08-01-2010 , 11:54 AM
Quote:
Originally Posted by turn & fall

If you think about it, it is quite likely that you have been running good and your 'real' winrate is likelier to be lower because your sample is very uncertain and the winrate itself is very unlikely over the sample.

It is still likely that you are a winning player even using this approach. It just means that you are a little less likely to be a winner.

I am going to write a paper on this topic for a group of mathematicians I am working with and hopefully they can show me how to use a Kalman Filter to solve this problem.
It is definitely likely that I have been running good (a good BB/100 is like what? 3-7?), but my goal from finding stats for such a small sample size is not to find out how likely I am to be a 16 BB winner. I also understand that even though there is a 95% chance between it says that I am between X and Y BB/100, that does not mean that all of the numbers falling in this range have the same chance of being my win rate. However, I was mainly interested in finding my worst case scenario because with such a small sample size, I really only care about seeing to what degree my current data indicates that I am a winning player, period.

Although we do know the statistics of other players, wouldn't you agree that each player has a different BB/100 against different opponents as well? Does my data seem more "accurate" to you if instead of just trying to figure out if I'm a winning player, I'm just trying to figure out my chance of being a winning player against the people that I encountered in these specific 12 sessions? (This would be useful to know if that would make it more accurate for the purpose of things such as home games with friends that people play). If you don't think it quite does then you didn't lose me, I get it and it makes sense. I was just trying to figure out if this would help with the accuracy of my data (since finding good results and then misinterpreting those results is never a good thing and can make someone make a silly conclusion that the carpet is magical because everything seems to want to go straight to it when let go. Grass and concrete could be magical too...or maybe the REAL reason for those results is gravity). Clearly if I was playing against better players my statistics would go down, and I would most definitely be the worst player and a big loser at some tables with cash game pros.

If your group helps you figure out how/if the Kalman Filter works for this problem, let me know!

Thanks for the help everyone! You are all much appreciated
08-01-2010 , 12:03 PM
Quote:
Originally Posted by turn & fall
Correct the approach is standard. And there is nothing wrong with it.

However there is a better method which is to apply bayes filters.

I might note that using bayes filters on normal distributions becomes very complicated and something that only graduates of mathematics can realisticly do. (BTW I am not a math grad so I do not know how to but I have an understanding)

There is a more simple approach that changes the guassian distriution from a continous data set to a discrete one.
^This.

If you find out how to do one of the more accurate, but harder ways of finding out a more accurate estimate, let me know. I like to think of it as my way is like multiplying your outs by 2 or using the rule of 4 instead of memorizing a chart that tells you your true outs (as that is TOO hard to memorize at the poker table..unless you were a mathematician and the 1% error mattered to you, and you had a photographic memory of things that didn't look like Megan Fox). Knowing how to do a more tedious and accurate way of doing it would be awesome and is really my whole purpose of creating this thread: to find the best, reasonably possible way to estimate whether or not you are a winning player. Cheers!
08-01-2010 , 01:26 PM
In looking over this thread I think that most everyone is over complicating this. While I am not an expert in stats I can say quite confidently that 50 hrs is not enough to know if you are a winning player using any theroms, standard deviatations....

Keep it simple for the time being. Track hours played, win/loss and hrly rate. I would think that after about 250 hrs of live play you will have a sense if you are a winning player. Once you have 250 hrs of play then start calculating standard deviation, risk of ruin...

After 500 hours of live play you will know. The interesting thing here is that as you continue to play, your game evolves (for better or wrose) and the games themselves may change, so you can never be sure if you will continue to win or lose.

I just started reading the mathmatics of poker, I am curious to see if my thoughts will change after reading it.

My two cents.
08-01-2010 , 01:33 PM
Quote:
Originally Posted by PokerSki13
In looking over this thread I think that most everyone is over complicating this. While I am not an expert in stats I can say quite confidently that 50 hrs is not enough to know if you are a winning player using any theroms, standard deviatations....
If you're not an expert in stats, why/how can you be confident about this?

It always seems weird to me when people who can't/won't do the math pop in to say that doing the math is "over-complicating" things.
08-01-2010 , 03:32 PM
Quote:
Originally Posted by RustyBrooks
If you're not an expert in stats, why/how can you be confident about this?

It always seems weird to me when people who can't/won't do the math pop in to say that doing the math is "over-complicating" things.
^ This

If I wanted to title the thread "What do you THINK and what have you HEARD is a good sample size?" then I would have named it that.
08-01-2010 , 04:55 PM
Quote:
Originally Posted by PokerSki13
In looking over this thread I think that most everyone is over complicating this. While I am not an expert in stats I can say quite confidently that 50 hrs is not enough to know if you are a winning player using any theroms, standard deviatations....

Keep it simple for the time being. Track hours played, win/loss and hrly rate. I would think that after about 250 hrs of live play you will have a sense if you are a winning player. Once you have 250 hrs of play then start calculating standard deviation, risk of ruin...

