Here is a puzzle I've been thinking of for a while. Assume that there are five people playing "five-card draw" poker ( http://en.wikipedia.org/wiki/5_card_draw
) using all of the 52 cards in the set. Each is given 5 cards, then they are allowed to either bet or fold. After they all agree on an amount of bet, they change from 0 to 5 cards of their hands with those coming from the remaining cards in the stack. In the end, the player with the best combination wins. ("Best", here, means a hand with lowest probability.)
If there was no "draw" phase, then the probability of each combination would be as described here: http://en.wikipedia.org/wiki/List_of_poker_hands
But because there is a draw phase where people can change upto 5 cards of their hands, (here is the question) would the probabilties change? For example, (and as some poker players say) would this draw phase cause a "flush" to happen less often than a "full house", and so make the flush a "better" hand? ("Better" is defined as less probable, again)
I really am stock with the calculations. As an alternative, I thought of writing a program which would use Monte Carlo simulation to assess this hypothesis, but I got stock again!