Non-nut flush on the turn (hypothetical)

Hypothetical situation:


Suppose you draw to a non-nut flush on the turn (let's say you played Jxs from one of the blinds), it's heads up, and your opponent has position on you. Is it correct to slow-play here? (I'd make up a full story for this if I were more awake. If I tried to do that now, the story wouldn't make sense and possibly open up a discussion on something else which I'm not particularly interested in right now.)


My instinct is that slow-playing here is bad to keep the high cards (A, K, Q) of that suit from outdrawing you. But I did a quick EV calculation, and it seems that checking is actually better. I want to spend more time thinking about the calculation I made (and double check... because it's late and I might have made a mistake), but I thought I'd throw this out there to see what other people think first.


Aaron

If your reasonably sure there will be a late position bet, go for a checkraise to thin the field.


Stu

...to thin the field.


The hypothetical is heads-up. So, thinning the field means winning immediately without a showdown.

You should bet and raise with you made flush.


Something is wrong with your EV calculation. You can't make money unless you bet and raise with your made hands.

I woke up this morning with a strong conviction that I was wrong, looked at the paper where I made my scribbles last night, and found the mistake. Not multiplying properly... . Here's the whole thing just for the sake of clarifying what I was aiming for.


==

I will make the following assumptions (all of which seem reasonable to me...)


1) If I check, he takes the free card

2) If I bet, he will call

3) If the flush card falls on the river, I will check-call

4) If the flush card does not fall on the river, he will fold (well, really I check and he

checks behind, and mucks to my flush)

5) It's a spade flush (just for concreteness)

6) The pot size is x.


There are 6 spades out (my 2 + 3 board + his 1), leaving 7 spades. There are 8 cards exposed (My 2, his 2, 4 board). Therefore he is getting 7:37 = 1:5.3 on his call.


Suppose I bet.


1) 16% of the time, he draws out on me, and I lose 2 since I pay him off.

2) 84% of the time, he doesn't draw out on me and I win (x+2) since he doesn't pay me off.


So my EV for betting is .84*(x+2) - .16*2 = .84x + 1.36


Now suppose that I check.


1) 16% of the time, he draws out on me, and I lose 1 since I pay him off.

2) 84% of the time, he doesn't draw out on me and I win x since he doesn't pay me off.


So my EV for checking is .84*x - .16*1 = .84x + .68


So I lose .68 by not betting. (The error was in the betting part: .84*(x+2) = .84x + .84)


==


So there it is.


Aaron

The profit from heads-up play does NOT come from fair-and-square solid hands: it comes from hands where YOU win by betting when the opponent has either little or nothing, folding a weak winner (you bluff) or a good-enough draw against what you actually have (such as a gut-draw against your no-pair Ace high, he has 9 outs but thinks he has 4). (Rarer but realistic is a strategy of encouraging the opponent to bet himself silly, but that's another topic...)


You should be REGULARLY assertive in heads up pots ..err.. well regularly LOOKING for assertive opportunities. Against all but the brain-dead, these opportunities pretty much dry up if the opponents knows you slow-play big hands heads up. If you check-raise when the flush gets there and the opponent knows you would slow-play an actual flush, you are losing your semi-bluff equity and can easily either lose a big pot or worse yet get muscled out of one.


And ... the opponent knows (correctly) people don't need good hands to raise heads-up, so you might as well raise with your big ones since they are quite likely to call with whatever was good enough to bet.


Sooooo..... I'm claiming that usually your EV on OTHER hands is increased a little (but a lot when its cumulative) when you play big hands assertively, and this increase is almost always more than the slight -EV you MAY get by doing so with that big hand.


- Louie