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pokerfanatic

03-06-2006, 11:45 PM Post subject: PokerFanatic's "Proof"

#1 (permalink)

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Hands, Time, or Human as primary varable for a PT Sample

Warning:
This "proof" is super long...
This has some thinking that you my or my not completely understand… It also consists of a lot of math terminology. I’m going to try and be as precise and clear as possible, so here we go...

Introduction:
This is an idea that Time or Hands are a primary factor of a sample size on how accurate the win rate is in the long run. I have heard that more hands you play the bettor, I have also thought that possibly time was important because of outside forces that one day you wont go on tilt for more then a small size of hands if you play 1k hands a week v 10k hands a week. Thus I decided to do prove that hands and time are parallel to each other and the Human is the “X” factor upon resulting hands and time is in fact the primary variable. When I say variable I mean Factor on how the function’s graph will look.

The “X” Factor is just the forces on the math that a Human will impose on a given function that will change the curse of the curve of that given function. For example, take the integral of 1/(x^2) it’s a smooth convergent function but take the integral of something like (1/(x^7))*sqrt(sin(x^3*16x)) it gets fucking ugly In a hurry.

The Proof Material:
Lets say Player A plays 10/20 6max, for 40 hours a week (6 day work week), plays 3 tables at all times. So Player A plays approximately 83 hands per hour per table for about 250 hands an hour, so 10k hands a week. He is a 1bb/100 winner over this sample, which will work out to be one month

Player B plays 10/20 6max as well, for 20 hours a week (6 day work week), Player B also plays 3 tables at all times. So Player B also plays the exact same amount of hands as Player A. However it takes Player B double the amount of time to play the hands. Player B is also a 2bb/100 winner over the same sample of hands. Though, the hands are played over 2 months instead of one month.

For reasoning purposes we will make the assumption that both players had the exact same starting cards and the exact same boards with the particular hand. We will also make the assumption that mathematically they both played the hands correctly. If this is the case why is Player B 2bb/100 winner where Player A is only a 1bb/100 winner?

Well, most of us will draw the conclusion Player B plays bettor or ran bettor then Player A, but I ruled that out they played the same hands the exact same way, so this conclusion can’t be accurate. So what is the X factor? What is the difference between Player A and Player B?

Well let’s break it down some:
a) Identical databases: hands, boards are same, sample size, math correct, ect.
Thus it is no longer the conclusion it was variance

b) Actually we can even say it’s a clone of the same player…
Thus one doesn’t play bettor then the other.

c) Both players play 10/20 6max, 3 tables, ect.
Thus we conclude that the difference is time per day
However, that’s only short term difference.
They are in long term equilibrium as Hands  infinity and Time  lifetime

Hands graphed over Time for Player A will look shorter. Player B has Player A’s data however stretched out over more time. Therefore, I can then conclude that the hands and time are parallel to each other. So I can say that Hands played rather then Time as a variable is inaccurate. Hands = Time, when taking the limits as each go to respected their respected lengths, ALL players will have the same sample sizes.

Conclusion:
So, I have to make the conclusion the “X” factor in this sample size are the Players. They determine, how many hands they put in, over a short term sample size however over the lifetime they will become equal compared to any other players hand sample. For example, Player A plays about 30k hands a month or 360k hands a year where Player B plays 360k hands in 2 years… Lets say Player A quits poker After one Year, and Player B keeps Playing For another Year, there hand samples become equilibrium, so I can say that as long as you don’t have an idea when each player will quit thus ending there hand sample sizes, they can only be equal in the long term by taking the limits of time and hands to infinity.

Humans as the tool of poker even when math is correct that doesn’t make it the correct play… Player A could have easily called down and been correct to do so on a few hands where Player B could have made a bettor play that was also supported by the math and it was the more +EV play. I also never said they had the same opponents did I? This is an outside factor as well wouldn’t you agree?

