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In hindsight, I think you are right @TaylorMaas that a call would be better than a 3-bet. However, my thinking was that the raise would cause Button to fold out some of his unsuited broadway cards (KQ, KJ, KT, QJ, QT, JT) and some aces (AT, A9, A8, A7, etc.). Postflop would be challenging if an overcard comes on the flop against this particular opponent. Although I don’t like the idea of being 3-handed after the flop with TT, if the BB did make the call, the Button would likely call the additional 6bb as well and we essentially have 2 hands vs. 1 to eliminate the short stack.
To be clear about my statement about wanting to get the BB heads up for all his chips, that was a hope, not a strategy with my 3-bet. The sizing of the 3-bet was going to be close to his chip stack anyway, so I just gave him the option to be all in with two over cards. If he calls and then the Button shoves, it is an easy fold.
The truth is, I just didn’t consider that the Button would shove over the top of my 3-bet with how deep we were…It was a great play, and I will definitely keep this one in the memory bank for similar spots in the future.