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Yep, this is BS. There's no way that the next roulette result could depend on the previous. After the ball has landed, the croupier will give the wheel a new spin and after a little while drop the ball again. So the next result does not depend on the roulette, but on the croupier; how fast does he spin the wheel, how late does he drop the ball.

And this is not the only part of the article that smells fishy.

> In a matter of hours, he flipped his $100 into $5,000

This kind of profit has nothing to do with the kind of edge you can get when you have detected some irregularities in the wheel. Maybe you'll have an edge of a few percent. If he really flipped his $100 into $5,000 he was not only seriously lucky, but was also gambling a far too large portion of his bankroll, risking a 'gamblers ruin'.

A roulette payout can be 35x the wager, so $100->$5000 only requires two consecutive lucky bets.

That assumes that the gambler is playing unskillfully, or assumes that they don’t care about going bankrupt.

If he's betting high enough to win 50x his stake over two bets with a winning edge, he's a moron.

A mathematician with a clue and a winning house edge would bet fairly conservatively and bet more as their bankroll expanded and bet less as their bankroll retracted to reduce their risk of ruin. Somebody making 50x their bet in an hour at roulette may sound impressive to many people, but it's obviously idiotic to any gambler worth their salt. It's so unlikely that it suggests incompetence at risk management more than it does genius gambling.

The comment you're responding to said $100 -> $5000. He's a moron to risk $100? There must be some context you didn't make explicit.

Staking $100 or $1 or $10,000 or 100BTC or 100 widgets isn't the important point. It's that the previous poster is suggesting that he could have made 35x his bet on a single spin, while missing that he would have had to risk over 95% odds to lose his entire bankroll to do that. He would have to bet everything on one spin. If you lose your bankroll, you can't bet anymore, and your edge over the house is worthless.

Now if you take a more conservative strategy, lets say you can lose 1% or win 35% of your initial bankroll, sure it may take longer but if you have an edge in your favor it should take a very unlucky streak of bad luck to go bankrupt and when you win your winnings will compound on top of eachother and the casino still will go bankrupt within a month if they don't ban you from playing roulette. So a more conservative strategy nets you more cash on average.

This is kind of a tangent, honestly I'm not even sure how unlikely it is for a gambler with a reasonably executed winning strategy to double up a few times over a long night if they're running hot. They would be doing this over hundreds of rounds of betting, so a small edge compounds rather quickly.

The bet sizing isn't totally implausible if the rest of the data is accurate:

The article implies he started out on double-zero machines with a 5.3% house edge. Assume 1 roll per minute and a Kelly-sized bet:

- It'd take on average 87h to 50x your bankroll at a 2.7% edge (half the supposed house edge). You're on average approximately doubling your money with every win, so he _might_ have just gotten a few more wins in the night than expected, but that would be very lucky.

- It'd take 9.5h on average to 50x your bankroll at a 7% edge (1.5x the supposed house edge). That's very achievable in a long night, and you're approximately quadrupling your bankroll every win, so just being a little lucky with a single extra win would drastically cut down the total time.

The "last 3 rounds" part is obviously metaphorical. It says he used teams of observers for a month to record up to 20,000 spins, not that he literally looked at 3 spins to determine the fourth.

It all sounds unlikely in today's data-driven world, but I suppose that in European casinos a half century ago they had roulette wheels that had been in service for 80 years without any real maintenance and would show massive bias without anybody noticing.

> I suppose that in European casinos a half century ago they had roulette wheels that had been in service for 80 years without any real maintenance and would show massive bias without anybody noticing.

Sure. But not a contingent bias. And certainly not a contingent bias that was bigger than any concomitant non-contingent bias.

You could think of the statement as being about knowing the actual bias as a function of only being able to look at the previous rolls. In other words, it is “contingent” on the specific roulette wheel being observed, not “contingent” on which exact rolls were seen recently, per se. But language and thinking on these subjects has evolved since 1969, so the way to frame it to a layman would obviously evolve as well. It’s been over 50 years, after all! Trying to understand the statement in the context of 1969 makes the framing much more reasonable.

Edit: I can also see how this framing might have been important to funding ongoing research, ie, perhaps you are right that there was some degree of unethical framing here.

