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Comment by ProjectArcturis | Hacker News Reader

The article says they generally bet "neighbors" bets which cover 5 out of 37 numbers. It also says they had win streaks of as many as 13 in a row. The odds of that happening randomly are (5/37)^13, or 5 in 1 trillion. Casino security was certainly correct that this was not normal play.

I don't know why they made so many small bets. They should have come in, made like 3 huge bets, and walked out.

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I think the article actually says something slightly different -- which changes the math a lot.

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.

Now calculate 13 in a row, and 10 in a row, and and 8 in a row, and a bunch more, by the same players in the same night.

You make small bets in a scheme like this to avoid the possibility of enough bad results wiping you out to zero so you have no capital to start again. Suppose you have $100 and can flip a coin to lose $1 on heads or win $2 on tails. The highest expected value per flip is to bet all $100. But you shouldn't do that since you have a 50-50 chance to go to zero and be unable to continue. You should bet something like 1/8 of your bankroll each time so you can survive a streak of bad luck.

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.

I'm aware of the Kelly criterion. But that formula doesn't take into account the odds of being noticed and arrested by the casino.

It seems like they had way better than even odds to win, but not perfect odds. Smaller bets smooth out your mistakes. Although when you are dialed in, maybe you can up the bet size? This is assuming the no outside assistance theory is valid.

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