After 500 hours of live play you will know. The interesting thing here is that as you continue to play, your game evolves (for better or wrose) and the games themselves may change, so you can never be sure if you will continue to win or lose.

I just started reading the mathmatics of poker, I am curious to see if my thoughts will change after reading it.

My two cents.
You obviously have not got very far. Winrates is one of the first things covered in MoP.
08-01-2010 , 05:33 PM
Quote:
Originally Posted by RustyBrooks
If you're not an expert in stats, why/how can you be confident about this?

It always seems weird to me when people who can't/won't do the math pop in to say that doing the math is "over-complicating" things.
I know enough about stats to know that 50 hrs is way to short of time to have enough data to determine if I am a winning player. if i am wrong please let me know how I or anyone can determine long term or even short term what my expectation is after 50 hrs?
08-01-2010 , 06:31 PM
Quote:
Originally Posted by PokerSki13
I know enough about stats to know that 50 hrs is way to short of time to have enough data to determine if I am a winning player. if i am wrong please let me know how I or anyone can determine long term or even short term what my expectation is after 50 hrs?
You are wrong. In probability you can never know anything is for sure. If you understand the mysteries if the guassian distribution you will realise anything is possible, just that some things are more likelier than other.
08-01-2010 , 07:49 PM
Quote:
Originally Posted by PokerSki13
I know enough about stats to know that 50 hrs is way to short of time to have enough data to determine if I am a winning player. if i am wrong please let me know how I or anyone can determine long term or even short term what my expectation is after 50 hrs?
Did you even read any of this thread? The whole point of this excercise is to determine with what degree of certainty you can place your win rate. No matter how many hands you've played, whether 1 or a billion, there is a measure of uncertainty in your measurement. You can *always* make qualified statements about your win rate.
08-02-2010 , 07:37 AM
The simple point I am trying to make is that the data in your HEM or whatever is likely to be corrupted due to guassian noise.

Guassian noise is basically the uncertainity inherant in the system, which in the case of a poker sample is quite obvioulsy luck. You may have been lucky you may have been unlucky but you do not know with your initial sample.

The bayesian approach basically cleans up the noise by using the underlying sample of winrates. It just means that a winrate of y has probability x of occuring if you picked a random player out of the population.

If the probabilty of your MLE (maximum likelihood estimate) of your sample (or the mean or the winrate) is in part of population sample that is unlikely, say 2%, then your 'real' winrate (without guassian noise) is likely to be closer the mean of the population of winrates.

However it is worth noting that it is possible that you have been running badly. And that your 'real' winrate is infact HIGHER. However this is less probable than your 'real' winrate being lower.
08-02-2010 , 10:55 AM
Quote:
Originally Posted by turn & fall
You are wrong. In probability you can never know anything is for sure. If you understand the mysteries if the guassian distribution you will realise anything is possible, just that some things are more likelier than other.
Isn't that the point of OP's original post though? He isn't trying to say anything with exact certainty, ultimately he concluded that most likely (95%) he is somewhere between a -3BB/100 and +2xBB/100 player? (I forget the exact high of his range) Sure there is a CHANCE he is somewhere outside of that range, just like there is a CHANCE a random dude's 1 outer trips will outdraw the nut flush on the river... theres a CHANCE, but knowing both hands, I'm pretty sure everyone is folding there anyway (pending ridiculous odds). There's also a CHANCEof there being a tsunami in New Jersey tomorrow, but no one is avoiding the shore because of it. He isn't trying to be exact, he's trying to guage a range and get an idea if he is a long-term winner. He doesn't even care about exact win-rate, just an idea of whether he is a "winner". It almost seems like you are trying to quote all these advanced maths just to show off, but you are totally missing the point of OP's question.

And you don't need advance maths and ridiculous huge sample sizes to get an idea if you are a winner or not. Like many people have said - there are too many variables, such as quality of opponents, type of opponents, the individuals playing style vs those opponents, ability to hand-read, etc... not even mentioning random luck, that you can never really know for sure.

For example - some guy who plays +2BB/100 over 1,000,000,000 at the micro-levels can consider himself a winner, but put him at a live \$2/5 table with a bunch of decent players and I'd be willing to bet most likely he will LOSE. That doesn't make him NOT a winner, just at those stakes he is not, nor vs that quality of opponents etc. Just like a very good long-term \$1/2 live winner vs Phil Ivey head to head... still a loser.

