[binions]

[ QUOTE ]
OMG, this is so simple to find, I don't get what you ppl are writting about. Just run all possible combinationas and find the EV, here is my crude and straightfoward method.

odds of hitting the cards we need on the turn is 10/47, river is 9/46

so to get through all the possible cases, i'm going to run it 2162 times

so first, u'll lose -2162 on the flop to see the turn card,

next, on the turn, 460 times u'll get your four flush draw. so u'll have to pay to see it, so -2*460

now, for u'r pay off, it will be final pot times 90. cause u'll hit 90/460 times.


so u hae FinalPot*90 = 2162 + 2*460 for 0EV


Final Pot = 34.24

so working backward, -2(him) for his call on the river, -2(you) -2(him) for the turn, -1(you) -1(him) for the flop bet, u'r left with 26.24

so pot needs to be 26.24 on the flop. with the pot odd on the flop, u can easily figure out the number of outs it equals.. add 1 for his bet, and u get the pot odd you need.

which is 27.24

so u need to get 27.24:1, so that is 1/27.24 * 47 = 1.73 outs. (out/47* pot = 1 ...out = 1/pot *47 )

Q.E.D.

[/ QUOTE ]

47*46=2162 possible combinations.

Assuming one opponent:

37*46=1702 of those combinations, you lose 1 small bet.

10*37=370 of those combinations, you lose 1 small bet and 1 big bet, or 3 small bets.

So, when we miss, we lose 2812 small bets.

We hit 90 times. 2812/90= 31.2.

So to break even, we need to win 31.2 small bets if we hit.

We win 1 big bet (ie 2 small bets) on the turn and river from our opponent when we hit.

31.2 - 5 = 26.2 is the number of small bets we need in the pot on the flop in order to call 1 small bet.