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Ehm, I really didn't mean to give you any shit here man. This is actually my way of honestly trying to discuss what you said, without any ad hominem actions or degrading ideas in mind. And I didn't see any 4:1 anywhere, I saw you say $45 into a $90 pot.. when I see this, people usually have the misconception to think 1/2 here.. if you however (correctly) read this as 1:2 or 1/3, then it's all good yes.
And eh, I did discuss the topic. If you have 22, against 32 hands (AK) you have 52% to win. Against 36 hands (AA/KK/QQ) you're the 17.5% dog. So your expected chance to win in this model would be:
(32/68)(52%)+(36/68)(17.5%)=24.4%+9.2%= roughly 1/3. So just about what you put in the pot.
But the difficulty, as I said, is that in the 22vsAK scenario, you win most of it when you both hit nothing and your 22 pair is the highest hand. But in a realistic scenario, it's rather difficult to judge whether your opp hit something or not. This leads to the sort of situation where he will only call your raises with a better hand, and fold with a lesser hand. This is a bad position to be in..
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