Some math that's supposed to help me figure out SNGs

[kamrann]

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If you need 3 3rd place finishes to make up for one heads up finish, you'd be willing to call with a hand that's a 3-1 dog, because you're getting an overlay.

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This is where you're going wrong, you don't need 3 3rd places to make up for one heads up. What you did wrong is you used expected profit in your calculations rather than expected payout. The $22 you invested is no longer yours, it's part of the prize pool. Using the payouts, you get E(3rd) = $40, E(HU) = ($100 + $60) * 0.5 = $80. So E(HU) = 2 * E(3rd). So 2 3rd places equates to 1 Heads Up, therefore you need to be even odds to make a call a break even play, as you'd expect.

In reality, due to the overlay of the blinds, it should be correct, by ICM, to call here as slightly less than 50%. I'm not sure why this doesn't quite fit with your calculations.

[pergesu]

According to what you said, you need to finish 3rd twice to make up for a single first place finish, so you can be at worst a 2-1 dog to make this break even.

[kamrann]

Yeah, I messed up. It's a bit confusing. But basically it's to do with what Freudian said about the remaining payouts. You're all guaranteed 3rd place money, so you're playing for 60/20/0. As such it doesn't make sense to apply any sort of valuation to finishing third, because it currently has zero value. I've just woke up and my head isn't working too well. I'll have a think about it...

[kamrann]

Yep, it's pretty simple really. The decisions you make at this point are based on making money from your current situation, which means finishing 2nd or 1st. If it was winner take all, then forgetting the overlay of the blinds you would call with 50%+ favourite hands, since if you were 50% to double up/bust in the case your equity doesn't change. 0.5 * E(3rd) + 0.5 * E(HU) = 1/4 of the prizepool, since E(3rd) = 0 and E(HU) = 1/2 the prizepool. And this is the same equity you already have with 1/4 of the chips.

What I forgot before was the payput structure affects this. With a 60/20/0, doubling up does not quite double your equity, so you need more than just 50% to make a call correct.

Go here and play around with the stacks with the payouts adjusted to 0.75, 0.25, 0. That should help you understand the situation better.