The point I am trying to make is that Hands is not the primary variable in a sample size, nor is time, Hands = Time in the long run!!! The difference between the two players is the Human “X” Factor!!!

Therefore, a sample size of 100k v 10k sure statically speaking 100k is a much bettor sample, but this is STILL short term thinking!!! So really to me 100k hands as a sample can give a decent estimate for win rates and 10k can do the same estimate as well only difference is the amounts of time they were played in and the human factor. Because the Difference in hands you have a difference in Time or in some cases visa versa.

So, really we could take an error estimate to the functions of Player A and Player B and my guess would be that it’s within +/- 3% of short term expectation. Take that same example of the integration problem of 1/(x^2) form 1 to infinity, you will get the answer to be 1. How can this be so you are finding the area of infinitely many terms? Well, look at the graph once you get out to 500k. Take the integral of same function from 500k to infinity, you will still get 1!!! The point I’m making is the fact this function never ends unless you force it to end, same goes for Hands, Time my be on a different portion of the tracks from hands for various players but they are still parallel and eventually congruent.

Now that I have gone though this I don’t think there is any debate about Hands v Time, because in the long run they are equal between Player A and Player B, we are only looking at short term samples in the first place, and forecasting a long term expectation.

Let me give one last example, a recreational player plays 10k hands in a year and runs fucking great for these 10k hands, there is nothing saying that over the next year he wont run fucking great again, or run bad, the math is fixed but how he plays the math and plays his various opponents then it’s completely reasonable that he will never run bad over his poker career.

What we know as correct mathematics is actually a bell curve that will give you the best results against a RANDOM opponent, however we also know that we change our play from a correct mathematical average that we all have memorized based on reads and previous plays of a PERTICULAR opponent. So we can’t say that when all things are ruled out as shown above that Hands or Time are the primary variables on a samples sizes curve, the human “X” factor is.

I encourage you to give your thoughts on this or even attempt to contradict this proof, regards PokerFanatic.

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elipsesjeff

03-07-2006, 12:20 AM

#2 (permalink)

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Points of weakness:

Quote:

For reasoning purposes we will make the assumption that both players had the exact same starting cards and the exact same boards with the particular hand. We will also make the assumption that mathematically they both played the hands correctly. If this is the case why is Player B 2bb/100 winner where Player A is only a 1bb/100 winner?

IF both players had the exact same starting cards and the exact same boards with the particular hands and they were both played correctly, then it is IMPOSSIBLE for Player B to have a higher winrate than Player A. Any reasons for this difference would not be attributed to the players, but to the opponents they played against. If you argued they were both against the same opponents that played the same way, then it doesn't make any sense at all how one player could have a higher winrate than the other.

Quote:

So, I have to make the conclusion the “X” factor in this sample size are the Players. They determine, how many hands they put in, over a short term sample size however over the lifetime they will become equal compared to any other players hand sample.

So, what you are saying is that the amount of money people make is dependant on the number of hands they played? hmm....

Quote:

Therefore, a sample size of 100k v 10k sure statically speaking 100k is a much bettor sample, but this is STILL short term thinking!!! So really to me 100k hands as a sample can give a decent estimate for win rates and 10k can do the same estimate as well only difference is the amounts of time they were played in and the human factor. Because the Difference in hands you have a difference in Time or in some cases visa versa.

The problem with your sample is that the 10k hand sample is a biased portion. It would be reasonable if your 10k hand sample was taken randomly throughout the entire person's lifetime, then compared to see if he were a winning player. But, the 10k hand samples we obtain are biased by short-term variance.

Quote:

Now that I have gone though this I don’t think there is any debate about Hands v Time, because in the long run they are equal between Player A and Player B, we are only looking at short term samples in the first place, and forecasting a long term expectation.

Hands cannot equal time, at least not in the sense you are using. Hands are equal to time*tables*hands per table per time. So, if you are saying that time is also equal to time*tables*hands per table per time then okay, but this is nothing new.

