4 ms·

Six standard deviations is 1 in 2 billion per Wikipedia here - https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule https://en.wikipedia.org/wiki/68%E2

Six standard deviations is 1 in 2 billion per Wikipedia here - https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rul.... 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-drawing-winning-numbers-largest-jackpot 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?)

Nevermark 4y ago
If it’s coin flipping, then winning 10 coin flips is 1 out of 1000. 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.
- majormajor 4y ago
  There was a lot suggestive about this group, but that includes a lot of subjective factors. 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?

Nevermark 4y ago

If it’s coin flipping, then winning 10 coin flips is 1 out of 1000. 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.

majormajor 4y ago
There was a lot suggestive about this group, but that includes a lot of subjective factors. 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?