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3. Why wouldn't you just push when he reraised you?

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Though it is probably not far from optimal strategy, personally I don’t like to put first place on coin flips, even when I am a clear favorite without a pair preflop (including AK).

I WANT FIRST PLACE.

My usual approach is pushing AA, KK preflop, at least a strong pair on flop; being QUITE sure it is very hard for upcoming cards to suck out on me.

The rest of the time, I try to grind my opponent down by 3bb bets.

Reading 2+2 though is changing my play. I am doing more pushing now.