Re: I hope this one is harder!
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you're almost never ahead here, the best would be if someone has K-Q and you were able to convince them you had an Ace by pushing.
check it down and hope that they all had under pairs and yours is the biggest.
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How often does it get checked down all the way 3 handed?
If you shove this and it is folded 50% of the time, then it is profitable. I don't like a shove, I like a bet of 500 and then proceed from there.
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If you push and win the pot, you gain 1900 chips. If you pauh and get called, by one player, you have about an 18% chance of winning the hand. 1900 - .18 x 5700 = 870. So if you get everyone to fold 35% of the time it is profitable compared to folding. Now you probably have some positive expectation by checking, so you may need more like 45% folds for pushing to be better than checking. So it is may be close between pushing and checking.
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