Help me understand BD flush odds with the turn accounted for.

[AdamL]

I understand the mathematical reasons for counting a backdoor flush as 1.5 outs.

However, I wonder if it isn't a bit too optimistic? You have to call a flop bet and THEN a turn bet (if you're on your way) in order to see your outs through.

Eg., I have AKs and decide my backdoor flush is the only way I can win the hand (for example's sake).

There is 1SB to me to call, and I close the action. The pot has exactly 23SB in it after the bet, so I am getting exactly 23 to 1.

I believe it is unprofitable to call. The reason being, if you hit your suit on the turn and miss on the river, you invest an extra BB.

I need help from the math types to explain either how I am wrong, or how I can take the turn bet into account for my flop decision.

Thanks!

[Andy B]

I don't know that I'm a "math type," but I can't sleep, so here it goes: you're right. If the only way you can win is to make a flush, and you expect to face a bet on fourth street, you cannot profitably call a flop bet in the scenario you describe. You would have to take into account how many people call on the turn to get an exact calculation. I'll simplify by saying that you're only facing the flop bettor. You anticipate having to call the turn bet, so you're getting (23+2):1.5 or 16.66:1.

I know it's more or less unheard of to have it be seven ways for three bets before the flop, or whatever it would take to get the pot up to the magic 23 bet level, and then have the rest of those players fold for one bet on the flop, but I'm lazy and I'm doing this for free. Your saying that the backdoor flush is the only way to win the hand when it's one bet to you is pretty contrived too, so there you have it. If you want to take other players into account, add "2" to the left side of the (23+2):1.5 thing. There's also the chance that the turn could be raised, but that's more involved than I want to get.

[reubenf]

[ QUOTE ]
I understand the mathematical reasons for counting a backdoor flush as 1.5 outs.

[/ QUOTE ]

Since you'll hit it about 4% of the time, then if you're just doing the math to see how often you'll hit it, it seems it's only worth 1 out.

[ QUOTE ]
However, I wonder if it isn't a bit too optimistic? You have to call a flop bet and THEN a turn bet (if you're on your way) in order to see your outs through.

[/ QUOTE ]

Don't you have to do that with -any- outs?

I think this is actually why BD draws are worth a little more than the percentages indicate. You can abandon them if they miss the first half and save a bet.

[reubenf]

Sorry about the doublepost /images/graemlins/frown.gif

[ QUOTE ]
Eg., I have AKs and decide my backdoor flush is the only way I can win the hand (for example's sake).

There is 1SB to me to call, and I close the action. The pot has exactly 23SB in it after the bet, so I am getting exactly 23 to 1.

I believe it is unprofitable to call. The reason being, if you hit your suit on the turn and miss on the river, you invest an extra BB.


[/ QUOTE ]

Here's the probability of each outcome.

1) 79% (37/47) of the time you miss the turn and just lose your bet.
2) 17% (10/47*37/46) of the time you hit the turn, miss the river.
3) 4% (10/47*9/46) of the time you hit the turn and the river.

You're losing one SB in #1 and three SB in #2 assuming no raises. So far your EV is -.79 -.51 = -1.3 SB. So in #3 you need to be making >32.5 SB (1.3/.04). You're at 23 now, you get two more per player that sticks with it on the turn, and you may be able to get more than two per player on the river as a BD flush is pretty sneaky and some people won't even notice it.

So it seems to me you need at least two more players who will stick around to the end without raising the turn, and it's pretty borderline there.