How My Son's Insight May Have Saved Poker

[Sherman]

[ QUOTE ]
The "non-people" side of poker isn't exactly rudimentary stuff. Anyone worth his salt can do some simple division to decide if he should fold his flush draw or not, sure. But analyzing patterns (I don't know, maybe you consider that "people"), calculating optimal bet amounts, and even doing regular pot odds against hand ranges isn't exactly simple stuff (even if there was no personal component). People wouldn't all basically do it optimally. To the extent that no two players are identically skilled at the people aspect, they're also not identically skilled at the math aspect.

But what you're saying is really just semantics. At least it seems so to me. Maybe two players aren't ever "exactly" the same, but that just depends on how you define it. If you had all of the world's poker results ever, surely you could find two players that for the most part proved themselves to be equally skilled. One might still be nano-tenths of a fraction better statistically, but so what? You can say that about anything that requires any reasonable skill.

The "people" aspect doesn't really make a difference. What's important is that poker is a complicated game that not everybody can play well. I agree with you about that.

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No matter how you define it though, no two people will ever have the same skills. Thus, in the long run (infinite trials) any two players playing heads-up one will come out the winner. This is critical to demonstrating that poker is a game of skill, and not of luck (though there certainly is a luck component involved).

I think we are in agreement, but not really sure. [img]/images/graemlins/smile.gif[/img]

[ALawPoker]

I'm not really sure either. I disagree with what you're saying but I agree with your point, heh. Basically, I think it's definitely theoretically possible that two players would be of the exact same skill. If you take two basketball players going one-on-one, it's possible (though yes, extremely unlikely) that they would be of such even skill so as to break even over infinitely many trials. However rare this is just depends how liberally you define equal. But theoretically it exists.

But yes, I agree that by proving players all have different expectations against each other you will be demonstrating that there must be skill involved.

[Daisydog]

[ QUOTE ]
Beyond this, in another post I indicated that skill level can be measured for all games based on two factors.

1) Variability in a person's outcome given infinite trials (Variability between people). This in and of itself is evidence for the existence of skill as stated above. The higher this variability the more skill involved in the game.

2) Variability in a given trial, or otherwise stated as the number of trials before a person's average outcome to be equivalent (or approximately equivalent) to his or her average outcome given infinite trials. This could also been known as variability within person's. The lower this variability the more skill involved in the game.

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I've been thinking of the skill/luck issue in a way that I think is the same thing you are saying. Specifically, for a game, the variation in individual outcomes, across all players and all trials can be broken down into two parts:
1. The variation among the players' mean outcomes (A)
2. The average variation of each players outcomes around his mean (B)

You could call A/(A+B) the degree to which skill is driving the outcome of the game. If I am understanding your post correctly, I am basically restating what you have already said.

By the way, this is basically the same thing that actuaries call "credibility" when experience rating insurance risks. It's also the r-squared.

Anyway, I've been doing some simulations in Turbo Texas Hold em and calculating these stats for various type of games (i.e., number of players and type of players) and based on the number of hands that is considered a "trial".

I also think this is somewhat simplistic for describing the amount of skill involved. I say this because I think a player's outcome around his own mean (quantity B from above) isn't due just to luck. Take Mike Matasow, for example. He might play very well one day and very poorly the next. This is not necessarily due to luck, but, rather, because there is something about him that makes him very inconsistent. In other words, sometimes he makes good decisions over a period of time and then has an extended period of time where his decisions are not as good. This would cause variation in his outcomes around his long-term mean that have nothing to do with luck.

I've got a bunch of other thoughts on this topic but it is getting too late. I'll try to post more later.

[Sherman]

[ QUOTE ]
[ QUOTE ]
Beyond this, in another post I indicated that skill level can be measured for all games based on two factors.

1) Variability in a person's outcome given infinite trials (Variability between people). This in and of itself is evidence for the existence of skill as stated above. The higher this variability the more skill involved in the game.

2) Variability in a given trial, or otherwise stated as the number of trials before a person's average outcome to be equivalent (or approximately equivalent) to his or her average outcome given infinite trials. This could also been known as variability within person's. The lower this variability the more skill involved in the game.

[/ QUOTE ]

I've been thinking of the skill/luck issue in a way that I think is the same thing you are saying. Specifically, for a game, the variation in individual outcomes, across all players and all trials can be broken down into two parts:
1. The variation among the players' mean outcomes (A)
2. The average variation of each players outcomes around his mean (B)

You could call A/(A+B) the degree to which skill is driving the outcome of the game. If I am understanding your post correctly, I am basically restating what you have already said.

