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If I knew short stack has pocket queen and deep stack will fold, is it profitable to go all in with Ace/King in the long run? Equity question here.
Very much so. Let's make some assumptions... first of all, let's say AKo vs QQ is 50/50... even though QQ is in reality slightly ahead, but it's obviously easier to calculate when we assume a coin flip.
Also, let's also assume the deep stack always reraises the shove with KK or AA. By making this assumption, we know when he calls the short's shove that we are never dominated, we are always at least 50% against him too.
We'll also assume no rake.
So... let's forget the deep stack called for just a minute. If everyone folded to the shove except for us, and we call, well we're 50-50 vs QQ. If we play the hand twice, we win one and lose one, we'll notice that our profit is $35... the blinds and the straddle, which we call "dead money". Likewise, the guy with QQ has made $35, since he had exactly the same equity as us (based on our assumed 50%). That's an average profit of $17.50 per hand.
Now, when someone calls, and then folds, that is also dead money. So this guy puts in $130, then faces a $900 shove. He hates life and folds. Thanks, that's an extra $130 every two hands we just won.
So you can see that by getting this guy to fold, we are printing money.
If we knew that the short stack would shove, and the loose deep stack would call, then limping AK was absolutely the perfect play, so long as we now reraise all in. But I doubt that's the case, since you say the short stack is tight. Therefore, we should be raising pre flop.
Only limp if you have a really good reason for doing so. Trying to see a cheap flop with AK is not a good reason to limp.
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