A Gambler Who Beat Roulette
bloomberg.com
bloomberg.com
I haven't finished the whole article yet but this part stood out to me. The casino had no real evidence they were cheating, just a vague suspicion that since they were winning at roulette the only possible explanation was that they were using some electronic device to cheat. With that vague suspicion they had the gamblers arrested and all of their electronic devices searched. After nothing was found their winnings were seized and payouts from the casino frozen. Again, at this point there is no evidence that they cheated.
https://en.wikipedia.org/wiki/Conspiracies_against_the_laity
From "Who is buying Powerball and Mega Millions tickets?" [1]
> The survey showed the most frequent lottery players earn between $36,000 and $89,999. About 56% of that group bought tickets in the last year. Fewer of those making under $36,000 bought tickets, only 40%. About 53% who make above $90,000 bought a ticket.
[1] https://money.cnn.com/2018/01/06/news/powerball-mega-million...
>But other studies have shown that when lower income players do buy tickets, they spend far more money on lottery tickets than wealthier players. A study published in the Journal of Gambling Studies found that those in the bottom fifth of income spent the most on lottery tickets, and more than twice as much as the richest lottery players - $433 a year vs. $193 a year.
Most everyone buys a Powerball ticket when it hits a cool billion or whatever it is; but that's not the vast majority of lottery enjoyers.
> The poorer lottery players also buy far more of the lower prize games, such as scratch-off instant games which account for the majority of lottery sales.
> The richer buyers are buying the multi-state jackpot games such as Powerball and Mega Millions. And the wealthier players are likely to be drawn in by the big jackpot prizes like those being offered right now by both Powerball and Mega Millions.
The lotteries are not exclusively taxing the poorest members of society, which is what you originally claimed.
I am one. Although, I only enter once per drawing, and only when the pot is large enough that I can pretend it's +EV.
There's a lot of games where I can't even pretend it's even close to reasonable odds, and I don't get much entertainment, so I'll leave those alone.
I do think casinos tend to be regulated to pay back a way higher % than lotteries though.
https://en.wikipedia.org/wiki/Jack_Whittaker_%28lottery_winn...
There really is no reason to legalize gambling casinos. It is just an inefficient way of moving money around. It doesn’t actually create new value for society as a whole. (Friendly poker games amongst friends and family with small pots are probably fine).
When you make gambling illegal you just drive it underground and fund organized crime, with all the additional crime and corruption that brings with it.
The arguments against making gambling illegal are similar to many of the arguments against making drugs and prostitution illegal, such as consenting adults should be free to do what they want as long as it doesn't harm anyone else.
So long minimum wage and workplace safety laws, welcome back indentured servitude.
In Korea, by law you have to prove you're a foreigner. In the Bahamas it is legal for the locals to bet, but the casinos kick them out. They've had enough experiences of a guy coming in on payday, losing his money, then his wife coming in the next day with a baseball bat to destroy the machine that took the money. Don't want any more.
That's almost certainly not the reason. They want the revenue but not the societal ills from gamblers.
Why should the government outlaw my ability to give my money away however I want to? If I want to go put all my money on black because it's fun to me, why should that be illegal?
There might be a crime involved when someone wins at roulette, there might be negligence by the casino in maintaining their games. There might be luck. Some people do win hundreds of millions of dollars on a $2 lottery ticket.
The police where I live do not follow up investigating store robberies, they do not follow up on people who pass bad checks, and they definitely do not follow up on eat and runs. More often than not they will answer the phone when someone calls 911, but not much more often than not.
So yes, the idea that the police seem to be at the beck and call of the casinos to detain people with no hard evidence that any crime at all has actually been committed is concerning. At least let us know what phone number they are calling that the police actually pay attention to.
Exactly. And so, the police investigated. When they determined there wasn't a crime (or at least had no proof or evidence of one), they released the accused and required the casino to pay them their full winnings.
Your "exactly" was wrong, because you're using a different meaning of "might be" than the person who wrote the quote, and given the childish "you said it" reply it seems like you did that on purpose.
Better than equal. Most Blackjack is -0.6% EV playing basic strategy, but with counting, each true count is an extra ~0.5% of EV, leading to big betting on high count hands with EV of 1-3%. Of course, that's why casinos kick out counters. They're literally "too good" at the game, and they don't want that.
6 decks, as opposed to 1 or 2, does make counting less accurate. But ultimately everything I said previously applies. Those stats are based on the current common game of 3-2 Blackjack, H17, 6-deck shoe, no continuous shuffle, and double after split.
Counting works but the way to profit from it is easily detected. You have to bet big when the count is favorable, and a casino will see that and stop you.