By the way, this is basically the same thing that actuaries call "credibility" when experience rating insurance risks. It's also the r-squared.

Anyway, I've been doing some simulations in Turbo Texas Hold em and calculating these stats for various type of games (i.e., number of players and type of players) and based on the number of hands that is considered a "trial".

I also think this is somewhat simplistic for describing the amount of skill involved. I say this because I think a player's outcome around his own mean (quantity B from above) isn't due just to luck. Take Mike Matasow, for example. He might play very well one day and very poorly the next. This is not necessarily due to luck, but, rather, because there is something about him that makes him very inconsistent. In other words, sometimes he makes good decisions over a period of time and then has an extended period of time where his decisions are not as good. This would cause variation in his outcomes around his long-term mean that have nothing to do with luck.

I've got a bunch of other thoughts on this topic but it is getting too late. I'll try to post more later.

[/ QUOTE ]

I don't see how A/A+B is any different from what I termed the skill/luck ratio (factor 1 / factor 2 or in your terms A over B).

I prefer my method because I don't see how adding A to B makes it any more diagnostic of anything. If you are familiar with an Analysis of Variance (ANOVA) framework, what I am suggesting is a Random Effects ANOVA where each trial (hand) is considered random and each person (poker player) is treated as random.

The variance between players (MS Players) over variance within players (between trials) (MS Trials) can give someone a pretty good feel for the relative amount of variance between players to within.

I don't really care about inconsistency from one day to another b/c that is by definition factored in as within person variability.

Back to the ANOVA framework, a better analysis would probably include the interaction (Person X Trial) variance as important as well.

Thus, we could compute the relative variance between persons (MSpersons / MSpersons + MStrials + MSpersonXtrial) and the relative variance between trials (within persons) as (MStrials / MSpersons + MStrials + MSpersonXtrial). This is similar to what you were proposing however, I think computing the relative variance in this instance doesn't really gain us much.

R. Sherman
Ph. D. Student Personality/Social Psychology

[Daisydog]

[ QUOTE ]
I don't see how A/A+B is any different from what I termed the skill/luck ratio (factor 1 / factor 2 or in your terms A over B).

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The only difference is yours goes from 0 to infinity and mine goes from from 0 to 1. But this is just scaling. Conceptually, we are talking about the same thing, and I thought I already said that.

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I don't really care about inconsistency from one day to another b/c that is by definition factored in as within person variability.

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I believe this source of variation has nothing to do with luck. Therefore, I'm questioning whether it makes sense to define luck as the "within person variabiltiy". By doing so, we would be overstating the amount of luck in poker. The luck of the cards is not the only thing that causes "within person variability".

[Sherman]

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[ QUOTE ]
I don't see how A/A+B is any different from what I termed the skill/luck ratio (factor 1 / factor 2 or in your terms A over B).

[/ QUOTE ]

The only difference is yours goes from 0 to infinity and mine goes from from 0 to 1. But this is just scaling. Conceptually, we are talking about the same thing, and I thought I already said that.

[/ QUOTE ]

Ah...I see. You are right. It doesn't really matter. It may be easier to conceptualize the 0 to 1 ratio better anyhow. Hmm.

[ QUOTE ]
I don't really care about inconsistency from one day to another b/c that is by definition factored in as within person variability.

[ QUOTE ]
I believe this source of variation has nothing to do with luck. Therefore, I'm questioning whether it makes sense to define luck as the "within person variabiltiy". By doing so, we would be overstating the amount of luck in poker. The luck of the cards is not the only thing that causes "within person variability".

[/ QUOTE ]

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I don't define luck as within person variability though. That is one component of luck. I am defining luck (or skill depending on your perspective) as the ratio of between person variability over within person variability. Neither one alone is sufficient to define luck.

[SGspecial]

[ QUOTE ]
Loosing is easy everywhere. Just for a try, ask an addicted roulette player to loose very quickly a huge ammount of money in exchange for some reward. His job will be the easiest way ever to earn some cash.
Moreover, I find it more difficult to hastily loose at poker. I've experimented reckless plays and many of these times became chip leader and feared at the table.

Anyway, that point is not useless: it proves that will and skill has a certain reasonable influence over random events. Not only in poker, but even in roulette.
The greatest weakness of the luck factor is the long term variable: the probability accepts as possible something that will never happen: the fact that #9 will sometime occur 1987 times in a row. This will never happen even if the Universe would last forever and zillions of roulletes would ceaselessly spin.

