06-23-06 [poker] - 1

06-23-06 [poker]

I've been thinking about short stacking with the Sklansky-Chubukov concept. The idea is that you can push all in and turn your cards face up and your move can still be profitable. Your opponents call with any cards that are good for the pot odds against you, they fold hands that aren't. Obviously if you shove AA they fold everything. If you shove AQ, they fold AJ, but can call with 22. This allows them to play perfectly, and yet it's still profitable in many situations because of how often they have to fold (and even when they do call, you're usually not in bad shape).

Now, obviously you're not actually exposing your cards when you push. You get AA and obviously push - they're going to call sometimes. When they do, they are making a mistake (in the true Fundamental Theorem of Poker sense - they're making a different play than they would if they could see your cards), and you get extra value. So, if you push only when Sklansky-Chubukov says you should, any time they make the play they *should* make (if they could see your cards) - you're still profitable, and often they will make other plays, and those just give you extra value.

The nice thing about this push is that it cannot possibly be wrong. It's gauranteed +EV. However, it may not be even close to the most +EV thing you can do. With a given hand where pushing is +EV by this measure, all that tells you is that you shouldn't fold it. You could push, but limping or making a smaller raise might be much more +EV.

Furthermore, there may be hands you can push that are not +EV by Sklansky-Chubukov, but are +EV in practice. For example, with a 20 BB stack, pushing AQo in this way is -EV because you are called by AK and any pair. In reality, it's much better, because your opponents can't see your exact cards. They will fold the baby pairs, which is good for you (more folds), and they might call with AJ.

In reality if you have some push range {PR} and they have some call range {CR}, you can optimize against each other, eg. you pick your pushes to be the most +EV things to push against their call range, and they pick what to call with based on your push range. The only thing we can say for sure is your push range is >= the Sklansky-Chubukov pushes.

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