The MIT Blackjack Team beat this, with the strategy to have one player at the table who would bet small while counting cards, incurring the expected slight losses to the house edge, and signal a teammate to jump in and bet big (like $5k per hand) when the count was favorable. Casinos now know to stop this - if you walk up to a table and want to bet big, they will require you to wait for the next reshuffle (or just reshuffle immediately.)
Of course it was! If they had lost using the same method there would have been no issue.
> It’s that these folks won in a statistically hugely unlikely way, and that alone is pretty damning evidence that something is off.
That's the casino's problem though, not law enforcement. Statistically unlikely equates 'we haven't seen this before' and that should not be enough reason to arrest people. The police should not be in the business of protecting the revenue streams of gambling installation operators. There should be some symmetry here, if the casino is a-ok with making money on gamblers then they should take their lumps when the situation is - temporarily - reversed. LE has no business here, tough luck they should have run a business where the flow is one way by design instead of one with a pretend two way flow.
> The catch 22 is the accused cannot defend themselves without divulging their secrets.
Which is precisely why the police has no business doing this. The burden of proof with respect to cheating is on the casino, and until they have something solid nobody should be arrested. That's the police acting unilaterally on behalf of one party. A more balanced response would have been to help the players cash their checks, after all the casino did not object to the reverse when the funds were deposited. It's fraud by the casino until proven otherwise.
If I gamble once, and only once, with a lot of money at very high odds, I might get very lucky and win a fortune.
But despite small odds of a massive pay out, the odds would have been very low, but not infinitesimal.
Whereas, if I consistently win much more than I lose over many bets, across seversl visits, and a group of people can do this, the odds of that happening rapidly become virtually zero.
Or in mathematical or scientific terms, confidence that pure chance is being broken far, far, far exceeds a 6-sigma threshold. It’s proven.
But legal proofs, for making judicial decisions of guilt or culpability, usually require an explanation of how it was done.
Ok that's pretty crazy, let's lower it a notch, throw out the sigmas, just talk about 1-in-hundreds-of-millions odds.
The article doesn't actually list the odds of their winning streak, but I'd wager a casino is gonna be suspicious well before the "one in a hundred million" level of streak.
Powerball can get there, e.g. 1-in-292M per here https://www.theguardian.com/us-news/2022/nov/08/powerball-dr...
So how many bets across how many visits does it actually take for it to be "proven"? Like, people can win powerball, someone may have had that 1-in-300-million casino run too. If they're independent events, you expect it to happen randomly eventually! Some poor lucky bastard will probably face a lot of questions one day.
I dunno, I guess if you want to win a fortune gambling, do it all in one bet, since getting lucky all at once vs getting less-lucky-but-for-a-longer-time is gonna attract a lot of scrutiny. ;)
(I kinda suspect, though, that a lot of people who were down the path of that 1-in-300M luck playing roulette would stop while they're ahead at some point. If you hit on 00 in roulette three times in a row do you go for a fourth?)
20 flips, 1 out of 1 million.
30 flips, 1 out of a billion.
40 flips, 1 out of a trillion.
With roulette, and overall gain (not a perfect score), say a ratio of 2 wins out of 3 bets, it takes more bets.
But in this case we are talking about many roulette games, with a recognized group of people, often playing in tandem. at multiple casinos.
The odds of their record of successes, as documented by the casinos, could be 1 out of billions or trillions easily. Maybe even more.
It's the pure math side I think is fun, because I find examples of people getting tricked by confidence intervals into developing blindspots to the randomness, and substituting "proof" for "very unlikely" fascinating. Comes from working in a lot of companies with ... sloppy ... methodology for their AB tests.
If you go to a casino and win 20 straight coin flips [or the equivalent in roulette or craps] don't you think they'd be pretty damn sure you cheated somehow?
There may be an investigation, but I'd be surprised if anyone is arrested before hard evidence of rigging a game is found.
In most jurisdictions where gambling is legal, it is carefully regulated and those regulations include not cheating.
Which does make it a law enforcement issue.
In places where cheating is not a law enforcement issue, it is a mafia-enforcement issue, which is even worse.
What about in something like betting on a boxing match and having the fighter throw the fight? Is that the casino's problem too?
If you're ok with someone cheating then it all makes complete sense what you're saying. If you're not then someone has to investigate. Do you really want the casino being law enforcement for anyone they find suspicious? I'm not on the casino's side at all but there's a big grey area here.
