RANDOM thoughts

[gumpzilla]

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I agree wholeheartedly. One would have to adopt an equity model to do these strict calculations...ICM should work very, very well here

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Now this is where my argument is. I agree that ICM probably does work very well here. That said, what is our justification for using ICM? We do not have proof that the results of ICM correspond to true tournament equity, and I think it's actually pretty obvious that it can't, since it leaves out so much information.

That said, most 2+2 STT regulars will agree that we should trust ICM. Why? Because it seems to mesh well with the advice of good, respected players. Why do we think those players are good? Because they win, ultimately. My argument is that if one says a good method for figuring out who is good at tournaments is to see how many mistakes they make, you need to talk about mistakes compared to what. And whether it's another good player or a mathematical model, it ultimately needs to be grounded in winning. I don't really see how you can talk about a player as being good if they are a long-term loser.

Irie's original point - that given large populations, even over pretty long stretches you'll find people who aren't so great doing well - is a good one, and is the reason why people make so much noise about sample size for looking at your ROI. But to go from there to saying that "statistical analysis of results is a horrible method of evaluating the skill level of a player" is a stretch, in my opinion. Practically, looking at their game and seeing how they play will be a faster method, but that's only because we have people whose opinions on how to play tend to be backed up by results, i.e. winning. And combining the two - looking at thought processes while getting some kind of short/middle-term statistical information - is better still, in my opinion.

EDIT: I also still think that the perfect information stipulation is kind of bogus. We don't have that kind of information in a game, and it's definitely possible to make moves that look correct from that standpoint that are wrong according to what we were thinking in a game, and vice versa. For an obviously extreme example of what I'm talking about, say I raise with JJ PF and somebody pushes over me, leaving me with 3:2 odds. Let's say that I put them on QQ-AA, AK. Calling here if I put them on that range is pretty bad, but let's say I do it anyway and they turn over 83. I've made a pretty gross series of mistakes - putting them on a range that is way too tight, calling against a range I shouldn't - but in Perfect Information land I look like a genius.

[GrekeHaus]

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Now this is where my argument is. I agree that ICM probably does work very well here. That said, what is our justification for using ICM? We do not have proof that the results of ICM correspond to true tournament equity, and I think it's actually pretty obvious that it can't, since it leaves out so much information.

That said, most 2+2 STT regulars will agree that we should trust ICM. Why? Because it seems to mesh well with the advice of good, respected players. Why do we think those players are good? Because they win, ultimately.

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The reason people trust ICM is because of it's base in a solid mathematical foundation. It starts with the assumption that if two players of equal skill are heads up, each person's chance of winning is in direct correlation with the number of chips he has (an assumption that has recently been challenged but is probably relatively accurate). From there, we are able to calculate the approximate percentage of times that each players will finish in each position and hence, determine his expect percentage of the prize pool. Its limitations seem to lie in the fact that it doesn't account for differences in skill level or strategical advantages gained or lost by having a chip stack of different sizes. For something like SNGs however, this model seems to be relatively accurate and a good general indicator of whether or not you should call or raise in a given situation. Mason Malmuth gives an example of how to do a simple version of these calculations in Gambling Theory and Other Topics.

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EDIT: I also still think that the perfect information stipulation is kind of bogus. We don't have that kind of information in a game, and it's definitely possible to make moves that look correct from that standpoint that are wrong according to what we were thinking in a game, and vice versa. For an obviously extreme example of what I'm talking about, say I raise with JJ PF and somebody pushes over me, leaving me with 3:2 odds. Let's say that I put them on QQ-AA, AK. Calling here if I put them on that range is pretty bad, but let's say I do it anyway and they turn over 83. I've made a pretty gross series of mistakes - putting them on a range that is way too tight, calling against a range I shouldn't - but in Perfect Information land I look like a genius.

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The point you seem to be making has to do with a strategical notion of mistake rather than a mathematical one. A sound strategy in any poker game is one that will minimize your own mathematical mistakes while maximizing your opponents mathematical mistakes.

In the example where you have KK UTG and you open push 5xBB. You know at the moment you push that you're making a mathematical mistake if any of your opponents hold AA. However, you are making the correct play in all other circumstances, so you're willing to live with the shortcoming of your strategy because you know that its pros outweight its cons much more than in a strategy where for instance you open fold KK every time you get it.

In the above example you give, your opponent is trying to make a mistake by raising which will force you to make a bigger mistake by folding the best hand most of the time. Of course, if you actually do fold here and your opponent flips over 83o, then you realize that there was a shortcoming in your strategy because of the fact that you failed to accurately assess the situation. Of course, if you feel that your opponent will only make a play like this every million hands and the rest of the time he actually will have AK or QQ+, then your strategy is fine. If he's making this play half the time, your strategy is terrible because it is forcing you to make mathematical blunder after mathematical blunder.