The amount of money won is a function, f(hands,position,opponent play, your play) You cant control how your opponents play but you can control how many hands you play, how you play and your position. Any attempt to prove that this isn't the case doesn't make sense (unless i missed some variables).

I suggest you take a statistics course that goes into detail on populations and sampling.

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|~|ypermegachi

03-07-2006, 12:32 AM

#3 (permalink)

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your use of infinity is flawed. if we take every human that ever existed on Earth, plus all the aliens in the universe, and added up all the hands they ever played, it's not even close to infinity.

pokerfanatic

03-07-2006, 02:27 AM

#4 (permalink)

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Quote:

Originally Posted by |~|ypermegachi

your use of infinity is flawed. if we take every human that ever existed on Earth, plus all the aliens in the universe, and added up all the hands they ever played, it's not even close to infinity.

do you know when you're gonna die? or quit poker, that's why i used infinity the total number of hands played over a lifetime can not be diffined UNTIL the player stops playing all together...

euphoricism

03-07-2006, 02:38 AM

#5 (permalink)

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Yeah Jeff hit it --

Quote:

Lets say Player A plays 10/20 6max, for 40 hours a week (6 day work week), plays 3 tables at all times. So Player A plays approximately 83 hands per hour per table for about 250 hands an hour, so 10k hands a week. He is a 1bb/100 winner over this sample, which will work out to be one month

Player B plays 10/20 6max as well, for 20 hours a week (6 day work week), Player B also plays 3 tables at all times. So Player B also plays the exact same amount of hands as Player A. However it takes Player B double the amount of time to play the hands. Player B is also a 2bb/100 winner over the same sample of hands. Though, the hands are played over 2 months instead of one month.

For reasoning purposes we will make the assumption that both players had the exact same starting cards and the exact same boards with the particular hand. We will also make the assumption that mathematically they both played the hands correctly. If this is the case why is Player B 2bb/100 winner where Player A is only a 1bb/100 winner?

Player A and Player B cannot have different winrates if theyre playing the same cards the same way against the same opponents. Player A is either not a 1bb/100 player, or player B is not a 2bb/100 player.

If we're assuming that Player A and Player B are for all intents and purposes 'identical' then their bb/100 has to be identical, therefore, if it takes player B longer to play that 100 hands, it doesn't matter - its still the same number of bets won per hundred hands.

What youve essentially proven is the converse of what you were attempting to.

We can't quantify the effects of time. Yes, over time our play might improve - but comparing player A and player B, if theyre identical, they improve in identical ways, and the bb/100 still stays the same.

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pokerfanatic

03-07-2006, 02:39 AM

#6 (permalink)

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Euph never said it was the same opponents... read closer, i actully said that they played aganst diffrent opponents...

|~|ypermegachi

03-07-2006, 02:49 AM

#7 (permalink)

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Quote:

Originally Posted by pokerfanatic

do you know when you're gonna die? or quit poker, that's why i used infinity the total number of hands played over a lifetime can not be diffined UNTIL the player stops playing all together...

then use a random variable X, not infinity. if we wanted to be crazy, and assume that some superhuman can play 1 hand every second, that's 36000 hands every hour. he/she doesn't sleep either. so 864000 per day. which is 315360000 a year. let's also assume that they are 20 now and will live to be 120. hundred years later that's still only 31 536 000 000 hands, which is nothing compared to infinity.

i kinda understand where you're coming from, but you should refrain from using pre-existing definitions that do not fit what you're trying to describe, as to avoid confusion.

|~|ypermegachi

03-07-2006, 03:00 AM

#8 (permalink)

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ok, i just read it again and i'm still confused all over the place...lemme try one more time slowly...

pokerfanatic

03-07-2006, 03:01 AM

#9 (permalink)

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Well, I see what you’re saying, and your numbers for that is impossible to obtain that's all I meant by infinity, though I see confusion coming from my use of the word...

