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Took a 3-game shot at the $11 4-man SnG's, won 1, lost 2, so I'm positive. But I have certainly found HU players who are as good as I am, and some who are better. So it's back the $6 game to learn more pokerz before I take serious shot.
Been thinking about ICM, and (duh) realizing it doesn't apply in HU. Not even in HU MTT's. Should have been obvious, I know. But there's a skill difference that matters.
I searched for ICM and found a thread about "ICM corrected by skill difference" which I can't find again (dammit - I knew I should have book-marked it). But the theory is simple enough: shift some chips from the less skillful to the more skill players before applying the ICM mathematics. Of course, for more skill difference, more chips are shifted.
And this math result feels worthless, but I'm exhausted. So I think I will post it and see if I can start poking holes in it later. If you're still reading, thanks!! Let me know what value this could have - or not have.
So that works for HU. Suppose I play BJaust HU, and let's just suppose he has a 2 to 1 skill advantage. If we played thirty times, he would win 20. So to perform ICM style calculations taking skill difference into account, we could first shift chips from one stack to the other.
In the BJ vs. Robb 2 to 1 skill difference example, we could compare 1500 chip starting stacks. Shift 500 chips from my stack to his, so the 2k vs. 1k chip stacks reflect the portion of the final prize money BJ is expected to win.
So the math is obvious for starting stacks, but what if BJ is evaluating a all-in call with JTs holding a 2 to 1 chip advantage along with a 2 to 1 skill advantage? We can do ICM style analysis if we can develop a formula for shifting chips to have the resulting stacks reflect percentage chance to win.
Of course, there's no real way to decide if it's useful until we do it. The formula should work at the margins: if BJ has 2900 and I have 100, the formula should still work. And vice versa. And in the end, it should lead to useful analysis. So let me offer this idea.
For the 2 to 1 chip advantage, take a fraction of chips from the worse player's stack and add it to the better player's stack. The fraction is
( 2 - 1 ) / ( 2 + 1 ) = 1 / 3
For the start of a match, it works. I have 1500, so we deduct 1500 * 1/3 = 500 and give them to BJ, so we have the 2k vs 1k stacks like we needed. Now, what if BJ has 1800 and I have 1200? Well, just deduct one third of my stack: 1200 * 1/3 = 400, so BJ's expectation can be based on a 2200 to 800 ratio, so he'd be a 5.5 to 1 favorite with only a 3 to 2 advantage in chips. If I had a 2250 vs 750 chip lead, we'd take 1/3 * 2250 = 1500, so BJ would have break-even chances as long he still had 750 chips in his stack. (This also presumes that the blinds are still small enough that BJ doesn't have to revert to push/fold and can exploit his full skill differential.)
So, back the JTs question. If BJ has a 2 to 1 chip lead and a 2 to 1 skill difference, should he call my all-in? Suppose blinds are 25/50. BJ posts the t50 BB, and I push. If BJ folds, he has 1950 and I have 1050. Adjusting for SD, take 1/3 * 1050 = 350, so BJ's equity advantage is 2300 to 700.
Suppose in this situation, I would push Axs, KJs+, KQ, and any pp (just trying to get a halfway decent range and keep things simple). Then BJ stoves it and finds he's got 40% equity against that range. If he goes all-in then 40% of the time he wins the whole match, and 60% of the times he ends up losing t1,000. Now, the stacks are reversed. So the unadjusted equity is 3,000 * .4 + 1,000 *.6 = 1,200 + 600 = 1,800. Shift a third of my chips over to BJ to find his SD-adjusted equity of 2,200.
So BJ should (by this yet-to-be-validate model) fold JTs and play his 2300 to 700 AD-adjusted equity. If he has AJo, his Stove equity would be 48% against the same range, so the EV for calling would be 3,000 * .48 + 1,000 *.52 = 1,440 + 520 = 1,960. Then adjusting for SD would mean taking 1/3 * 1,040 = 348 chips, and shifting them, which would come out almost identical to folding. So calling vs. folding is breakeven for AJo.
Now, I'm not sure that any of this is meaningful, or will lead anywhere. I just wanted to post it so others could critique as they see fit, and so that I could get the ideas down on "paper" so I can work on some endgame scenarios and see if it can be helpful in assessing calling in push/fold scenarios or, likewise, deciding what range to push/fold ourselves.
I do know this - if I have a skill advantage, I need to be much more conservative about getting all the chips in. Coin flips favor those likely to lose.
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