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From SNGPT:
The KQ hand with the BB calling anytwo yeilds an EV of -3.1% not exactly what I would call a clear push.

The KT hand comes down to whether the BB will call as often as he should give the pot odds he is getting. If he will call with only Any Pair/Any Ace any Broadway then it is basically breakeven ICM-wise which is good enough for me in a spot like this. But that range has him calling about 20% of the time and I just don't see this guy folding 4 times out of 5. Certainly looking back on it, it was probably my best chance to do something.

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He won't call with any two.. look

Seat 6: HERO ( $1120 )
Seat 5: BB ( $2870 )

Thus BB has 2470 as he's put 400 into the blind. To call your push is virtually half his stack.. do you really think he does this just because of pot odds? Unless he's a donk, then he would realise it's -$EV despite being +chipEV to do so.

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I'd call with probably half my hands or more there. I don't consider myself a donk.