Re: Number of players dealt in affecting flush draws?
2 hearts are in your hand. 2 hearts are on the board (this is what I think you are still missing). There are 9 left in the deck of 47, so the concentration of hearts is only 19%. On average, 5 opponents will hold 1.9 hearts, and 9-1.9 gives you the 7.1 you were looking for.
It's true that, if you asked before the flop, you would say that 5 opponents would have 2.2 hearts on average given that you have 2 of them. However, once the flop comes up with 2 hearts, that presents you with some evidence that hearts in your opponent's hands are actually rarer then your original calculations (look up Bayesian probability for the reasons). So you will have to recalibrate your assumptions, and you come up with the 1.9 number. The math to prove all this is quite lengthy, but will result in the same number as you get when you treat all unknown cards equally (which is a much easier calculation and the one used in all the odds charts).
|