ok I probably should have folded before paying the $110, but after that, we're basically going to play a four way all-in and won't I win often enough to make it worth it?
bluff, I review this hand in episode 4 of the Steamin Steve Hand Review.
I don't believe you can really call that first $110 (from, was it, two players?).
Holding AT here, you are almost certainly dominated -- with all that raising and reraising, I would bet dollars to donuts that someone's got an ace AND has you outkicked. You'd actually have a better chance (not much better, but anyway...) holding something different -- even lower cards.
It's fun to watch that go down on the computer screen, though. But I definitely wouldn''t think you'd want to do that with real money!
By the time you have to call the first $110, you're down to around a 20% chance of winning (depending on the ranges you put your opponents on.), and there is even one more player left to act. If he jumps in, your equity is even lower. And even if the original raiser just calls, you're going to the flop out of position against three players who are all voluntarily putting in significant money. So I think your assessment is correct that you probably should have folded there, losing only your small blind.
I also think it would still have been a good fold to have bailed when the four-bet came back around to you. At that point, you don't really have the immediate pot odds to call. You don't have good implied odds because the stacks that are left behind are so small. If you get that miracle AAT flop, are you going to get paid enough, often enough, to justify the extra $400 risk. With nobody getting out, I think you have to tighten the ranges you give to the middle position and button players to be more like what you'd give the early player. That just drops your equity even further. As Think said above, you might be slightly better off with lower cards, since it is a strong possibility that the four of you are blocking some of each other's outs. I'd have to assume that at least one player has me dominated. And given the stack sizes, I'd also have to assume that the money is going in on the flop. And I am not going to be a huge fan of that on most flops.
Once you get to the flop and come up with the nut flush draw, I think it is fine to shove it in. You do, at that point, have enough equity to justify chasing the flush, since your risk is limited to $715 more.
So once you get to that point, you'll win enough times to justify the shove in the long run. However, you'll go broke trying to get to that point often enough to make the math work in your favor.
After posting my comments, I see that this hand was the subject of the latest Steamin' Steve hand review. We reach the same conclusions, but Steve, as usual, does a great job of breaking down the reasoning behind it.
I just read your analysis. Great minds think alike!