbers will reduce the overall gap. Does that mean the optimal strategy is playing a single number? Did you test your method via simulation? I can't see how it works with my little knowledge of statistics. Can someone chime in?
- nurettin 7y ago
  Yes, I meant uniform distribution. My method was to give it a higher chance to have a lower gap between the numbers to see if it would make a difference within a montecarlo simulation and it did. So if you have say 16 slots and you need to choose four numbers, according to my simulation, highest likelyhood of winning is to spread out your numbers like [3 6 9 12] or [4 7 10 13] and lowest likelyhood of winning is to spread like [1 2 3 4] [2 3 4 5] all the time. Not exactly sure why.
  - 7y ago

trymas 7y ago

I am even more impressed by the `easylang`[0] itself, which was used to create the demo. [0] https://easylang.online/ide/ https://easylang.online/ide/

paulcarroty 7y ago

It's absolutely obviously for people who know the basics of Probability theory. Not sure if modern high schools covers it now. But it's only a part of the problem. Second part - money and gaming easily can be addictive like drugs.

doomjunky 7y ago
Everything that makes your brain feel good, can be addictive. Not the drugs are addictive, feeling good is.
- TremendousJudge 7y ago
  Yes, that's what psychological addiction is. Make no mistake though, chemical addiction is very real. Alcohol withdrawals can be fatal

learnstats2 7y ago

My experience of going to high-end casinos, mostly in London, is that: - Many players were plainly cheating in some way, by marking cards and sometimes colluding with the dealer, but the casino didn't appear to mind because they were cheating in an ineffective way and still losing money to the house edge. - (Related: you would just be banned if you won an amount of money that showed you were beating the house edge: see also the Phil Ivey lawsuit) - Some players were gambling large sums of money generally on games with a small house edge, and looked bored like they were there to do a job. I assume from their behaviour they were laundering money.

matwood 7y ago
European casinos I have found to be boring compared to American casinos. A craps game in an American casino can get raucous in a good, exciting way. Even more so at a 'cheap' American casino. Contrast this when I was at the Monte Carlo casino in Monaco where they somehow sucked the fun out of craps.
- learnstats2 7y ago
  Las Vegas-type casinos are definitely selling entertainment. European casinos seem to be selling something else.

arisAlexis 7y ago

I am very surprised that this is something that needs to be said in a hacker news site? Would there be community members here that don't understand basic arithmetic and stats?

dalore 7y ago

This actually taught me that the losing strategies win more often then we thought. I got positive 2 our 4 times for the single 13 choice. And for the strategy to double your bet to cover your loss actually worked for me! Day 1: $10870 Day 2: $12980 Day 3: $10630 Day 4: $8190 Day 5: $7560 Day 6: $9100 Day 7: $9090 Day 8: $10130 Day 9: $12080 Day 10: $12870 Day 11: $12910 Day 12: $14110 Day 13: $15450 Day 14: $15030 Day 15: $15500 Day 16: $14230 Day 17: $13700 Day 18: $11190 Day 19: $12250 Day 20: $14190 Day 21: $16070 Day 22: $12880 Day 23: $12820 Day 24: $11480 Day 25: $12470 Day 26: $14920 Day 27: $9940 Day 28: $10240 Day 29: $9020 Day 30: $10740 Day 31: $12600 Day 32: $14880 Day 33: $17220 Day 34: $15700 Day 35: $17920 Day 36: $18150 Day 37: $14080 Day 38: $16150 Day 39: $18140 Day 40: $19960 Day 41: $20000 -------------

raubtier 7y ago

One strategy not mentioned is to double on win, not on loss. That way you only play with money you've won. Then you set a rule when to stop gambling, for example after 8 wins. This strategy works if there's enough span between min- and max bet. It was a strategy that worked till the 60s when the casinos killed it by closing the min-max gap. I proved it by simulating a million times.

