Calling is the worst option here, that leaves us with shove or fold. So what kind of range is the SB raising here? A raise/fold line would be pretty awful imo - if villain is bad enough to be doing that, then obviously we should shove. However in my experience this is is a good but not great hand, like AJ+, 77-JJ - QQ-AA probably isn't raising 7bb's, they'd want more action. The problem with that range is he isn't folding that much to a shove, so we have to treat his raise like his shove. Against that range we're 60/40. The question is, with the BTN having almost no equity in the tournament, do we risk a ton of equity win a 60/40 edge? My instinct is to say no, but we should look at the math. This is where I'm kind of confused though, and I'm not sure which math is right, but I'm gonna try to look at it two ways.
So using a 50/30/20 distribution, the equity distribution is ~39/39/22 (we probably actually have more than this, because ICM overvalues short-stacks), and if we win the heads-up, our equity is 49% and the shorty's is 31% (again, we probably have more than that). You may notice that this doesn't add up to 100% - the reason is the guy in third accounts for 20% of the prize pool. This also means that if we lose, our equity is not zero - rather, it's 20%. So 60% of the time, we have 49% equity, and 40% of the time, we have 20% equity. On average then, this move has a value of 37.5% equity, which is a little less than the 39% we would have if we just folded our hand.
Here's the other way to look at it - sixty percent of the prize-pool has already been awarded (20% guaranteed to each person), so that means 40% of the prize pool is left to be awarded. When the next person gets KO'd, 20% more of the prize pool will be given out (10% more guaranteed to the two remaining players). So I believe this makes our model 75/25 now, which means we have ~47% of the equity. Then, if we win this, we get heads-up, and now we're playing for 100% of the remaining prize pool, so our equity when we win is going to be the amount of the total chips we have, or about 95%. So we're risking 47% to win another 48% (95-47). So we're basically getting 1:1 pot odds, but our win odds are 2:3, so that makes it a clear shove, and we should be shoving with 99+ and AK.
So I have no idea which way is right (or if either of them are right
), but one way tells us its a fold and one says it's a shove.
