More on Hand Combos

Every poker player has been in this spot before: A late position player raises, and you get dealt a monster like KK and raise it up from the small blind. The big blind and late position player both call. When rags flop, you continuation bet, and the big blind pushes all in. The late position player folds, and you need to decide what to do.

Sure the big blind could have flopped a set, but you can't always fold because you're afraid of a hidden set on a somewhat uncoordinated board. It's more likely that the big blind is pushing an overpair like JJ, and you call and take his stack. A set would usually smooth call or put in a smaller raise.

So if I'm holding KK, I'm going to call most of the time unless I have a read or a feeling that someone is overbetting their set for value.

But what about from the big blind's perspective? Sure he'll lose when I have AA, KK or QQ, but he'll win any time I was raising preflop and continuation betting with AK, AQ, KQs, JJ, TT or 99, which is a pretty accurate list of my 3-betting range from the small blind (except for times when I'm making a play, but let's not delve into that).

I want to find out if it's possible that the big blind is right to push with a hand like JJ, knowing that he'll lose to a higher overpair but also knowing I'll fold lots of hands that he beats. Using hand ranges and EV calculations, I'm going to dissect this kind of hand.

Here's the hand:

5/10
Hero posts small blind $5
Villain posts big blind $10
Villain has $1,000, Hero has him covered
*** Dealing down cards ***
Hero is dealt Ks Kc
Villain is dealt Js, Jd
LP raises $45
Hero raises $140
BB calls $135
LP calls $100
Pot: $420
*** Dealing Flop *** [ 2s, 6h, 7c ]
Hero bets $300
Villain is all-in for $860.
LP folds.
Hero calls all-in for $560.
*** Dealing Turn *** [ 6d ]
*** Dealing River *** [ Qs ]
Hero wins $2,140 with two pairs, Kings and Sixes.

Let's assume that the big blind will push all in on any undercard flop and I will call 100 percent of the time with AA, KK and QQ. Let's also assume that I'll fold AK, AQ, KQs, JJ, TT and 99 100 percent of the time. Up until the point the Villain goes all in, there are many times when I would have played that range identically, as well as had a strong read on him that he had a hand like JJ.

AA, KK and QQ add up to 18 possible combinations that have my opponent slaughtered (6 combinations of each).

AK, AQ, KQs, JJ, TT and 99 add up to 16+16+4+1+6+6 combinations, which equals 49 hand combinations that I'll fold.

If my math is right (and it may be totally wrong, in which case I would appreciate being corrected):

There's a 27 percent chance (18/67) that my opponent will lose his stack by making this play, and a 73 percent chance (49/67) that he'll win what's already in the pot.

.27 * -$1,000 = -$-270
.73 * $580 ($140+$140+$300)= $423.40
EV = $153.40

This initial calculation makes it look like this is a profitable play to make with JJ.

But wait. What about those times that an A, K or Q flops, and the JJ has to fold to a continuation bet? I did the math for this once before, and the odds of any one of any three cards flopping is 55.3 percent. That means there's a 55 percent chance that my opponent will lose what's already invested in this pot, if we assume he folds 100 percent of the time an overcard flops:

.55 * -$140 = -$77

And he'll push the other 45 percent of the time (12 percent of the which he gets busted [.45 * .27], and 33 percent on the time he'll win what's already in the pot [.45 * .73]):

.12 * -$1,000 = -$120
.33 * $580 = $191.40

Grand Total:

-$77 - $120 + $191.40 = -$5.60.

So it would appear that given this range, calling from the big blind with JJ and the intent of making this play will lose you money in the long run, but not much -- only $5.60 on average -- as long as the LP player folds (which may be a big "if").

I'm not going to do the math all over again right now, but I would think widening the SB's hand range and changing the BB's holding to QQ would be enough to put this play into +EV territory.

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For a different hand combo example, here's an old 2+2 hand that I referred to in the last post's comments: 3/6 Set Kings turn play.