Re: WOHEP: Backdoor flush outs estimates
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Backdoor flush draws are 23:1 to hit, which is equal to 1 out with 2 cards to come.
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Can you show your derivation?
I used:
10/47 you hit a flush draw on the Turn.
if you hit the flush draw, then you will have 9 outs.
10/47 x 9 outs = 1.91 expected outs
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Do you agree a backdoor flush draw is 23:1 to hit? 10/47 * 9/46 = 4.16% which is 23:1 against.
If so, look at any standard odds chart. 1 out with one card to come is 45:1 assuming 46 unseen cards. 1 out with 2 cards to come is 22.5:1 with 47 unseen cards (or 21.5:1 if there are 45 unseen cards).
Bingo. See Ed Miller's SSHE at p. 102 for confirmation on the math.
Anyway, I have seen Ed Miller (and I think Abdul) say a backdoor flush draw is worth 1.5 outs. But this has to do with:
1. The fact you can fold on the turn when you don't pick up a draw;
2. The fact that you get paid off relatively more often than a flopped 4 flush when you hit.
So the math "out" is inflated by 50% to 1.5 outs given these implied odds/game considerations.
But the math is a backdoor flush draw is 23:1 against which is equivalent to 1 out.
To say you have 1.91 outs on the flop means you have an 8% chance to hit your hand by the river. That's simply false with respect to backdoor flush draws. You don't have an 8% chance. You have a 4.16% chance.
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