Recall the quoted passage:

> “If numbers 1, 2, and 3 won the last 3 rounds, [I could determine] what was most likely to win the next 3.”

That is unambiguously claiming not just a contingent bias, but a bias contingent on the previous three rounds. My math was based on a one-round contingent bias. That is already in the realm of extremely unlikely. Three-rounds is just flat-out impossible.

I don't think it's unambiguous. I think the parent's interpretation is also quite possible (even probable, given your point that the contingent interpretation is impossible).

> That is unambiguously claiming not just a contingent bias, but a bias contingent on the previous three rounds.

No it isn't, only that three rounds may be enough to predict the bias. Whether the bias actually depends on previous results is irrelevant to the quote.

> three rounds may be enough to predict the bias

That is an even more absurd claim.

Would a bias contingent on the previous 3 be considered Markovian in this case?

Wouldn't this be a very simple example (simple to the point that it's obviously exaggerated and wouldn't happen in a real casino): each spin of the wheel takes it exactly one whole rotation plus one number, which if the dealer always picks up the ball and spins starting from the previous winner would mean the next winner is always the next number around on the wheel?

It's pretty clear that you've never actually seen a roulette wheel in action. Introducing a bias intentionally (i.e. trying to control where the ball drops) would take extreme skill. Doing it unintentionally is impossible.

I've played roulette many times, and yes I agree that doing it with skill on a fair wheel would be impossible. I thought we were talking about potentially rigged games, and just as I couldn't roll fair dice to the same number 20x in a row I'm aware that dodgy dice can be made, so why couldn't a dodgy wheel (or accidentally dodgy by being so old that a noticeable pattern emerges) be made?

He didn't say contingent bias, you did. Nothing he's written is in any way related to prior individual rolls.

He said he knew how to place a winning bet, he never said it was because the previous results were exactly 1, 2, and 3 and no other numbers. Those results can indicate something other than a "contingent" bias; because they landed on 1, 2, and 3, the wheel is leaning more towards that half of the wheel, meaning he could therefore assume bets on that half of the wheel were more likely to hit, which would then allow him to accurately say he knew what to bet next (a complex bet) that would pay out (win more than wagered).

You're thinking about this mathematically, when the edge comes from mechanical physics.

1 2 and 3 are distributed around the wheel, there is no "that half"

Not perfectly evenly distributed, which is the point.

There was a Spanish family that took advantage of that and won big in European casinos. They recorded a large number of results, found biases big enough to overcome the house's edge, and used them. The casinos responded by moving the tables around and moving wheels between tables, but the family has spent so long observing the wheels that they could recognize individual wheels by the wear and tear they had accumulated over the years.

But this was not contingent biases. The odds of a given number were not dependent on what number had previously come up.

These people were covered in the episode "The Roulette Assault" of the old History Channel series "Breaking Vegas" [1]. You can watch this episode at the Internet Archive [2].

"Breaking Vegas" also did an episode, "Beat the Wheel", on Doyne Farmer and Norman Packard's computer-in-a-shoe that used physics to predict roulette outcomes. These are the people who were the subject of the book "The Eudaemonic Pie" which another commenter has mentioned. You can watch "Beat the Wheel" at the Internet Archive [3].

There's one more "Breaking Vegas" roulette episode that is very interesting. It is called "Ultimate Cheat".

The Spanish family was definitely not cheating. It is not against the rules to gather data--in fact many casinos encourage it because 99.99% of the time someone gathering data thinks they have some foolproof system for winning when in fact they have completely botched it and casinos love these people. They blow a ton of money before they figure out that their system is completely worthless (at best).

The "Eudaemonic Pie" people may or may not have been cheating depending exactly on how the rules of the casinos were written back then.

The guy in "The Ultimate Cheat" was definitely cheating. At first he was cheating using a particular method. He was successful at it, but then casinos installed video cameras that recorded everything at the tables. When he would win, they would detain him while they checked the tape, and the tape showed the cheating. This seemingly put an end to his career as a roulette cheater.

But then he started winning again, and when the casinos checked the tapes they showed the win was clean. They were certain he was cheating and they were scrutinizing his wins in excruciating detail, but they could not find any problems with them.

There was a good reason for that. His wins were in fact entirely legitimate. He legitimately put a stack of his chips on a number, did not influence the wheel or ball or croupier in any way, and if his number came up by chance (which happened just as often as you would expect it to) he collected his winnings.