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How can a roulette player guarantee losses by poor play? I think you've picked the one game where it really is impossible to make decisions that give you odds more than a trivial amount worse than playing in a perfect manner.

[J_B]

It would seem that in particular Golf is one of the sports with quite possibly the largest luck factor. In golf where you are standing in relation to the ball as well as the ball itself, temperature, and wind all play in as factors. I feel that if luck were not a significant factor, a golfer *should* be able to hit the ball to the same place in at least 2 out of 3 swings. We all know, this is nearly impossible. (assuming outdoor golf.)

However, a good poker player can gauantee the long term results of his game! How can Doyle win WSOP 2 years in a row. Not to mention many other good players winning for years and years.

There is also the Fundamental Theorom of Poker. Where is the Fundamental Theorm of Golf?

For as far as this goes, I do feel that we can lop poker into the same category as blackjack. Blackjack has been proven to NOT be a game of chance, but rather a game of skill!

I do hope that at some point someone will place the game of golf in comparison to poker in a court. I feel that this would prove our point that card games are games of skill and not chance. (or that golf and football are in fact games of chance.) I bring this up because in golf there are huge cash prizes for the players. These a certainly along the lines of gamboooooooling!

Keep in mind, the fact that a game is or is not profitable does not neccessarily mean it is or is not a game of chance. Roulette definately falls on the chance side. Craps can fall in there too. Card games, absolutely not. It can be proven that in ANY casino card game that there are optimal and non optimal ways to play. It is this very thing that makes these games of skill. Again, noting of course that an optimal play may still not be profitable, but will be more profitable than a suboptimal play.

[SGspecial]

[ QUOTE ]
It can be proven that in ANY casino card game that there are optimal and non optimal ways to play. It is this very thing that makes these games of skill. Again, noting of course that an optimal play may still not be profitable, but will be more profitable than a suboptimal play.

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I think this is the key to the current debate, which is really more about the legal status of poker vs. other casino type games which have now been heavily restricted. In any casino game vs. the house, there may be an optimal way to play but even playing this way will not give you positive expectation in the long run. Playing like an idiot or completely randomly won't either. The argument is that in poker games vs. other private players, you CAN gain positive expectation with greater skill, tho I guess that you'd have to show that it would outweight whatever rake or tourney fees you're paying to play.

Actually, years ago pro player Andy Bloch cut his teeth in poker by playing a game called 6-card Hickok against the HOUSE at Foxwoods. Apparently, some genius had invented the game but Andy found a strategy that actually gave the player +EV and played it for hours on end at a profit. Eventually, Foxwoods wised up and closed the game, but I guess this is an example of a casino game that really could be called a game of skill (even if played without card counting).

[Sherman]

[ QUOTE ]
It would seem that in particular Golf is one of the sports with quite possibly the largest luck factor. In golf where you are standing in relation to the ball as well as the ball itself, temperature, and wind all play in as factors. I feel that if luck were not a significant factor, a golfer *should* be able to hit the ball to the same place in at least 2 out of 3 swings. We all know, this is nearly impossible. (assuming outdoor golf.)

However, a good poker player can gauantee the long term results of his game! How can Doyle win WSOP 2 years in a row. Not to mention many other good players winning for years and years.

There is also the Fundamental Theorom of Poker. Where is the Fundamental Theorm of Golf?

For as far as this goes, I do feel that we can lop poker into the same category as blackjack. Blackjack has been proven to NOT be a game of chance, but rather a game of skill!

I do hope that at some point someone will place the game of golf in comparison to poker in a court. I feel that this would prove our point that card games are games of skill and not chance. (or that golf and football are in fact games of chance.) I bring this up because in golf there are huge cash prizes for the players. These a certainly along the lines of gamboooooooling!

Keep in mind, the fact that a game is or is not profitable does not neccessarily mean it is or is not a game of chance. Roulette definately falls on the chance side. Craps can fall in there too. Card games, absolutely not. It can be proven that in ANY casino card game that there are optimal and non optimal ways to play. It is this very thing that makes these games of skill. Again, noting of course that an optimal play may still not be profitable, but will be more profitable than a suboptimal play.

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While your ideas appear interesting, I find them to be absolute nonsense.

You mention Doyle winning two WSOP bracelets in a row. Ever heard of Tiger Woods winning four Majors in a row? How is that possible if golf is a game of luck?

Read my earlier posts. Golf is clearly a game of skill because there is variability in long-term individual results.

Regards,

R. Sherman
Ph. D. Student Personality/Social Psychology