What is the real impact of chip position on fold equity?

[ddubois]

I'm looking for something more quantitative and mathematical. I want to follow up this post by looking at the EV of pushing certain hands, using the EV spreadsheet (http://ddubois.bounceme.net/poker/OddsBets.xls) I started on in another thread. But to do that, I need a better ability to gauge fold equity; right now I have been accused of only considering hand evaluations when guessing at my fold equity and I think these accusers were very astute. (Yes, I know calling standards is player dependent as well. One step at a time.)

Assume for all scenarios UTG and BUTTON have middling stacks of 2000 and have folded to your SB. Assume for all questions 200/400 blinds.

Case 1) SB-HERO 1000, BB-VILLAN 5000
Case 2) SB-HERO 2000, BB-VILLAN 4000
Case 3) SB-HERO 3000, BB-VILLAN 3000
Case 4) SB-HERO 4000, BB-VILLAN 2000
Case 5) SB-HERO 5000, BB-VILLAN 1000

What range or percentage of hands will BB call with? For ease of comparison between different responses, I would prefer your answer come in the form of top5%, top10%, top25% (http://home.earthlink.net/~craighowald/data/matchup2.html), etc., but it's a free world and a free forum. /images/graemlins/smile.gif

I think everyone will agree the largest decreases of fold equity occur at the fringes. In #1 and #5, villan will call with a huge variety of stuff. But 2-4 I'm not so sure. So here are my off-the-cuff answers:

1) top 40%
2) top 15%
3) top 5%
4) top 10%
5) top 40%

[CrisBrown]

Hi ddubois,

I don't think you can separate steal equity from player reads, because steal equity is probably the most player-dependent element of an overall equity estimate. While stack size is certainly one element in steal equity, what you need more is an accurate player-stack read, i.e.: how will this player respond to this stack situation? I'm just not sure that a player-independent model will help you all that much. But I could be wrong. /images/graemlins/smile.gif

Cris

[tallstack]

Maybe you could look at this from the point of view of what should the Villain call with? I will assume that your chip levels are prior to putting in the blinds. With 200/400 blinds the pot odds for Villain to call would be:

Case 1) SB-HERO 1000, BB-VILLAN 5000 - Pot Odds 1400:600 or 2.33:1
Case 2) SB-HERO 2000, BB-VILLAN 4000 - Pot Odds 2400:1600 or 1.5:1
Case 3) SB-HERO 3000, BB-VILLAN 3000 - Pot Odds 3400:2600 or 1.31:1
Case 4) SB-HERO 4000, BB-VILLAN 2000 - Pot Odds 2400:1600 or 1.5:1
Case 5) SB-HERO 5000, BB-VILLAN 1000 - Pot Odds 1400:600 or 2.33:1

You could look at what fraction of hands you would push with in each scenario and then see how many hands in that category would be correct for the Villain to call with (assuming pot odds were the only justification for the call, or maybe by using the ICM). It wouldn't be perfect, but it would be a start.

In your first example, say you might push with 70% of hands (your estimate may be different than mine here). Given the chart for 67% of hands, the Villain would be getting the correct pot odds to call you with any two. In the third example, if you would push with the top 25% of hands (again your numbers may be very different) then the Villain would be getting correct pot odds to call you with approximately the top 10%.

Of course, you will have opponents who call too much, and those who call too little, but it might give you some guideline of a reasonable call frequency.

Dave S

[ddubois]

You could look at what fraction of hands you would push with in each scenario and then see how many hands in that category would be correct for the Villain to call with

This is circular - what fraction of hands it's correct for me to push with depends on what fraction of hands my opponent will call with.

I know player reads and my table image are important, but I think we should be able to come up with some eduacated guesses for the average opponent. Even relative numbers would be intersting, i.e., is villan more likely to call when I have 4k to his 2k, or 2k to his 4k? I think the latter?

I would still like to see some estimates.

[tallstack]

[ QUOTE ]
This is circular - what fraction of hands it's correct for me to push with depends on what fraction of hands my opponent will call with.


