Enough odds to call?

[fyodor]

I posted this in the Theory forum and then realized it is probably more appropriate here:

6 handed table. Both blinds have folded but 4 people put in 3 bets to see the flop. Flop gives you nothing but the backdoor nut flush. Even your Ace is no good because you are pretty sure you are outkicked. They all put in one more bet. You are now getting 16/1 but you have to hit runner runner.

Obviously if you don't hit on the turn you are gone and if you do hit you will be getting 11/1 on about a 4/1 shot so you will be seeing the river at that point.

I guess on the flop you are essentialy getting 16/1 on a 4/1 shot at a 4/1 shot. Is this worth playing?

[stinkypete]

Here's a simplistic view of it (with rough numbers):

80% of the time you'll miss on the turn and lose 1 small bet.
16% of the time you'll his on the turn and miss on the river and lose 3 small bets. (Let's assume you only have to call one bet on the turn.)
4% of the time you'll hit your runner runner flush and take down the pot.

0.8 * -1 sb = -0.8
0.16 * -3 sb = -0.48
Total EV on losing plays: -1.28sb

So you need to make that up on your 4% winning plays.
1.28sb/0.04 = 32 sb.

So you'd need to expect to make 32 sb to keep playing, and if there's only 16sb in the pot so far, I'd say that's not enough.

[Mano]

You will lose 1 additional small bet when you call and non-heart comes on the turn. You will lose about 3 additional small bets when heart comes on the turn, but non-heart comes on the river (sometimes turn is raised, sometimes checked through so counting this as a wash - YMMV depending on the texture of the game). You will win 16 small bets + additional turn and river bets when you get your backdoor flush (assuming it is always good when it comes). So let's see what the EV is if you call:

EV = -1(37/47) - 3(10/47)(36/46) + (16 + 2x)(10/47)(9/46)
EV = -1.29 + .042(16 + 2x) where x is the number of turn and river bets go in by your opponents. So if .042(16 + 2x) > 1.29 your call should be profitable. Solving for x we get x = 7.35, which means you can call only if you are confident of getting 8 additional big bets from your opponents on turn and river when you hit.

[stinkypete]

that's what i said. /images/graemlins/grin.gif

[fyodor]

Thank you both. It looks like a clear fold.

I now have a better idea of how to do the math myself as well.

[Mano]

When I started replying, noone had yet posted. Just goes to show great minds think alike /images/graemlins/smirk.gif