What he did was take what he had been doing originally, the method he had to abandon due to the cameras, and apply a brilliant twist to it. That method is post roll bet modification. You put down a stack of low value chips on a number, and if that number wins you try to swap that stack for a stack that has low value chips on top and a high value chip on bottom displaced a little so it is not visible to the croupier.

The cameras catch you doing the stack swap and the jig is up.

His twist was to apply it to losing bets instead of winning bets. He would bet a stack of low value chips on top with a high value chip on the bottom. If he won he did nothing. But if he lost he tried to swap the stack for one that only had low value chips.

The casino was only scrutinizing his wins so he got away with cheating on his losing bets for an embarrassingly long time. You can watch "The Ultimate Cheat" at the Internet Archive here [4].

If you are checking out "Breaking Vegas", there is one more I will recommend even though it has nothing to do with roulette. That's the "Counterfeit King" episode, on the Internet Archive here [5].

That's about a guy who was making counterfeit casino tokens. They were good enough that the casinos only knew they were there because their token counts were unexpectedly going up. When the casinos sent tokens back to the manufacturer to check, the manufacturer said they were all legit.

The downfall of this counterfeiter is instructive. One day he was using his tokens in slot machines. He was playing a fairly expensive machine and it jammed. He just moved over to the next machine and continued. A guard saw this on live surveillance and became suspicious because when a machine eats a high value token the gambler is always very annoyed and comes complaining to casino staff to get their token back. The gambler just going "meh" and moving over a machine was just not believable. That got him on their radar as someone up to something which led to them discovering he was the counterfeiter.

[1] https://en.wikipedia.org/wiki/Breaking_Vegas

[2] https://archive.org/details/breaking-vegas-s-1-e-10-roulette...

[3] https://archive.org/details/breaking-vegas-s-1-e-08-beat-the...

[4] https://archive.org/details/breaking-vegas-s-1-e-01-ultimate...

[5] https://archive.org/details/breaking-vegas-s-1-e-06-counterf...

Breaking Vegas was a fantastic series. My favorite episode was the one where a programmer working for the Nevada Gaming Commission hacked the ROMs of slot machines and was able to activate a jackpot with a secret combination of coins.

For those who want to see it, that episode was "Slotbuster" and is on the Internet Archive here [1].

It looks like all 14 episodes of "Breaking Vegas" are there [2]. I haven't seen them since around the time they were originally broadcast, but my recollection is that most of them were quite worth watching.

[1] https://archive.org/details/breaking-vegas-s-1-e-02-slotbust...

[2] https://archive.org/details/@vegasfan

> It is not against the rules to gather data--in fact many casinos encourage it

Except when it's blackjack and you're counting cards.

you are allowed to count cards at most (all?) casinos in the usa.

It's legal, but if you're too successful, a lot of casinos will show you the door, sometimes preventing you from converting your chips back to money. See https://youtu.be/rjfLuM-Pqr8

You are right if it was just a simple bet on one number. But I suspect the article is skipping out on the full description. My guess is that it involved a system where multiple bets were placed each spin - Roulette's odds can be narrowed if you place bets on a color, a third, high/low, and a number, making sure to minimize doubling down on any possible result. That puts you in a position where almost every spin, one of your bets wins and offsets some other losses. When the spin lands on the bets with higher payouts, you win more and balance out the spins where you got lesser payouts. All told, you'll slowly lose money all night, and one of two things happens - you one number hits and you win big. Or the zero hits and you've lost. It is a very complex and pain-staking way to flip a coin. But, if you have any way to game that one number, and can afford to just let those bets ride for the hours for that advantage to play out... I could see it working.

Also, back before casinos were computerized, people did spend years learning the specific machines in a specific casino. They would often do it in teams, so each person would take an 8 hour shift, and share the winnings at the end.

I have a very hard time believing that a roulette wheel could have a contingent bias such that the next outcome depended on the previous one

The funny thing about Roulette is not the hardware but the fact that the random sequence begins with a human being.

I can honestly believe that a bored roulette croupier could reproduce an outcome by consciously (or unconsciously) releasing the ball with the same velocity and direction at the same wheel speed. When you do the job for hours on end wouldn't it be plausible that there's some amount of muscle memory that takes over?

