[MarkGritter]

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Here's a hand from last night, number 104 in our match. G has the button.

G gets 4478A and raises, T calls. T draws 3, G discards A4 and gets K7. T checks, G checks.

I felt that the odds were good that T had caught up, and that any 2-card draw he has is better than mine. I would bet with an (unpaired) 9 or lower. My two paired cards help marginally here.

T raps pat, G draws 64 (87644). T bets, G folds.

T's perspective:
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I make a loose defense with 54 and draw 239. Mark draws two but I whiff my checkraise attempt. I'm pat, he draws two again and folds the third round, showing 87644.
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Good? Bad? Indifferent?

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I think you are 100% on point with your check. He will have improved by 1 card at least 50% if not greater of the time.

TT [img]/images/graemlins/club.gif[/img]

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Well, let's see here...

I know T has two low cards, and I've see 44778KA. That leaves 43 cards in the deck. T's best case for improving is holding 47, so any 23568 and maybe 9 is good (23 cards), worst case is having 23, so a 45678 or possibly 9 is good (19 cards).

Thus, given what I know, T will brick on all three cards somewhere between (24/43)*(23/42)*(22/41) = 16% and (20/43)*(19/42)*(18/41) = 9% of the time. Since there are only 4 SB in the pot, trying to take it down here is not profitable. (No better than 5.25:1 odds of doing so.)

If he has improved to a 2-card draw, what can he have that I'm obviously ahead of? Not much, by my estimation:

985 (very rough defense, might fold)
984
983
982
97w
9ww (some of these matchups are interesting, T could be ahead.)
876 (unlikely)
875

Compare with
87w
86w
8ww
76w
7ww
6ww
www
+ all one-card draws
+ all pat hands

The three card nine draws are nonobvious, I might have to think a bit more about them.

ETA: of course, the combination of folding equity and whatever equity I do have against T may put me over 50%. But I'm comfortable with a check here.