How your hole cards affect the flush chances in Omaha.

[Filip]

What got me thinking about this little problem was after being berated by railbird after i cracked his friends nut straight with a flush. I had 3 clubs in my hand and he thought that i sucked for playing the hand.

Using a Hypergeometric probability distribution, h(x,n,M,N), where

x = Sample: number of clubs, 3 to 5
n = Sample size: 5 (flop, turn, river)
M = Population: number of clubs in deck, 11 to 9
N = Population size: 48 (the cards left after my 4 hole cards)

I add the probabilites for x = 3..5 and of course alter M = 11..9 accordingly. The results for how the number of clubs in my hand affect my chances of getting a flush are as follows:

2 clubs, P(flush) = 0,071577243

3 clubs, P(flush) = 0,05407451

4 clubs, P(flush) = 0,039294424

Nothing chocking or unexptected there. But now to my question.

In a full table game (10 players) we have 40 cards out and i cant stop to reason that if i got 3 clubs in my hand the affect they will have on the flop,turn,river will be neglected by the other 36 cards out.

Since 40 cards out of 52 are being dealt out i say that these 40 cards have a discrete probability distribution of suits. So what if the 4 cards i choose to look at (my hand) out of the 40 happens to be 2,3 or 4 clubs.

Hence i come to the conclusion that the chances of me getting a flush are the same no matter what number of clubs i hold.

Thoughts?


/Filip