[StellarWind]

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Is the flop fold really that easy?

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Don't recall saying it was easy. I think it's close but you should fold.

3.5 seems pretty reasonable for the overcard outs.

2.5 is too much for the backdoors. I'd give you 1.5 for the K [img]/images/graemlins/spade.gif[/img] but the queen is worth less.

A clean 3-way backdoor straight (KT/T8/87) is worth 1.5 outs, but that assumes that if you turn a straight draw you will be adding four or eight new outs. First off the 87 branch is just a chop so 1/4 out disappears right there. Second there is a risk that our backdoor straight will complete the flush. But the biggest problem is straight draw cards are toxic. If we get our king we add four straight outs, but our 3.5 overcard outs need to be reduced. Really it's not even a call on the turn at 5-1. Similarly an eight would add six outs for the half-chopping double gut, but the 9865 clump doesn't make me feel very good about spiking a pair on the river. He called 1.5 preflop so his board pair is apt to have a nearby kicker for two pair or the straight. The ten is also lame and a seven is completely uncallable.

Note that it doesn't matter if you disagree with my judgment that a turned king cannot be called because the decision is obviously at least close.

Mathematical concept: suppose that it is just barely correct to call the turn if card x comes. That means the EV of calling is just barely positive because folding has zero EV. Then the possibility of turning card x is virtually immaterial when deciding whether to call the flop.

When you decide to pay 1 SB to call the flop you are saying that the hand you will get on the turn will on average be worth at least 1 SB. Getting an off king in our example hand is obviously a very bad result whether you think the turn hand has EV = 0 (turn needs to be folded due to inadequate odds) or EV = 0.1 SB (barely worth calling the turn in your opinion). Either way the king possibility won't make a meaningful contribution to justifying a flop call.

The problems described above drain away much of the EV that you would normally get from picking up a straight draw. So even though you might soldier on after picking up such a draw, it's a salvage operation and there isn't much money in it. I'm not inclined to pay much on the flop to try to create such a draw, meaning I'm going to sharply reduce the number of outs I take for the draw. Saying a backdoor draw is worth an out is a shorthand way of saying it adds the same EV as a real out.