Quote:
Originally Posted by Lottery Larry
Now, what are the odds that this dealer has dealt 6k to-the-river hands in the last 6 weeks, or 1k hands per week? Perhaps if he's dealing every day... And do we calculate the odds that one person gets 4 SFs before 5-9 other players get a SF... in 6 weeks?
OP, the red flag is getting bigger, and darker....
Either the estimate of hands dealt per hour and hours played per day is correct, or it isn't. For the sake of discussion I'm just assuming it's correct and that the hands counted were all dealt to the river. If it is an overestimate, then it reduces the likelihood that the player hit his 4 straight flushes, but it also increases the likelihood that no other players hit any.
I'm also assuming that the usual HHJ requirements are in place, i.e. that both hole cards must play in order to make the best hand. With this requirement, a player will make a straight flush once every ~6,746 hands. This excludes hands that would be counterfeited, such as a player holding Ah5h on a board with 2h3h4h6h, since it would result in a 6-high straight flush and the Ah hole card wouldn't play. The probability of one player making four straight flushes in 6,000 hands goes from 0.119 using any 7 cards down to 0.0129 (~1.3%).
Basically, you want to know what the probability is that one player will make 4 straight flushes in 6,000 hands, while the other 8 (assuming every hand had 9 players dealt in) make a total of 0.
The probability of 0 straight flushes occurring in the other 48,000 hands dealt is 0.0008 (0.08%). In practice, this would happen more frequently because players would fold some hands that would have made a straight flush if it were played out to the river. But with a jackpot in play I think it's reasonable to work off the assumption that players are likely to see flops with qualifying hands and chase down the draw if they hit the flop.
Anyway, the probability of both events occurring (one player hitting 4 times and the other 8 players hitting 0 times) is just 0.0129 * 0.0008 = 0.0000105 = ~0.001%.