Having watched a few a work in my lifetime it sure seems like they even take it as a challenge to try and work up duplicate numbers. Maybe as a 'fuck the house' move, a cure for boredom, or perhaps a way to drum up more business when you get a streak on the tote board? Who knows.

> I can honestly believe that a bored roulette croupier could reproduce an outcome by consciously (or unconsciously) releasing the ball with the same velocity and direction at the same wheel speed.

I can believe that too, but that's not the claim being made here. The claim is that the bias was bound to particular roulette wheels, not particular croupiers. Also, even if a croupier had a reliable contingent bias, you'd still need a ridiculous number of data points to figure that out.

There might be hidden variables. Maybe the previous results are a sign that a particular croupier is working that day, which is why you can count on some specific bias for the next numbers.

I.e. some hidden process is causing both of the events, the first event is not causing the second. What you will observe is a high probably of the second event conditioned on the first.

> Maybe the previous results are a sign that a particular croupier is working that day

A more reliable indicator would be, oh, I don't know, looking at the croupier's face and seeing who it is? Just an idea.

Ok, maybe the croupier is not a "hidden" variable, but it could be whether he had coffee that day, which roulette wheel is being used, the lighting conditions in the room, whether he was able to park in front of the building or had to walk from the parking lot, etc. Any event that happens some of the time and causes 1, 2, 3 as the first three numbers can very well be causing a specific distribution of the next numbers.

I.e. correlation doesn't imply causation but translates to dependent probability distributions and therefore a "if A then B is likely" just because A can be observed before B.

This is believable to me because I can force the results of a coin toss.

I'm not really sure how, but some tactile awareness of a coin's weight, air pressure, what side is currently facing up, etc. must all factor in.

For context, I am trained as a magician (so there's a degree of mastery of the properties of coins, and fine muscle control), but this is not a magic trick

What is your success rate?

I haven't tracked it in a clinical, laboratory setting.

But if we were in a bar and you bet me $100 bucks that I couldn't get heads 20 times in a row I'd feel comfortable taking the bet

About 50%

If a croupier really was influencing the outcome of the spin, consciously or not, it would involve the exact moment when he dropped the ball. E.g. every time he would drop it in the area of the 10, it would end up in the area of the 3. But in that case there is no point in observing previous roulette outcomes as was described in the article. You would have to observe the croupier instead and the moment he was dropping the ball.

Either the article is not describing accurately what happened or the whole story was BS. There is no way that a croupier or roulette wheel is influenced by the previous drop of the ball.

> can honestly believe that a bored roulette croupier could reproduce an outcome by consciously (or unconsciously)

The fantastic book, The Eudaemonic Pie, mentioned elsewhere in this thread, describes another groups attempts to beat roulette with prediction.

Along the way they encounter a croupier who always bets his tip money on 17. Why? “Because if I do everything just right, I can actually hit seventeen. Not that I can do it every time, mind you, but I can get close to it. I set the wheel going at a steady rate, and then I flip the ball in this nice regular way when the zero is lined up in front of me, and I swear I can hit seventeen with better-than-average odds.”

In the story, they tell the audience that he weaved a false narrative to the public about super computers. There's no reason not to believe that this is also a fabrication.

In fact, the amount of press around the guy seems to work as an invitation for people to come to casinos. I wouldn't discard the whole thing as a total scheme, a fabrication set up between the "professor" and the cassinos interested in attracting naive gamblers in this perfect marketing stunt!

>What possible mechanism could cause that?

As a pure hypothetical, definitely not saying it's what happened in this case: if the wheel's bias is based on where the ball is initially dropped in, and a human operator is the one that chooses where to drop in the ball, it's possible that the operator does something simple like choosing a spot opposite the number that last won the round and that this human bias affected the result in some way.

Probably none of these are true:

1. He explained himself clearly to a journalist. 2. The journalist understood what he was saying. 3. The journalist relayed it clearly and accurately. 4. He or the journalist didn’t exaggerate his success story.

To your specific point I read that as a layman’s explanation of bias, and not at all as actually implying that if a 1, 2, 3 comes up then it’s sure to be a 4, 5, 6 next.

Yes, I expect more obfuscation to keep the casino owners guessing.