As far as protecting casino revenue, casinos have a complicated arrangement with governments but in most jurisdictions the reason they are legal is to pay hefty taxes on gaming revenue (also normal income tax, separately). Thus the police are, when investigating similar claims, protecting government revenue. The casino is just the conduit to generating that revenue.
You have to win small. As another poster put it below, the role of the player is to lose.
Anecdotally, I used to travel to a coastal city 650km away every two weeks for around 5 years. My Saturday afternoons during this time were usually free and I was bored. For two months I spent those Saturday afternoons (til around midnight) sitting in the casino noting the frequency of each pie slice of the wheel on as many different roulette tables that I could simultaneously view (between 6 and 8 at a time).
Divide the wheel into 5 pie slices (one will be a different size from the rest) and make 5 columns on a small page - one for each pie slice. Each time that slice "wins" (no matter what the number is) simply make a checkmark in that column. Over time this forms a histogram. If any one of those columns is an outlier, then that wheel is biased.
I found one biased wheel (casino had maybe 14 tables in total?), which remained unfixed and remained biased for the next 13 months or so, and I repeatedly just placed small bets on all numbers in that slice that was biased.
I made a respectable amount of money (about 40k ZAR) over 13 months.
I have no illusions that had I been placing maximum bets on each spin, I'd have been escorted out of the casino after the first visit.
Yes, the Police exist as the private military of the rich.
Their job is literally to protect the assets of the rich, and that's exactly what they will do whenever you "get one over" the rich.
The same is also true with sports betting in the UK. Because sportsbooks are so bad at managing risk in the UK, they will shut down winning accounts (unlike in Asia where the huge books actually winning accounts to improve their line and make more money) and use the whole range of AML/consumer protection rules to tilt the odds in their favour.
The reality is that casinos can't beat that minority of customers that are smarter than them...so they cheat.
This is true but it should have a big footnote. Disregarding Asian bookmakers that like to void winning bets from time to time for no apparent reason, Pinnacle, which is the book you’re referring to, lets winning players bet at such low limits that making money off them is an excruciating process.
You have to understand that the limit is a function of the volume they take after you set their line. That is how the economy works. Your profit is paid out of their profit from squares after the line is set. So if they aren't doing volume after the line moves, then they are just going to leave the limit.
I think it should be within the casinos rights to decline to continue to take bets when something is happening that they don't understand and is far outside of their expectations of statistical probability.
To quote Buster Scruggs: "Can't no one compel another man to engage in recreation."
I do think they should be obligated to honor the bets they actually made, though.
It's like those Minecraft speedruns; you can't necessarily prove it's false (at that point), but if there's a 1/10,000,000,000 chance that an outcome is achieved legitimately, what would you expect them to do?
What they said was “You are done for the night at our casinos. You are welcome to return tomorrow.”
They were very nice about it and I had no issue with it at all. It’s their house.
The net effect is that if you start to win meaningful amounts on a consistent basis, 'fairly' or not, the casino will simply ban you from playing. Players misunderstand the relationship between players and the house. Casinos however are under no illusions. The role of players, in the aggregate and over time, is only to lose. If you don't fulfill your role they won't let you play. Beating the house in the long-run isn't possible because casinos have no interest in losing.
Hypothetically, if you were somehow able to consistently win meaningful amounts at casino gambling games through some kind of fictional magic or psychic ability which could not be countered, the only way you'd be able to monetize that ability would be to either: 1) Win such small amounts you remain unnoticed (probably less than a couple thousand dollars a week), or 2) Continually travel the world seeking out new casinos that haven't yet banned you. As the article shows, casinos work together and word spreads quickly so neither option is very appealing. If you had such magical powers it would be dumb to monetize playing gambling games against casinos. Much better to either play games against other players or to pursue large open markets like stocks and commodities. Even then you'd have to put up with constant investigations by the SEC suspecting insider trading. You'd also need to meticulously pay all taxes and comply with every regulation due to all the attention you'd attract. It would probably be a good idea to create your own 'explanation' by operating as a hedge fund, investing in creating a large research department and hire a bunch of quants to devise proprietary algorithms. Even then, it would be smart to never "win" too much more than the best legit hedge funds. If you're too much of an outlier for too long, some people will take increasingly extreme measures to determine your "secret."
I don't know why they made so many small bets. They should have come in, made like 3 huge bets, and walked out.
Yes, they placed these "neighbors" bets, but it sounds as if they had several of them in motion on each spin. If they're covering an average of three clusters per spin, our random odds become (15/37)^13, which is approximately 1:125,000. Still plenty of grounds for suspicion, but if the casino is open for action all year and hosting 1000 or more roulette betting episodes a night (i.e. 13 spins/player), something this improbable SHOULD happen several times a year.
