Reraising with AJs (is Cris crazy)?

[CrisBrown]

Hi All,

I know some of you will read my reply to M.B.E. in the "leak" thread, where I said that AJs isn't a bad reraising hand, and think I've completely lost my marbles. Some of you will think I lost my marbles a long time ago, and the more astute will realize I never had any to begin with ... but anyway....

Okay ... here's my math on it:

The situation is this: you and Opponent have roughly equal stacks (we'll call it 5x each). Assume Opponent is a good NL tournament player, familiar with the Gap Concept (either explicitly or intuitively), etc. Opponent open-raises for about 20% of his chips (x). You have AJs.

If you push-in, you estimate that he will fold about 50% of the time, although he knows YOU know the Gap Concept, so he may (occasionally) call you with a slightly weaker hand (such as ATs, KQs, QJs). AJs will win or chop about 33% of the time against KK, QQ, JJ, AK, and AQ, and about 67% of the time against the weaker hands he'd call with. (There is only a negligible chance that he has AA, as you have an Ace.) Put it all together, and you figure you'll win about 40% of the time when he calls.

So ...

* If you fold, your EV=0. (Obvious.)
* If you reraise, then:
-- 50% of the time he folds, and you win x.
-- 20% of the time he calls, and you win 5x.
-- 30% of the time he calls, and you lose 5x (and bust).

Your EV for reraising is .5(x) + .2(5x) - .3(5x), or .5x + 1x - 1.5x = 0.

So reraising with AJs, in this situation, is a break-even situation, just like folding. Obviously, the better play is to fold, because reraising carries a 30% risk of ruin. But reraising isn't quite as dreadful as it seems at first peek.

Cris

[M.B.E.]

Cris, if AJs reraises all-in, I don't think it will win the hand 40% of the time it is called. 30% would be more accurate.

That said, I think it's fine to reraise all-in with AJ in many situations, especially when you're in the blind and there is a very good chance (say 65% or better) that the original raiser will fold.

Also, in your example from the other thread, you said the player had AJo, not AJs.

[CrisBrown]

Hiya M.B.E.,

Some random sample hands:

cards %win %lose %tie
As Js 32.29 67.33 0.38
Kc Kd 67.33 32.29 0.38

cards %win %lose %tie
As Js 31.48 68.06 0.46
Qs Qc 68.06 31.48 0.46

cards %win %lose %tie
As Js 26.88 68.90 4.22
Ac Kc 68.90 26.88 4.22

cards %win %lose %tie
As Js 26.54 68.17 5.29
Ac Qc 68.17 26.54 5.29

cards %win %lose %tie
As Js 33.68 64.66 1.66
Jc Jd 64.66 33.68 1.66

cards %win %lose %tie
As Js 58.02 41.48 0.50
Kc Qc 41.48 58.02 0.50

Note that AJs will win or chop about one-third of the time vs. KK, QQ, JJ, AK, and AQ. I was surprised, as I thought all of those would be much bigger favorites. It's usually a ~7:6 underdog to lower pairs, a ~3:2 favorite over hands like KQs. Combining all of those -- weighted by the probability of Opponent having and calling with each -- is how I got the figure of roughly 40%.

Cris

[M.B.E.]

KQs probably will fold to an all-in raise.