Even if you're going to talk about the strategical notion of a mistake, it still all comes down to math.

[gumpzilla]

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For something like SNGs however, this model seems to be relatively accurate

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I think that this statement implicity suggests "because it suggests winning play," which ties in with results again. There are mathematical underpinnings for ICM, but it is an approximation and much more open to question than doing similar calculations in cash games, obviously.

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The point you seem to be making has to do with a strategical notion of mistake rather than a mathematical one.

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Well, yes, because strategical mistakes are what's relevant to determining whether or not you're playing well.

Expanding the math further in the KK example, when you take into account how rarely he'll have AA, it becomes clear that it would be a mathematical mistake not to push. I dislike using the term mistake to mean "he turned over AA" and the like because it suggests that the play was wrong. If you push with KK in that situation, you're not making a mathematical mistake - you're theoretically gaining x BB, occasionally winning more and occasionally losing to AA, but on average there's some gain.

[The Yugoslavian]

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I don't really see how you can talk about a player as being good if they are a long-term loser.


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If they are making profitable decisions..then yes, they'd still be a good player.

Some of the players who actually have very good stats will have a much different skill level. So, some of these players will actually be good, some will be ok, and a few will actually be bad. This is just the beginning of the problem when interpreting posted stats....I have no beef with the stats themselves (even though it may seem like I do sometimes), they just are what they are. However, I find that the ones public on this forum are *very* problematic, to the point of actually being close to worthless.

I'd much rather look at HHs from players in order to gauge their skill level than look at a snapshot of their stats.

Yugoslav

[gumpzilla]

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If they are making profitable decisions..then yes, they'd still be a good player.

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Profitable decisions will eventually correspond to results, if you play long enough (otherwise how are we showing profit?). Obviously luck is a huge factor, and it takes a while, but if you play 5000 SNGs and are at an ROI of -20%, the odds of you actually being a winning/good player are very, very poor. At the very least your game selection would need some work.

[GrekeHaus]

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If they are making profitable decisions..then yes, they'd still be a good player.

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Profitable decisions will eventually correspond to results, if you play long enough (otherwise how are we showing profit?). Obviously luck is a huge factor, and it takes a while, but if you play 5000 SNGs and are at an ROI of -20%, the odds of you actually being a winning/good player are very, very poor. At the very least your game selection would need some work.

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Right. This is at the heart of what Irie and Yugo are trying to get at. It's highly unlikely that a player with a -20% ROI after 5,000 SNGs is a winning player. However, when was the last time you read a post saying "Here are the results for my last 5,000 SNGs"?

Of course, part of the problem with assessing your play based on statistics is that you will very rarely have a large enough sample size to do so. Even if you do, a sample size that large will take a while to accumulate. During that time, the players in your game will be changing and your game might be improving or degenerating. So even if you have an ROI of 20% after your first 5,000 SNGs, it doesn't mean that you're currently playing at a 20% ROI clip or even that you're currently playing winning poker.

[gumpzilla]

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Right. This is at the heart of what Irie and Yugo are trying to get at. It's highly unlikely that a player with a -20% ROI after 5,000 SNGs is a winning player. However, when was the last time you read a post saying "Here are the results for my last 5,000 SNGs"?

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You don't see those, no. But, then again, how often do you see people who haven't already established themselves as good players get a favorable response to "Here's my ROI after 500 SNGs"? I think people are generally reasonably aware of the sample size issue when dealing with unknowns.

[PrayingMantis]

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I'd much rather look at HHs from players in order to gauge their skill level than look at a snapshot of their stats.

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I agree completely. But that doesn't minimize the significance of the data one can find in _big_ sample size stats (results, that is).

Anyway, I think it is a very interesting theroetical discussion, that is getting to different paths from the issues discussed in the OP. It has a lot to do with the big question of being / not being "results oriented": we hate and despise "results oriented" thinking in this game, but we just can't ignore the fact that "results oriented" thinking has still a lot to do with the ability of any player to learn and improve. So it's kind of a paradox, that I'm always thinking about.

[The Yugoslavian]

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I agree completely. But that doesn't minimize the significance of the data one can fine in _big_ sample size stats (results, that is).

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Yeah, I just don't trust almost any of the stats posted on this site in measuring a player's ability. It's very hard for me to look at posted statistical results as a useful guideline in any way. I'd rather look at HHs.

I definitely agree that having a fairly large to large data sample is a good thing. This is why I'm finally back to keeping my STT stats. [img]/images/graemlins/wink.gif[/img]. Besides, I believe I got everything I could out of not keeping stats. It wasn't the true obstacle of my growth as a poker player.

Yugoslav

[Moonsugar]

Read the book a few years ago. It is good.

As long as you are reading financial books, there are some books by behavioral economists that will blow away (or confirm) your ideas on the average person's risk acceptance v. risk aversion. News flash: People are dumb! Thaler, et. al.