Re: NL25 KK
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I said push and pray. There's two whole cards in the deck that will convince us that we're strong enough to call/bet if we check this flop. You're basically folding a 3/1 pot if you're saying wait and see, because you're just not going to catch up. It's just... not going to happen. If you really don't think there's at least a 25% chance he's got QQ/JJ, you've got the sickest read on villain in the history of 25nl. Both stacks are very short; do you really think he doesn't call anything without an ace?
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Firstly, I don't think the point is that we're trying to catch up by checking. The point is because of our pot-odds all our chips are going in regardless of turn (we never fold this hand), doesn't matter if it helps us, him or neither of us..
With your second point, I think the thing is given he has JJ/QQ (or other hands we beat), the amount of times he calls our shove is much less than the amount of times he shoves to our check (+ calls our turn shove), thus a check is more +EV
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