Message Board : Okay, here's me donking it up

Well, let's look at this purely mathematically then.

I'll assign Villain's range to be:
AK,AQ,44+, any diamond suited connector from 76 up, plus KJd. 

We shove.  For this exercise lets just assume the third player folds 100% to our shove.  Let's also assume that Villain will fold 77-JJ, AQ, AK and call with 44-66, QQ-AA, and the flush draws.

So we need to figure out how many hands he is folding vs. how many hands he is calling with. 

77 88 99 TT JJ - six ways to make each one, or 30 hands.
AQ - since we have the diamonds, there are 6 other AQ hands.
AK - since we have the Ad, there are 13 ways to make this hand.

QQ(3) KK(6) AA(3) 44(6) 55(6) 66(6)  30 hands.
KJd 76d 87d 98d T9d JTd KJd - 7 hands.

Villain folds 49 hands out of 86, or 57% of the time.

Villain calls with 37 hands out of 86, or 43% of the time.  When he calls, our equity against his calling range is 42%. 

57% of the time we win the $38 pot to a fold.
43%(58%) or 25% of the time we lose $61.20 and double up Villain.
43%(42%) or 18% of the time we win $61.20 plus $7.50 in dead money, or $68.70.

Expectation = .57($38) + .18($68.70) - .25($61.20) = $18.73

I also did the exercise with Villian calling with all his pairs and with AK in addition to the calling hands used above, and our total expectation came out about the same.

We'd have to narrow Villian's range a bit to come up with negative expectation.  This isn't really the outcome I expected.  Looks like shoving works here, if I didn't make a mistake.

spadebidder said:

I asked a fulltime live pro (for 20 years) about this hand and he said he would very rarely ever push with a 15-out draw….. He said Internet players like to risk all their chips on draws way too often.

Where's the 15-out draw in this hand?   Your opponent is representing a range of which QQ+ makes up a huge part.   If you see 15 clear outs here (or “almost 15″), you probably need to rethink how you evaluate draws in light of prior action.

I disagree with the pro's apparently dismissive opinion of “Internet players”, though.   (To be fair, he may have been referring to cases like this where it really is more dubious, because you're not necessarily even money if the 3-bettor has a tight range.)   Sometimes it's correct to shove the chips in on a big draw.   A legit 15-outer is about even money, and Ed recently wrote that such big draws often do better to get the money in on the flop.

But the resulting swings aren't fun unless you just like gambling, I won't dispute that!

I ran some numbers too .. thinking of his likely hands and your chance to win:

A6 - 46%

A7/A3 - 73%

K6 -50%

AA - 36%

66/55/44 - 25%

other overpairs - 45 - 51%

Him having a diamond in his hand accounts for around -3% for you.

The BEST you could hope for is that he's on a straight draw with no diamond where you are 2.5:1.  I can't believe how poor the odds are .. I would have guess they were better.  Not much, but somewhat. 

I think this particular hand demonstrates poor fold equity pretty well.  What could he have that he would fold?  A6, K6, 88, 99, TT, *maybe* JJ or QQ or a weaker diamond draw.  If he's in with 2 other diamonds, then he will call and we're in good shape.  Otherwise, I think we're mostly up a creek.

I guess I will be folding more often in these spots.  Not always though