I played my first set of STTs the other day, just 4 speed $11s (which were far too fast, not the blinds, just the constant beeping) and did pretty badly, got a 3rd place and didn't reach the money in the other three. Micro sample so fairly meaningless even at < -50% ROI. (I could already be a winning STT player snad not even know it

. It's just slightly more likely that I'm not if I play every one the same as those.)

Rather than leap back in the next day (with saner time controls) to I started thinking, as is my manner.

Everyone talks about the ICM so I thought about that. The lottery calculations are too complicated to perform mentally even for three players (and the ICM doesn't affect heads on the end), but a simple estimate should be possible. For the 50/30/20 distribution it seems that your equity in the remaining prize pool is between 1/n (equal share) and the fraction of the total chips you're holding (this is probably a sign of fair distribution), tending to be higher the more skewed the distribution of the remaining chips is. Okay, so how does this affect my decisions... not much really. Pretty marginal frankly.

I turned my attention to push or fold problems, 3 players remaining for simplicity (two is exactly equivalent to a cash game without the option of standing up until someone's broke, chip EV = $ EV). The only difference from a cash game here that initially struck me is that the chips you win as the short stack are of less value than the chips you already have and that knocking out a short stack is... probably more valuable than the chips you lose if he wins. Still not _really_ helping much, especially as other opponents are going to (mostly) be aware of this too, considered writing something to calculate something equivalent to S-C (unexploitable pushes, but using the ICM to calculate $EV this time) for various tournament situations and seeing how different it really is, but too much trouble. Somebody's probably already done it anyway and it'd be duplicated effort.

Then I thought of the third player and realised something which is probably obvious to all you tournament players but was an alien idea to me: he profited from his fold. It wasn't just neutral, he got a free chance at stepping up the prize ladder through the action between the other two. I thought about this some more and realised that folding is always +$EV in a tournament (although certainly not always the best option) and the looser your opponents, the more +$EV it is! (Okay, it's actually neutral in one case: your remaining opponents are colluding and won't play against each other, they'll also even up their stacks by chip dumping to keep their combined $EV highest.) Furthermore there's the "opportunity cost", but this may be partially offset by the reduction in $EV from position, which isn't taken into account by the ICM.

And furthermore, folding is, unless I'm mistaken, more +$EV for the short stack than the chip leader. Here I finally actually found some use for the ICM. The short stack has a low expectation so the free shot at moving up is of greater value, he was unlikely to do so otherwise. The chip leader's high stack $EV represents a better shot so he can be more aggressive as his fold EV is lower. The $EV of folding is probably proportional to... hmm... the sum of the $EV of all your opponents stacks?

Have I got this all right? Anything else different between cash games and tournaments?

(I also thought a little about calling an all in, perhaps the more important problem. Perhaps a good estimate of fold $EV will leave a simple way to calculate how much equity you need to call.)