refrigerator 7y ago

For people interested in applying Monte Carlo methods, here are some tools that make it easy: - Causal: https://causal.app https://causal.app (I'm working on this, web app) - Guesstimate: https://getguesstimate.com https://getguesstimate.com (no longer in development but very cool, web app) - Palisade @RISK: https://palisade.com/risk https://palisade.com/risk (Excel plugin) - GoldSim: https://goldsim.com https://goldsim.com (very technical, desktop app)

joyjoyjoy 7y ago

How about the lottery? If the Megamillions jackpot is, lets say 500 MM, your changes are not higher to win it, but more is paid out in that drawing than paid in.

stibba 7y ago

From personal experience: this is absolutely true. There is this csgo gambling scene on the internet. It's basically betting with real money but masked as a value of weapon skins. I have made some idiotic decisions in the past regarding these websites and I still regret it a ton. The problem really is that these websites also allow people of any age to gamble with their weapon skins (aka money), and it's fairly easy to buy new skins with actual money. What's interesting though is that it's easy to observe a ton of gamblers for a long time. And since there is usually also a chat, interacting is also possible. These sites usually have 14 numbers for roulette where 1-7 is red and 8-14 is black, 0 is green which gives 14x your bet. Red and black give you 2x. If you observe enough gamblers long enough (which I did), you see the same pattern over and over and over again. It goes like this: 1. Gambler starts out with a random amount of money (could be high or low). 2. Gambler wins big (usually like 1-3 times on green) 3. Gambler feels lucky and gives out money to 'passive' beggars* in the chat. ( Sometimes I would feel bad for the gamblers and hint them in the chat that they should cash out, no one ever listened ) 4. Gambler continues and might win some more, or lose some but not all. 5. Gambler has been betting for such a long time that he/she is back at where he/she started. ( Beggars keep begging but gambler says he is down so doesn't give out money right now ) 6. Gambler suddenly wins big on green again (or went all in) and feels like a king again. 7. Now Gambler cashes out (by buying a skin) the money with which they started and continues with what his/her leftovers. 8. Gambler loses the leftover money on the website. 9. Gambler deposits the skin that was previously withdrawn again. 10. Gambler loses everything now and the beggars focus on a different big gambler. 11. Gambler usually comes back within a week or month and loses more money. 12. The cycle continues. * People, usually kids, that lost their (usually small amount of) money earlier and our now cheering for some big gamblers so these gamblers might send them money on the website. I personally also lost a (for me) quite big amount of money on these sites over a decent period of time. Later, I was able to sort of stop my addiction and I made a bot which predicted random results (red/black/green) in the chat. It got me like 30 dollars of tips from people that had probably used the bot but the website changed some things so my bot stopped working and I have been too lazy to fix it. Last thing: I also kept some stats of the roulette because I had to know the timing of the roulette so my bot wouldn't predict if it was already rolling. I added an extra feature for myself so I could see how many times red/black and green were rolled and how many times my bot got the predictions right. Obviously this always ended up in a big loss for my bot (in terms of predictions, I did not bet money with my bot) in the long term.

IngoBlechschmid 7y ago

The Python examples are delightful! If you input them at https://www.speicherleck.de/iblech/zufall-im-browser/index.en.html https://www.speicherleck.de/iblech/zufall-im-browser/index.e... (with slight modifications), then you get continuously-updated histograms of the results.

potatote 7y ago

I do not have a lot of background on statistics. Hoping someone here could explain why in Roulette game, although the apparent chances of getting number between 0-18 (inclusive) and 19-36 (inclusive) are the same, we lose money if we keep playing more and more numbers of games.

obenn 7y ago
The 0 does not count as a lower number. There at 18 numbers in both the groups 1-18 and 19-36. Each of these give a 18/37 chance of winning, which is lower than 50% and therefore loses in the long run when the money is being doubled on a win.
- potatote 7y ago
  Ah...I see. I am not much of a gambler either, so this is a very useful piece to know why Roulette gambling, in the long run, turns negative for the gambler. Thank you.

mateo411 7y ago

The American roulette wheel has 38 slots, which include a zero and a double zero. The French roulette wheel has 37 slots. The house edge on the french wheel is half of what it is on the American wheel.