I also wouldn't trust that "13 in a row" reporting from something like this. That's likely exaggerated or misreported or misremembered from an unreliable witness for the sake of the splashy story.
Perhaps you should keep reading before posting:
Was there any legal way to stop Tosa and the others from collecting their winnings? he asked. No, the officer said. There was no other option. The Ritz would have to pay up
Let's face it, lots of people get arrested because of suspicious activity, and that totally sucks and has real consequences, but this situation is not especially different than any other, because of influence from the casino. If a person is suspected of robbing a store, they'd likely be detained as well.
If you like the article, the book is also great.
Or it is so the casino can argue roulette is a game of skill instead of chance. But this would be paradoxical.
Slow things down, require all bets to be placed before the croupier spins the wheel and throws the ball, and you'll have taken away some of the mystique and the adrenaline of betting on this bouncing, glittering thing that's happening right now in front of your eyes, and some of the casual gamblers will get bored and walk off.
> There’s one surefire way casinos could stop prediction: calling “no more bets” before the ball is in motion. But they won’t. That would cut into profits by limiting the amount of play and deterring casual gamblers.
With casinos it's the opposite. Their customers regularly lose their shirts. Maybe the games aren't rigged, maybe they are, as someone who regularly loses (as most gamblers do), they might as well be rigged and I would not be surprised if there was regulatory capture and the consumer would have no way to know.
And, besides, if it ever got out that a casino was doing that, it would basically fold up overnight.
> There’s one surefire way casinos could stop prediction: calling “no more bets” before the ball is in motion. But they won’t. That would cut into profits by limiting the amount of play and deterring casual gamblers. Instead, the industry seems willing to pay a toll to a select few who know the secret, while trying to design out the flaws that make the game vulnerable.
For more, see: https://boingboing.net/2017/07/27/wearable-computing.html
[1] If the name doesn't ring a bell, he discovered that Boolean logic could be used to analyze and design electric switching circuits -- as a Master's thesis. He went on to a storied career at Bell Labs where he invented Information Theory.
He mostly switched at some point to betting on sports. He arbitraged the odds that the bookies used compared to odds that were apparently more accurate, probabilistically.
I asked him how he could possibly have a better sense of the probabilities than the bookies, whose job it is to get this right. He replied that the bookies don't set the odds based on probabilities, but rather just so that they have an equal amount of money on both possible outcomes, and therefore they would always make money no matter what.
So the odds that the bookies used were often not good measures of the actually probabilities, but rather often more a measure of public sentiment. And he could take advantage of this difference.
> Though roulette was considered by many to be purely a game of chance, Jarecki was convinced that it could be “beat.”
> He noticed that at the end of each night, casinos would replace cards and dice with fresh sets — but the expensive roulette wheels went untouched and often stayed in service for decades before being replaced.
> Like any other machine, these wheels acquired wear and tear. Jarecki began to suspect that tiny defects — chips, dents, scratches, unlevel surfaces — might cause certain wheels to land on certain numbers more frequently than randomocity prescribed.
Similar to Tosa, people questioned Ungar's poker prowess as to whether he was cheating or not (it's a pretty deep conspiracy rabbit hole that you can go down if you'd like). People wondered if he had some secret method for reading his opponents — like whether his blue glasses were letting him read marked cards, but it turned out to be like Tosa, he was a product of pretty deliberate and intense practice.
In both cases, it's a weird example of humans being exceptional at pattern matching in ways you almost can't imagine after deliberate practice.
Ungar is most famous for his WSOP win calling down with a ten high to win.
I think a fascinating aspect to all of this is the other idea in any edge based game where nearly all great players will start on a winning streak and how incredibly difficult it is to discern whether you are lucky or good (there's a small chapter in "The Signal and the Noise" about that specifically with poker players).
1. if they spot you singularly winning way too hard, they will cut you off 2. if you can distribute the wins wide enough between enough individuals you might get away with it
There ARE exploits and you can get away with them. People find them pretty regularly and the ones who get away with it are really organized.
My favorites over the past years: Weak PRNG in the Buffalo slot machines [1], and people cleaning that, and the guy who figured out an exploit in the game king brand video poker machines [2] - One got away with it and the other didn't, it's worth being aware of how.
[1] https://www.wired.com/2017/02/russians-engineer-brilliant-sl...
They're big enough to cheat you using violence or even the judicial system, so if you do this you're strategizing against that as much as you are strategizing to win the actual game.
> Bliev, Gudalov, and Larenov, all of whom are Russian citizens, eventually accepted plea bargains and were each sentenced to two years in federal prison, to be followed by deportation.
