[ChrisV]

[ QUOTE ]
If i understood you correctly, you would prefer playing back with 1200, because if you get called and lose you lost only 1200 whereas if you resteal the pot the result would be the same.

I would be more happy to play with 2000 because if I get called and I win, I win 2000. If I lose the result would be the same (bust).

[/ QUOTE ]

This has much the same flaw as taking coinflips for big stacks: it hurts you more to lose than it helps you to double up.

In the situation where it's you and the villain with 2000 chips each and 5 other stacks with 1200, here's your fold, successful resteal, and double through equities:

Fold: 0.1825
Resteal: 0.2169
Double through: 0.3163

A successful resteal increases your equity by 18.85%. Doubling through increases your equity by 73.32%.

Same stacks, except you have 1200 and it's one of the other stacks with 2000:

Fold: 0.115
Resteal: 0.1499
Double through: 0.2197

Here restealing increases equity by 30.35% and doubling through by a gigantic 91.04%. Therefore you should be much more willing to resteal with 1200 (making percentage comparisons is correct, since this takes into account what is being put at risk to achieve the gain).

[ QUOTE ]
OTH, with A9s , I would be somewhat less likely to play back with 2000 than with 1200. But if I do as you propose and increase hand strength so that I would play back no matter what, I sure preferred playing with as much as possible up to the amount of villain's stack.

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That's not quite what I meant. I meant if you aren't willing to play back with A9s at all, ever, then pick a better example for yourself.

There comes a point at which you'd actually prefer them to call than fold to your reraise. At that point, it's a value raise rather than a resteal. But that point comes later for 2000 chips than for 1200 chips (because of the reduced equity gain of a double through). And at all points before that, when it's a true resteal, you should be preferring to resteal with the smaller stack.

EDIT: Just a couple more things:

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If I lose the result would be the same (bust).

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This is your mistake. The result "bust" isn't the same each time any more than the result "double up" is the same each time. You lose more equity when you bust with a bigger stack.

Also, in the maths above I'm ignoring the fact that a bigger reraise causes your opponent to fold a bit more often. I don't believe this affects the conclusion for a couple of reasons.

Firstly the subset of hands which your opponent might do different things on is small compared to the subset of true steal hands (like QJ) where he always folds.

Secondly, if you do get called, doubling up gives you a bigger equity gain with the small stack than the big one. This cushions the blow of getting called a bit more often.