What are the Odds of two people having a flush in poker?

[PokerSki]

What are the odds of two people having a flush in Texas Poker? Lets say 2 players both have two harts, and there are 3 harts on the board.

 

[Collin Moshman]

Good question. If we've flopped a heart flush, at that point the remaining cards/suits are:

13 spades
13 clubs
13 diamonds
8 hearts
------------
47 total cards

Assuming our opponent is equally likely to have any of these cards in his hand (not a good assumption!), then:

Probability of his first card being a heart = 8/47

Probability of second card being a heart = 7/46

Probability he holds a flush = 8/47 * 7/46 = 56/2162 = 0.026

So about 2.6% of the time, our opponent will hold a heart flush also.

Lastly, if you meant what's the probability before a single card is dealt that 2 or more players will flop a flush in the hand, the answer appears to be (based on Googling) around 0.21%.

 

[Percivalpl]

Well... from what I know math doesn't lie... maybe if you play a billion hands it will be 2.6%. In my experience it's 1/4 Oh and the opponent has an ace of course.

 

[Collin Moshman]

Kind of like 55 vs KQs all-in pre. The math says almost exactly 50-50. But the guy with 55 knows that he's actually like 10% to have his hand hold up