I don't quite follow here. What is fraudulent/illegal? Surely if you offer a pattern based game for money it should be legal to analyze and learn the pattern?
Card counting is a perfect example - you absolutely can count cards in the right type of blackjack, and you absolutely can get an edge and casinos absolutely know this and can ban you no questions asked if you are tagged as an advantage gambler.
Always rubs me a bit the wrong way actually, given that by its very nature the casino is advantage gambling 99% of the time whether you know it or not...
I'm not a statistician though and analyzing historic draws is beyond my ability.
if you know wheel rpm plus an estimate of the speed the croupier throws the ball, you can get a pretty good physics sim of where the ball lands.
Card counting is well known and casinos encourage it, because MOST people can't do it well enough, and they shuffle often enough.
A family went to casinos around Europe and observed the roulette wheels, keeping extensive records on where the ball landed. They were not covert about it. They'd just openly write down the results.
You might think casinos would not allow that, but actually they love people who do things like that. A person taking notes is a person who thinks they can invent a system to beat the casino, and those people often lose a lot of money before giving up.
The family took all that data and analyzed it to find wheels that had slight consistent biases that were big enough that bets based on them would come out ahead long term. They then went around making those bets and won long term.
The family members had spent so much time looking at wheels that they could recognize individual wheels by things like scratches and discolorations and other ordinary visible wear and tear, so even if a casino moved a wheel the family would recognize it and know which bets to place.
There are a couple other "Breaking Vegas" episodes I remember as standing out.
"Ultimate Cheat" [2] is about another way to win at roulette, but this one involved a team cheating on the bets using a twist on an old cheating method.
There's an old way to cheat on bets where you place small bets that consist of a stack of minimal value chips. You adjust the stack so that the croupier cannot actually see the bottom chip. You and your teammates all do this.
If one the bets wins you try to use sleight of hand to replace the stack with a stack that consists of minimal value chips except for a high value bottom chip, still arranged so the bottom chip is not visible to the croupier. Your teammates can help by trying to distract the croupier so your sleight of hand won't be spotted.
When the croupier goes to your winning bet you point out the amount is wrong and point out the high value chip in the stack that the croupier missed.
Casinos are on to that, and if they suspect at all that you are doing it before paying out they will go to the security tapes to make sure no one tried any sleight of hand on the winning stack.
The team in this episode realized they could work this the other way. Instead of trying to retroactively raise the value of winning bets they could retroactively lower the value of losing bets.
So now the first stack is a stack of low value chips with a high value chip on the bottom with the stack askew to hide the high value chip. If the bet wins no sleight of hand is needed. The high value chip is already in place. If the bet loses that's when they try sleight of hand to switch it for a stack with all low chips. That's easier than switching a winning stack because the croupier is paying attention to the winners.
If the casino goes to the tape after a win no problem. The tape will show no tampering because there was none.
The casino security people knew the team was up to something for quite a while and were scrutinizing every one of their wins and getting really annoyed and frustrated that they couldn't figure out what the heck was going on.
"Counterfeit King" [3] was about counterfeit casino tokens. Manufacturers incorporate a variety of anti-counterfeiting measures in their token designs, but Louis Colavecchio was able to match them all. The only reason anyone knew there was counterfeiting going on was casinos were finding themselves gaining token. No one, including the token manufacturers, were able to figure out which tokens were genuine and which were Colavecchio's.
[1] https://archive.org/details/breaking-vegas-s-1-e-10-roulette...
[2] https://archive.org/details/breaking-vegas-s-1-e-01-ultimate...
[3] https://archive.org/details/breaking-vegas-s-1-e-06-counterf...
My recollection of the family in the "Breaking Vegas" episode is that they were not looking at the ball release and making predictions. They were taking their records of a large number of observed outcomes and then could come up with a list of bets to make when they later returned to the wheel.
It is not that you can predict the next number from the previous, but the next quadrant on the wheel given the previois outcome is not completely random.
This took place in late 1970s | early 1980s.
It's much simpler with todays tech to do something similar with good camera feed and computer vision (rather than a spotter with clickers watching ball and wheel).
Imagine you wrote a checkout function that, because of some obscure bug, doesn't actually charge the person's credit card. Now, someone notices. Next thing, this person orders a half-million dollars of merchandise from your store before you notice the error on your end. Are you obligated to send it all to him?
Softly, softley catchy monkey. Win less over a much longer time.
I really am at a loss as to why they acted so. They were on a good thing, and with care they could have kept at it for years.
Ah yes, all the high roller capitals.