So basically SB had a combo draw, and BB had a 1-pair hand, which he turned into a retarded bluff. It is for sure tilting to find out, that we folded the winning hand to a donkey like this. But poker is a long term game, and if we run this situation 100 times against random opponents, folding AA on the flop is going to give us the best results.
Also people playing like BB in this hand might win a lot of small pots, but they will lose most of the big ones, and in the long run they will be big losers in the game. So its ok to let them bluff us now and then.
Moreover even in this situation, which was the absolute best case scenario, we still had less than 50% equity on the flop. So while calling would have been profitable 3-ways against their exact holdings, we did not give up a massive amount of chip EV by folding on the flop. And we preserved our stack, which is also important in tournaments.
So I still think, this was a good fold. But I would of course make a note on that BB player and not give it a lot of respect, next time I see him raise the flop. Apparently he is able to raise with any "piece of the board", but we had to see a showdown, before we could know, that this was the case.
Even in a freeroll we should assume, our opponents use a somewhat reasonable strategy, until we have actual proof of the opposite. Getting into a "oh its a freeroll, so I call" mentality will just create bad habits, as Jon Poker has already said.
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