Hehe really this post only purpose was to get people thinking about a stupid thing such as short term and long term hand samples… All I was getting at was hands and time are only going to be effected by a player, time is only the lifetime of a poker player career however we have no idea when a random player will quit completely, so theoretically even a sample of 500k hands can be considered short term sample if you were to play another 500k or whatever…

No hand amount or time amount will give you an exact answer to stats questions, because of the players curve the math so drastically. I was just trying to make a point that when people say the sample is too small, what they are really saying is if you plan to play many more hands in your career THEN the sample is small but if they quit right then that’s the exact amounts of what they won or lost.

It’s not a issue of Hands, because you need Time to play a lot of hands, so time and hands are related. The variable in the mix is not math or hands or time, its human’s.

I think my proof was just a really draw out explanation of what I just said…

|~|ypermegachi

03-07-2006, 03:07 AM

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ok...let me summarize....is this what you're trying to say?

Quote:

Originally Posted by myself

hands/time are irrelevant because they as they approach infinity the sample size of all players become the same (i.e. they are all infinity). so the only useful stat we can use when we analyze sample sizes is the opponents played during that sample.

edit: this is fanatic's stuff [
well you have to figure there is going to be some sort of error in the samples based on this fact, i mean tell me if you played 1k hands the exact same way, aganst a table full of bad players, then you play identicly aganst a table full of solid players, do you think you will have the same winrate?
]

|~|ypermegachi

03-07-2006, 03:54 AM

#11 (permalink)

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wtf, you edited my post! ABUSE OF POWER!!! ABUSE OF POWER!!!

pokerfanatic

03-07-2006, 04:26 AM

#12 (permalink)

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Quote:

Originally Posted by |~|ypermegachi

wtf, you edited my post! ABUSE OF POWER!!! ABUSE OF POWER!!!

opps must have click edit instead of quote my bad man...

|~|ypermegachi

03-07-2006, 04:29 AM

#13 (permalink)

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anyways, the answer to your question is obviously no. my winrate against crappy players is expected to be much greater than solid players.

pokerfanatic

03-07-2006, 04:30 AM

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Quote:

Originally Posted by |~|ypermegachi

anyways, the answer to your question is obviously no. my winrate against crappy players is expected to be much greater than solid players.

So yea I think that you could factor in this idea to find an error estimate...

euphoricism

03-07-2006, 01:52 PM

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Quote:

Originally Posted by pokerfanatic

Euph never said it was the same opponents... read closer, i actully said that they played aganst diffrent opponents...

Well then theres you "X factor" - its the opponents. It still has nothing to do with time

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euphoricism

03-07-2006, 02:09 PM

#16 (permalink)

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If youre still trying to convince me that someone who played exactly 100 hands of poker has a statistically significant sample, even if they never played another hand for the rest of their lifetime, I'm still telling you to take a statistics class. :]

They simply cannot draw anything meaningful past, "You won for those 100 hands" or "You lost for those 100 hands". It is useless as a mathematical extrapolation of future earnings, and useless as a performance-based refining tool.

Essentially what youre saying is this: No one has won or lost at poker until they stop playing poker. Great philosophy, but useless in practice. Youve also said that 'long term' is a generic word that has no definitive number correlation, a true point. A sample size of 500,000 hands over a lifetime of 500 billion hands is fairly insignificant. Sample size must be relative to population.

All you've really proven is what some of us have said all along - in limit, your bb/100 is simply an arbitrary useless statistic.

Given a sufficient number of hands at ONE stake, and assuming you NEVER improve as a player, you forever play exactly the same, it will approximate your winrate.

However, no one meets those criteria.

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pokerfanatic

03-07-2006, 02:23 PM

#17 (permalink)

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Quote:

Originally Posted by euphoricism

Quote:

Originally Posted by pokerfanatic

Euph never said it was the same opponents... read closer, i actully said that they played aganst diffrent opponents...

