[adanthar]

Most of this came out of a talk I had with a friend today and from a few posts in MTT's I made last month. The reasoning is scattered, and I want to set it down on paper and bounce it off people so I can see how much of it is worth refining.

The value of a stack: It's a given that on the bubble, short stacks are worth more than their chips. It is also a given that a big stack that is playing correctly is also worth more than his chips, due to his pushbotting any two. (If the other guys are morons and will call a pushbot, his stack is correspondingly worth less, but that just gives all the EV from the play to the short stacks.) So, the corollary to this is that medium stacks, even played correctly, are worth less than their chips.

There are some funky implications from this. One is the obvious one about taking close gambles midgame. Another is the 'Gigablock' idea that even a -EV play can be good if the result when you win is a big stack and a loss does not take you below everyone else. Another logical conclusion is that when a big stack raises a medium stack, the medium stack does not lose as much EV as the chips say by folding. There's some other things in there I want to play around with when I get bored later, too.

But the problem with the math is that if everyone plays correctly, the big stack will feed the short stack and starve the medium stacks. How do you overcome that, other than by being dealt aces a lot? I'm not sure of where I am going with this, but I think there's a solution somewhere. One thing that I'm thinking is that, when the big stack does occasionally fold, the medium stack becomes the effective big stack and can bully some himself.

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Bubble v. ITM: The bubble payout is 50/30/20/0. This leads to lots and lots of situations that get posted very often where the big stack raises, shortie folds and you autofold QQ or something because the EV of folding is too high. Fine. But there is actually another bubble ITM - when it's 3 handed, 60% of the money is taken off the table and the payout effectively becomes 30/10/0. Why don't we have a bunch of 'ITM fold' posts? Part of the answer is that the payout ladder is much steeper ITM, but that's not all of it because there is obviously still a benefit to finishing second.

Let's examine the $ value of your chips for a second, assuming this setup in a $100 SNG:
4 handed, 250/500: UTG - 500, you (button) - 2500, SB - 2000, BB - 5000

Here, ICM says your chips are worth $287. Now let's say UTG goes all in, you fold, and BB eliminates him:

3 handed, 250/500: you - 2500 (before posting), button - 2000, SB - 5500

ICM now says that, blinds aside, your chips are worth $112 of the remaining $400 in the prize pool, a $175 difference from before. I'm pretty sure that the reason that it's not the full $200 is that you gained $25 in equity solely from the fourth player's elimination.

Now let's assume that thanks to a bunch of split pots, blind steals and other stuff, the big stack eliminates the SB with you still at 2500 chips. Obviously, your stack will now be worth $50 of the remaining 200. That's a $62 drop, when it should be $100; you gain...1.5 times more in $ equity from removing the third player as from the fourth player (although it's less when expressed as a percentage of the prize pool).

Although I could very well be totally wrong and I'm not sure where to go from here, my suspicion is that the missing equity means you need its equivalent in cEV overlay to make an otherwise even money push. The conclusion is that when you are the middle of three stacks, we're all playing a little too loosely 3 handed (and the corollary that *having* a big stack is more important than most of us thought because the benefits of bullying extend to ITM.)

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Extending ICM to 5 handed play: For similar reasons, it doesn't make much sense that most people that are playing '2+2 style' suddenly tighten up a lot 4 handed while playing a much more normal game 5 or 6 handed. There should be a way to extend it to all similar situations with big/small stacks and adjust accordingly. Most of the better players do it intuitively, but I would like to know what the exact math is.

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A bubble System: I've been too lazy to adjust that robotic 10+1 bubble point system to actually make real sense, but the fact that I got that far in 30 minutes shows the proof of concept. I think I'll do it at some point as practice and then bounce ICM scenarios off it until it works; I believe only a few hours separate it from being 95% accurate.

Anyone want to comment on any of this?