Friday, September 07, 2007

More know you love it

Picking up from yesterday, it would appear that making an all-in move on any undercard flop with JJ in that situation was a break-even play at best.

Dustin, a commenter, pointed out that I failed to account for times when JJ will suck out on the turn or river in this situation, which will happen about 8 percent of the time. To fix this:

(.55 * -$140) + [.12 * (.92 * -$1,000)] + (.33 * $580) = -$77 - $110.40 + $191.40 = $4.

But even though we get a positive number, this equation still doesn't account for the times the LP player hits his hand and busts the JJ. So I still don't think this play is +EV.

It's interesting to note that this play becomes more favorable for the JJ player if he's playing a smaller stack, and worse when playing a bigger stack.

After all these calculations, I'm thinking that it might make more sense to make this play with QQ from the big blind against two raises. Personally, I don't like pushing all-in or 4-betting preflop with QQ unless I have a strong read, but I also hate folding what may be the best hand in this situation.

So let's run the same scenario with QQ, assuming that the QQ player in the big blind will cold call the reraise preflop, fold if an Ace or King flops, and push all in on any undercard board.

Six combinations of AA and KK will call and be way ahead, one combination of QQ will call and be tied for a $70 profit, while 44 combinations of AK (16), AQ (8), KQs (2), JJ (6), TT (6) and 99 (6) will fold. An Ace or King will flop about 40 percent of the time.

(.40 * -$140) + {[.60 * (6/51)] * -$920} + {[.60 * (1/51)] * $70} + {[.60 * (44/51)] * $580}= -$56 - $64.94 + $0.82 + $300.24 = $180.12

Again, this equation is flawed because it ignores the chance that the LP player will flop a big hand. But it's pretty amazing that QQ seems to do so well under these circumstances.

Based on this math, I believe that when there's a late position raiser and a small blind reraiser, calling with QQ and pushing any undercard flop is often the best play.

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