Betting into a 4-flush question

[Sinnister]

Does anyone have an exact percentage of the time that when against 2 oppts in Hold'Em they wont have a flush card.

I was playing a hand with kk where turn ended uup putting for to a flush on the board and i check folded because I wasnt sure of the correct play.

[henrikrh]

Well a VERY VERY basic way of looking at it would be that 1/4 random cards are of that one suit, so the chance one card isn't is 3/4, for four cards thats 3/4 x 3/4 x 3/4 x 3/4

The answer from that is 31.6% chance of neither player having it.

However when a 3 flush is on people with that suit are more likely to be in to try and hit it, so you should discount that, I would say 20% is a good bet, maybe lower.

Don't trust my calculations and logic, I'm not on the same level as some of these guys.

[henrikrh]

BUump, can anyone reinforce or refute my conjecture? I would really like to know if I am making any wrong assumptions other than not discounting the two non-suit kings the player is holding and the cards on the board. Enlighten us.

[waffle]

multitabling, so post is sparse

assuming opponents have a random card distribution (we're discounting the fact that players are more likely to call on the flop w/ a flush card).

4 flush on board
2 in hand, non-flush

46 cards left - 9 flush, 37 non-flush

2 opponents - choose 4 random cards
chances of neither having a flush?

37 * 36 * 35 * 34 / (46 * 45 * 44 * 43)

40.4%

[waffle]

There's only 52 cards in the deck, so it's best to use all the information that we have at our disposal (what we know about the board and our hole cards). Using the 3/4 guess instead of the correct information lead to a significant error for final answer.

[imported_piki]

I put this into pokerstove:

You hold K[img]/images/graemlins/diamond.gif[/img]K[img]/images/graemlins/club.gif[/img], vs. two random holdings.

Board is 2[img]/images/graemlins/spade.gif[/img] 4[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/spade.gif[/img] Q[img]/images/graemlins/club.gif[/img].

Only a [img]/images/graemlins/spade.gif[/img] beats you here, so I think the results are exactly what we're looking for. According to stove, odds of your hand being good are 2:3 or 40%.
Vs. 3 opponents it's ~24% and HU it's ~64%.

-pix