Quote:
Originally Posted by naplesplayer
Our poker parlor has a jackpot for a royal flush holding 2 of the five cards needed. As many times it is hit, these odds have to be wrong. I could go in to a lot of detail about no. on hands deal daily , but it is pointless. We hit jackpot 8 to 13 times a month. The formula does not compute for the no. of hits, no even close. Looking @ another thread the odds are for a 5 card draw game. NOT holdem. Odds more like 32000. to 1
In hold em, the probability you hit a royal flush by the flop is the same as in draw poker. However, we can compute an upper bound for the probability that you hit a royal flush by the river. If we make the assumption that you will play any two suited cards 10+, and that you always see 5 board cards, then the probability is
4*C(5,2)/C(52,2)*C(47,2)/C(50,5) = 1/ 64,974 ~ 0.000015390
Or odds of 64,973:1
In practice, the probability you hit a royal flush is less than the number computed above since you will not always see the flop with any two suited cards 10+, and that you will not always see all 5 board cards.