How do I calculate the probability of getting flush in texas hold em poker after the 3-card flop?
Specifics: N players at the table (N = 2 to 10)
Review of rules:
Each player gets two cards face down. Then after pre-flop betting, a flop of 3 cards is dealt open faced to the table. If players are still active, there will be another card dealt to the table (the turn), and a final 5th card dealt to the table (the river card).
All but two players fold after the 3-card flop; so now it is heads-up (i.e., one on one).
One player has two hearts and there are two hearts on the flop.
What is the probability that in the either the turn or the river, another heart will show up producing a flush for the player having the two hearts?
Some say the answer is a function of N, but others say it is independent of N. I am looking for a math derivation rather than some numbers that can be found in any poker book. I don't play poker, but I think I gave wrong advice to someone years ago, and now I need to make amends before online poker is made legal in my state next year.