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Rather than analyze your play, let me ask a question. Post flop, if you had bet between .75 and 1.5 times the pot and then had been re-raised, would you have been able to lay the aces down?
If the answer is no, then pushing was the right move for you.
For me, I try to give the other guy at least a little bit of credit for calling my preflop 4xBB raise with something. I agree that any 3 was unlikely (although I would have considered that a loose player had called with A3s). Hell the pair of tens was unlikely too, but there it was and it cost you your stack. If you had bet the pot (or there about) and he had nothing, he probably folds. If you push all in and he has nothing, he probably folds also. Same result, much less risk.
Not a criticism, just a different perpective.
Other side of the same coin:
I played a hand just this morning that went like this:
Me 10 10
Him ??
I raise preflop from SB to $2.00
He calls and has position on me.
FLop is J 10 4 (rainbow)
I check
He checks
Turn is A (my greatest wish come true)
I check
He goes all in (yeah!)
I sit for a second and try to figure what he has, my logic is:
He must be on one of 2 hands
AK, AQ
I discount AJ and A 10 because I think he would have bet the flop since he would have hit TPTK.
I discount a pair bigger than my tens because I think he would have raised me back preflop with JJ - AA
I discount a pair smaller than my tens becuase I think the 3 over cards on the board make it unlikely.
I call and the river turns a blank. He shows A 8.
I wonder what he thought I might have. Why not bet the pot instead of pushing in $28? Sheesh. Thank god for these people.
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