Some Heuristics and a Question to the Forum

[HesseJam]

Yesterday I thought about dynamics in SnGs, ie., how the result of a current hand influences future EVs.

Bear with me this is going to be a bit complicated and perhaps hypothetical. The example:

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Observation from like 10K bubble hands:

PS 15+1, 4 Players (Bubble) Level 300/600 + 50 Ante.

If you are in BB and have the biggest stack they will fold to your BB in 29.7% of the cases.

If you are in BB and have the 3rd biggest stack they will fold to your BB only in 14.2% of the cases.
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Rewind:

One hand earlier, you had been UTG and thought about pushing. You suspect that BB might call a lot since he is the smallest stack. The stacks are close enough, however, that if you lose to BB your stack will drop to rank 3.
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Calculation:

Let's assume for the moment that you would fold atc when you are in the BB (makes the calculation easier and illustrates the isolated effect):

cEV (after posting) when you are in BB as stack No 1: 29.7% x 1100 chips= +327 chips = 2.4% of all chips.

cEV when you are in BB as stack No 1: 14.2% x 1100 chips= +157 chips = 1.2% of all chips.

delta cEV between No 1 and No 3 stack scenario = 170 chips = 1.2% of total chips.

Let's be lazy here and convert 1.2% cEV into 0.6% EV.
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Rewind again to the UTG hand:

I go back to my UTG hand and put into SnG the calling ranges ranges and my hole cards. I yield an EV of +0.5%. I also see that I will lose roughly 25% of the time because I will be coinflipping about 50% of the time.

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Question:

Is it correct to account for the effect that if you lose you will forego an additional EV of 0.6% because they will fold around less => there is an additional EV tax of 25% x 0.6% = 0.15% on the UTG decision?


Those who made it this far might wonder wtf the relevance is. The relevance is that so far I have looked only at one single element of a future hand. There are many more and the effects add up. I estimate that there are certain spots where all the effects might add up to +/- 1% EV or even more. Knowing these spots would be quite valuable, IMO.

What do you think?

[Roland32]

I think I followed your thought process here and I agree. This is something I have always done, I belief that the value of the chip lead regardless as to % of chips is undervalued in ICM. I think this is also a huge reason why those out there who taught themselves soley through sngpt have so much trouble with 5-7 players left and why some otherwise winning players have negative values at certain levels.

Are we speaking of the same concept?

[HesseJam]

The concept is more general and deals with dynamics at large. The example here deals with the value of having the chip lead and it is probably not a coincidence why I took it because I suspect that dynamic effects are more pronounced there than at other scenarios.

Staying with the issue of having the chip lead, it has also the reverse effect that if you are at 3rd stack postion and a push might propell you into first you might consider pushing at lower EVs.

[microbet]

Do your 29.7% and 14.2% figures come from your actual data or are they hypothetical?

As far as the number .6% at the end, I think one of the biggest problems is that you don't differentiate stack sizes at all in the fold around percentages. I'm sure there is a difference between being a slight big stack and being far and away the big stack.

In this particular case I agree that there can sometimes be some effect, but it won't often be large. If a particular steal or fold won't change your stack rank, it won't make much difference and if it does change your stack rank then, in most cases, there won't be significant separation between stacks.

[skipperbob]

A Thoughtful SnG'er/2+2'er [img]/images/graemlins/crazy.gif[/img]Just WoW [img]/images/graemlins/blush.gif[/img]

[djames]

How did you convert cEV of 1.2% to $EV of 0.6%? The cEV I get since you only need your stack and the expected value of the chips resulting from the play to derive 1.2%, but, to calculate $EV you need the stacks of everyone, no?

I didn't follow your example that well, but I assume you're trying to value any particular elements not incorporated into ICM, such as ability to bully, blinds coming around, skill, etc. That your plan?

If you're able to be precise enough to measure these affects in isolation, you can't just add them up as they are likely not independent. I would think more intuitive arguments for including these affects to further ICM are more valuable (at least at the moment) than precise ones. If the board could ever agree on how to intuitively include these effects into a new model, perhaps that could further ICM. To my knowledge this is still a very open problem.

[microbet]

The example is really an adjustment to blind discounting. Perhaps if you do blind discounting in some situation, big stacks should have less blind discounting than small stacks.

The other, and counter, effect that hasn't been much talked about in terms of ICM is the possible added/or subtracted equity involved in passing up a push and letting other stacks tangle. People may forget that you can lose equity if two later stacks tangle and end up with less of a disparity in chips, such as when shorty doubles through big stack.

The main problem, imho, is that except in some unusual and yet easily apparent situations, the effect on equity calculations is small compared to the error in assigning ranges.

[kevkev60614]

A few more thoughts on the pile:
1) You have to factor in the probability that you don't get called by BB, alone. BTN or SB could call, or you could get multiple callers. It could get folded around. I know you've already thought of all this, but assuming that your push will get called by BB alone might be a crazy assumption.
2) If BB is so short that he's almost definitely going to call your push, he's almost definitely going to push next hand, anyway, so your 29.7% is probably a pipe dream.
3) Maybe it's being folded to you in the BB as the bigstack so frequently because you're pushbotting correctly and you look like a maniac. Changing your strategy to find a greater edge could make both edges disappear.

Still, I like where your head's at. And maybe given this information there are cases in which we should fold where ICM has a push as greater EV. I dunno. But we should always be cognizant of likely future EV situations when making the current decision.

[Sparta45]

OP, I only skimmed your post because to read it word for word would make my brain explode.

But I think I understand your general idea and I agree with you. Nice post.

[Sparta45]

Also, to whatever extent I understand Gigabet's stack sizes post, I think what you are referring to is sort of like a first cousin to what Giga was referring to.

IMO anyway.