[/ QUOTE ]

It is circular, no doubt. You are in effect saying that you can't decide what fraction of hands to push with unless you know how your opponents will call, and I am saying they will call based on how often they think you will push. But if you assume that your opponents have their eyes open then they will adjust to your aggressiveness as you will to theirs. It pretty much has to be circular. There is still a large likelihood that this will converge to a solution.

You get to act first in all of these situations, so the best your opponent can do is formulate a calling threshold to counteract your push. If both you and your opponent are playing the situation as best as possible, then it should converge to a case where you are both making a correct decision (especially with the high blinds here).

For example, in situation 1 the more you push the more likely that he should call you with any two. If it is still possible that your equity goes up even when he calls with any two, then you can raise with that percentage of hands, or increase the percentage of push hands until your equity no longer increases. I haven't done this, but I believe that it will converge. In the other cases, the push and call frequencies will be lower, but you should find some stable range where you are both making the correct decision, and that would be a good start for the Villain's call frequency.

Dave S

[PrayingMantis]

Your ideas here are interesting in essence, however...

[ QUOTE ]
but I think we should be able to come up with some eduacated guesses for the average opponent.

[/ QUOTE ]

I have never met the "avarage opponent". But you're not the only one who tries to solve theoretic poker problems with such a problematic term (IMO). David Sklansky was using quite frequently the term "typical opponent". But to tell you the truth, I don't think this animal exists. This game (and especially tournament poker) is so much situational and players' dependant, that psychology is a huge factor in it. And by psychology I don't mean the stuff you can learn at university, but the real person-to-person, minute to minute, real life behaviour.

That's why I find simulations so problematic in regard to real poker. Sometimes they give you some interesting resuls (like the great ones eastbay is doing), but it is still extremely far from the interaction between human beings at the table. And as you know, humans are very far from acting in a "rational" way, especially when it comes to gambling. And it is gambling.

And even if you succeed in getting to some very rough numbers, in some simulation or mathematic analysis, beating (or crushing, for that matter) SNGs is so much about those endless marginal situations, that without a strong "feel" of the situation, you won't be able to achieve it. And by "feel" I don't mean some mystic thing, but your whole understanding, poker knowledge, expirience, reads, strategic reasoning, specific last hands of this specific SNG, and so on and on, all of these _together_. The problem is, you can't simulate, or calculate this "feel".

But I'm really interested to see if you come up with some interesting results. I hope you will. /images/graemlins/smile.gif

[gergery]

First to comment on your post
1) top 40% - I agree
2) top 15% - I’d say top 10%
3) top 5% - I’d say between top 5 and top 10%
4) top 10% - top 15%
5) top 40% - top 67%

Interesting. My gut-feel answers indicate that I’m more willing to call with a shortstack. Probably because I put the bigstack on a wider range of hands as a bully. By contrast, I’m less willing to call as a bigstack, probably because I don’t want to give up that advantage lightly, and I have more time to assess his play/get read, make right call.

Per tallstack’s point, you can work this backward. For example:
Case 1) If you’re getting 2.33 to 1, and you (dubois) recommend calling with top 40% of hands per your first post, then the bottom of the top 40% range of hands are holdings like Q5s, T9s, JTo. Which are all about a 1.8 or 2.1 to 1 underdog vs. say, the top 10% of hands. Which means that you have correct odds to call even if your opponent is only pushing with the top 10% of hands here. But a shortstacked Hero in SB would push a much greater range of holdings than that, I think.

So the conclusion here is that you are correct to call with a much wider range of holdings than you (or I) indicated above, IF you cared only about Chip EV, and were looking just at this one hand in isolation.

The fact that you had a tighter range indicates that you want a bit of an insurance premium on this (ie. you don’t want to call as a 1.8 to 1 underdog getting 2.3 to 1 on your money – you actually seem to want a larger premium, ie. you want to be only a 1.4 to 1 underdog getting 2.3 to 1). This also seems to hold true for the other scenarios tho I haven’t done the math out completely. Alternatively, it might be a way to calculate exactly how much folding equity is worth – the overlay you pass up here is the value you ascribe to your folding equity on future hands.

Interesting post dubois. This seems to indicate to me that I should be more willing to call my opponent with a wider range of holdings.

--Greg