Well then theres you "X factor" - its the opponents. It still has nothing to do with time

Nor does it have to do with hands we were both wrong...

all I’m saying is that Hands and Time are equal in the long run and are less relevant then opponents you played and your play it's self, you must figure in an error % for these "X" factors then figure in give an error estimate to the time + Hands portion of the equation...

I'm just saying that it's more then just black and white...

euphoricism

03-07-2006, 04:59 PM

#18 (permalink)

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It has plenty to do with number of hands. If player A and B play the exact same hands mathematically exactly correct, given an infinite sample size, IE the *long run* they'll have essentially identical winrates.

Youre trying to quantify the unquantifiable.

Its not to say that time doesnt have an effect - if we play tired, we should sleep and play later. If were angry, we should cool off and play later. This can of course effect your play.

But assuming youre playing in good games, with good seat selection, position, at the right times of day, youre not tilting, etc etc -- Whether you play 1000 hands on monday or play 1000 hands on friday will not effect your long term winrate, even though on monday you might win 4bb/100 and on wednesday your might lose 2bb/100.

What youre saying is that there is another factor other than hands that makes up your winrate over a given sample size.

Yes, this is a true statement.

Us poker players have termed such nonquantifiable variables as "variance". It has no mathematically significant use (although PT attempts to describe it in terms of your Standard Deviation from the Mean.. a good attempt, I guess, but its not particularly useful)

So yes, you have decided that variance exists. :]

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Ltrain

03-07-2006, 11:03 PM

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I am not a math whiz, but I think a better factor than the number of hands in this debate is can you ever quantify a standard deviation for 100 hands? 10,000 hands, 100,000 hands? For example, if we can determine for a certain limit that a player has a winrate of 3 bb/100 over 1,000 hands, but his standard deviation is +/- 6 bb, then he can't say he is a winning player, but if his winrate is 2 bb/100 over 100,000 hands with a standard deviation of +/- .5 BB, then he can truly say he is a winning player.

So what determines our standard deviation? The player, the cards, the player's method of playing the cards, the opponents who may be flipping coins to make decisions... Can these actions ever be quantified? Will a player ever sit still long enough to ever determine anything with a mathematical certainty (i.e., Mr. control group who plays 1 million hands of 2/4 with no improvement and quits) What if the player moves up in limits and his previous method of playing doesn't work as well? What if a TAG player is well situated for ring play but gets crushed by LAG 6 max maniacs? What if the competition gets better? In theory, the number of hands should help determine a player's winrate, but the reality renders the number of hands meaningless.

"Don't judge a man until you have walked a mile in his shoes. Then you are a mile away, and have his shoes." - Anon.

ArcticKnight

03-11-2006, 05:11 AM

#20 (permalink)

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There are lots of variables at play, but I can't see time as anything other than a situational context within the variable of "hands." (except when it comes to reads on opponents, then it is a direct variable)

In order for time to have an impact on the variable of "hands," you would need to show that (1)you are playing too many hands (tables?) too quickly, thus inducing errors in your play, or (2) that you are playing hands too slowly (i.e 200 hands a week, maybe) and thus not experiencing enough situations to reinforce and capitalize on correct play, (frequent application of knowledge is key to learning retention).

All things being equal, I can't see where playing 5,000 hands a week versus playing 10,000 a week could include "time" as a variable unless a player's ability to play correctly is shown to decrease with too many or too few hands, but this does not seem to part of the "proof" or argument.

Where time does factor in directly, though, is on "opponent reads". When multi-tabling, I doubt I could be convinced that any player will say he can get as good good reads on 6 tables (let's say 600 hands of 6 max per hour) than he could on 3 tables (300 hands per hour).

So for me, "time" becomes a variable when the ability to "read" opponents drops from its optimum due to missing information, information overload, lack of time for synthesis and analysis, etc...

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