Re: Is this a terrrible play or am I a big dummy?
The question is whether or not BB gets more $EV from the increased chance of you busting out if he calls and checks down versus pushing the SB out and increasing his chances of winning the pot. Without doing any math on it, I've gotta think the 2200 (Edit-- actually 2500 with the BB, 25%... even better) chips in the pot -- 22% of the chips in play -- is worth more than the gain in $EV he'll have from the increased probability you'll bust out. Especially with a hand like AK, which is probably way ahead of your hand range (and it was in this instance). Intuitively, I wouldn't do this with anything worse than AK though, since when he makes this play and loses he's now the short stack.
I think this is close though even with AK, and may be worth doing ICM on (I'm actually curious how close it is).
Oh, and for future instances like this, don't be a table coach, and DEFINITELY don't direct players who disagree with you to 2+2 to prove your points (I realize you didn't do the latter, but don't follow the lead of the player who did).
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