Sats and fuzzy maths

I played the online IWF sat last night and came close again, 13th, 9 tickets.

A weird hand with 18 left: I have just over average stack at this point, so I'm in reasonable enough shape and know a doubleup and I almost certainly snag a ticket. Blinds are 800/1500 and I have just over 20K. I pick up pocket Kings in the hijack and think this could be it.

Utg raises to 5000. I check the HUD and see this is the first hand he's played in 32 since he moved to the table and my gut reaction is uh oh, aces. It comes around to me, I agonise over a decision until the clock runs down and then fold.

Afterwards, I thought this was horribly nittish and a couple of others players agreed. Obviously in a normal tournament I snap shove, but satellites are different. After I busted out (shoving A6 from the SB into A10 in the BB) I wanted my kings back, but after going through the hand and the maths with the brother, it seems it's actually a correct fold, at least theoretically.

At the time, my fold was based on
(a) strong possibility that the guy has aces. It's at least 25% of his range and maybe as much as 35%
(b) I estimated my chances of a ticket at approximately 60% if I folded
(c) I figured if I shoved I was probably only getting called by aces, and since he covered me, 4 times out of 5 I'm out

I think his range here is Aces, kings, queens, ace king. But even if I broaden it to jacks, it turns out that the fold is correct under ICM.

Here's a summary of the math:
(1) My estimate of my equity (60%) at that point is pretty much spot on: when you do the math it turns out to be 60.3%
(2) My estimate that if I shove, get called, and win, I'd have 90% equity is also pretty close (actual figure is 90.8%)
(3) If I get called and lose, my equity drops to 0% obviously, since he covers me
(4) If I assume his range is JJ+, AK, then AA is 26% of his range. So 26% of the time, he calls with his Aces. Of this, I'll suck out about 5% of the time for an equity gain of 30%, and lose 60% the other 21% of the time. Overall loss of equity from this scenario is 11.1%
(5) If he has KK (just over 4% of the time), he probably calls and we chop the blinds for an equity increase of 5%. Since this only happens 4% of the time, this scenario is 0.2% +EV overall
(6) If he calls with JJ, QQ or AK, I win 76% of the time, lose 24%. This happens 70% of the time (assuming for simplicity he doesn't fold), so a 30% gain in equity happens 53% of the time (overall), and a 60% loss the other 17%. Overall gain in equity from this scenario is 5.7%
(7) If he folds, I gain 10% equity. So even if we assume he folds all his weaker hands, this represents an equity gain of 7% overall.

Since (4) minus (5) is greater than either (6) or (7), then it's a correct fold regardless of whether he folds or calls with hands weaker than KK. Folding is 3.9% better in overall EV terms if he folds all weaker hands, and 5.2% better if he calls.

Obviously in a normal tournament where the prize pool is weighted towards the big prizes, folding would be a huge mistake, but in a satellite at this point, it's theoretically correct.

Incidentally, I'm pretty sure my opponents call with A10 in my exit hand was a clear theoretical mistake although I haven't done the maths.

I was intending to play the super sat tonight but after talking it over with herself, she persuaded me it's best to give it a miss and just buy in directly if I'm in a state to play tomorrow. The foot swelling is coming down, they still won't fit in shoes, but another 24 hours might do the trick. The other factor is that even if I played the sat and won a ticket, I might be dog tired the next day and not at my best, so I'm buying in to a 500 plus tournament for the first time since Drogheda.

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