Re: heads-up battle
Check-Raise on the end.
You cannot 3-bet the river since he's already announce a few times he has at least a big pair, and when you bet into him on the river you are saying you can beat AA, so you can expect him to just call (thus my advise to check-raise the river). 3-betting the river looked hopeless to me, especially since he's going to 4-bet with the now likely big flush.
I notice that the information you got confirming he had "a big pair" didn't do you any good since you called on the turn with your 1 or 2 (or actually zero) out hand anyway. If you figure to call him down anyway, perhaps just go into check-call mode on the flop.
- Louie
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