Posted by Dr Fro 3:22 PM
I promised a post about middle-ish pairs getting re-raised, inspired by a hand against Adam. The facts below have been changed from what happened a week ago, but the conclusion is the same.

Assume everyone starts with $300.
Adam has 99 UTG
BB=$2, SB =$1.
He raises to $12 and gets re-raised to $75, so it is $63 to call.

He has 3 options:

Option 1: Fold
Since all money invested so far is a sunk cost, the EV of this option is exactly $0.

Option 2: Call
This is a bad option and I will first say that the reason why is the best case scenario is to be about a coin toss. Several possible hands are huge favortites. I seriously doubt A9 or 88 or lower would be making this move.

The math:
Assuming the only hands to re-raise here are AA, KK, QQ, JJ, TT, AK, AQ, AJ (see footnote below). The first 4 can be made in 6 possible ways making 24 hands. The last 3 hands can be made 16 ways for 48 possible hands. So 24/72 hands dominate you (19% chance of Adam winning) and 48/72 hands are a coin flip (52% chance of Adam winning).
52%*$90 + 48%*(-$63) * 48/72 +
19%*$90 + 81%*(-$63) * 24/72
= an EV of -$0.27.

Of course, that is all pot odds, not implied odds, which are much more difficult to calculate. The fact that Adam is out of position only hurts the case for calling. So far, folding looks better than calling. What about a raise?

Option 3: Raise
First assume he pushes all in for $288 and gets a call. The math is:
52%*$315 + 48%*(-$288) * 48/72 +
19%*$315 + 81%*(-$288) * 24/72
= an EV of -$40.77.

That doesn't sound very good. Ahhh, but what if Adam's opponent folds, giving Adam fold equity? He wins $90.

Now if Adam thinks that he will get a fold 31% of the time, this is a break even proposition. It seems to me quite reasonable that he would get a fold > 31% of the time. Maybe only AA, KK, QQ call...that would mean 75% of the hands would fold. Even if his opponent is quite loose, it still seems pretty reasonable to expect him to fold more than 31% of the time.

Conclusion:
Don't call. Fold or Re-raise all-in. Adam was probably right to not re-raise me because I am known to stand my ground (to a fault) and thus he may think he gets a fold < 31% of the time.

Footnote:
I know people will take all sorts of exceptions to the above analysis, including the range of hands I selected. However, 2 points should be noted: 1) The above assumptions are consistent with the play in the games in which I play and 2) tweaking the assumptions doesn't change the main conclusion that calling is wrong, wrong, wrong.

4 Comment(s):

Posted by  Anonymous, at 2:21 PM, June 19, 2005  

I like your thought process Fro.

One correction and one observation.

First, the correction: there are 30 possible overpair hands out - (AA, KK, QQ, JJ, TT) * 6 = 30 not 24.

This changes the rest of the calculations, which result in a 37% fold rate necessary to make reraising all-in +EV compared to folding:

Call EV
19% * 603 * 30/78 +
52% * 603 * 48/78 = $237.03 average stack if you go all in and Villain calls.

Stack if you go all in and Villain folds = $378

37% * 378 + 63% * 237.03 = $289.19, which is $1.19 +EV compared to folding (which results in stack of $288).

So, Villain needs to fold at least 37% of the time to make pushing +EV. If Villain will call with AA, KK and AK, then that's 28/78 hands, or 36%. Very close call.

Now the observation: calling out of position with the intent of going all in on the flop no matter what is an option. It's called a "stop and go" play, coined by Greg Raymer, and it's not always "wrong, wrong, wrong."

It works better than pushing preflop when your stack is smaller and you don't have ANY fold equity by pushing all-in preflop. In this case, for example if your stack was $150 and facing a $75 bet, a stop and go would be a much better play than pushing all-in, because Villain won't fold anything getting 3:1 preflop.

The stop and go creates fold equity on the flop when you have the best hand (ie 99 v AK and no A or K flops), and when a scare card hits (ie 99 v. JJ but an Ace flops).

Binions

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Posted by  Dr Fro, at 3:13 PM, June 19, 2005  

Thanks for the correction...

FWIW, I originally did the calc on TT (which is what Adam told me later that he held) which gives you 24 higher pairs. I forgot to change that part of the math.

It seems that Stop and Go increases the chance of getting the fold you would like and for less money. I'll look into it...

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Posted by  Anonymous, at 9:44 AM, June 20, 2005  

Well said, Morris.

I didn't challenge the assumptions of hand range, because Fro said not to for the purpose of the math exercise.

I will say that you are either going to be a small favorite (v. overcards) or a big dog (v. overpair) to the $75 raiser, and that's generally a situation you want to avoid.

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Posted by  Dr Fro, at 11:03 AM, June 20, 2005  

Thus, Adam was right to fold.

A bit of game theory:

I knew my reraise indicated more strenght than I actually had. I figured Adam would be smart enough to fold, which is the biggest reason I reraised. To a more foolish player, I would maybe not reraise.

If he called, I am 50/50, with position. Not bad for me.

If he reraised, then I figure he is only holding AA, KK. An easy fold for me.

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