I'm a recreational player - over the course of my life, I know I can win in the micros, and if I'm on my "A" game, I can win (or at least make the best decision possible) with mid-stakes online and live \$1/2. I don't have a billion hand samples of anything to show maths and know my winrate, but I know Im up overall with microstakes, and probably a little down overall with the higher stakes, but taking out my completely "bad" sessions (not counting luck, but tilt sessions, drinking, tired, etc) at the mid and live stakes and I'm up. I don't really care about my winrate, but I know I'm up in certain areas, and I do my absolute best to play in those areas and during my "A" game and I'm happy knowing that. Any large pots I play, I go back over the hand in my head (knowing the results) and see if theres any way I can improve and if I made the right decision and just had the cards fall the wrong way. Generally I do, and that makes me more comfortable that I'm a winner. And that's all I care about. The only time all these maths really matter is if someone is playing at the same stakes with generally the same players, and does it ALL the time. (eg. an online grinder who is planning on making a living doing that)

Even playing \$1/2 live, I know I can be anywhere from a big-time fish to big-time winner, based solely on the table and who I am playing against. I dont need a sample to know that, and usually I can tell within about an hour of play... and if I am the fish, generally I will try to change tables or walk (unless of course there are no other options and I still feel like playing, in which case I will know that ultimately I'm going to lose the money and consider it an investment in learning the game from players better than me).

Conclusion - I am 95% confident OP is a winning player, when playing within his stakes/limits and when he is on his A game!
08-02-2010 , 12:10 PM
BTW you have taken my qoute out of context.

I am trying to be precise as I realistically can. Ofcourse there is variance but we want out mean (winrate or maximum likelihood value) to be as close to 'real' as possible.

My point is that although his technique is correct it is 'probably' ultimately inncorrect. The reason for this is he is using a classical statistics technique that although he has done it correctly is probably wrong.

The reason it is probably wrong is that the model assumes that the parameters of the game are constant. Which we know they are not in the medium to short term. Basically there is luck involved. This luck is called guassian noise in its proper term which basically means that the information being used to get the normal distribution is corrupted and therefore the end result is corrupted.

Its a bit like this. Imagine an election poll. The statistician only looks at one state. He looks at the mean vote and the standard deviation of that state. He works out using that sample that candidate X has a 80% chance of being elected. Ofcourse the problem here is the the sample he has collected from has been corrupted because it is only one state. For example this state maybe in the deep south which is notoriusly Republican which is not representative of the entire USA.

A Bayesian statistian would look at one state and collect the data. But then refine the probability of candidate X winning by using an underlying assumption about the rest of of the USA, for example that votes are evenly spread with a larger standard deviation. The Bayesian method reduces the probability of X winning to 60% for whatever reason because it accounts for the underlying distribtution of votes.

This is what I am saying about winrates. The OP has just used a sample from one state and I am saying he should incorperate assumed data from the entire population to get a better estimate. This assumption being most players are losers of around -4bb/100 hands I have found (not sure on that BTW and I am still trying to find the SD)

Having these figures is very useful for working out bankroll management strategies, risk of ruin, kelly criterion and the like. You can not put into an forumla an 'I reckon'...... you need a figure.

I am genuinely trying to help not just 'showing off' and I am also interested in this topic because I am writing a paper on these types of techniques.
08-02-2010 , 12:13 PM
Quote:
Originally Posted by turn & fall
You are wrong. In probability you can never know anything is for sure. If you understand the mysteries if the guassian distribution you will realise anything is possible, just that some things are more likelier than other.
08-02-2010 , 12:24 PM
Quote:
Originally Posted by turn & fall
Its a bit like this. Imagine an election poll. The statistician only looks at one state. He looks at the mean vote and the standard deviation of that state. He works out using that sample that candidate X has a 80% chance of being elected. Ofcourse the problem here is the the sample he has collected from has been corrupted because it is only one state. For example this state maybe in the deep south which is notoriusly Republican which is not representative of the entire USA.
It seems you have quite deep understanding of the issues discussed, but this comparison seems flawed, unless you're implying that there is some systematic bias in OP's sample. A just analogue to your election example would be, if he had played only on friday nights with drunk opponents and expected to have a proper estimate of his winrate against typical field during less fishy hours.
08-02-2010 , 12:49 PM
I got the answer you all looking for!

How to find out if you're a winnign player?
You go to you cashier on you pockersoftware or if you play live you check your wallet and then you play poker. AND NOW here comes the KEY after the sessions is completed you look inside the wallet again and you use this equation: Monney after session = X Monney before session = Y

X - Y = If you get a positiv answer your a winning player otherwise you should prolly try chess.
08-02-2010 , 03:05 PM
Quote:
Originally Posted by turn & fall
BTW you have taken my qoute out of context.

I am trying to be precise as I realistically can. Ofcourse there is variance but we want out mean (winrate or maximum likelihood value) to be as close to 'real' as possible.

My point is that although his technique is correct it is 'probably' ultimately inncorrect. The reason for this is he is using a classical statistics technique that although he has done it correctly is probably wrong.

The reason it is probably wrong is that the model assumes that the parameters of the game are constant. Which we know they are not in the medium to short term. Basically there is luck involved. This luck is called guassian noise in its proper term which basically means that the information being used to get the normal distribution is corrupted and therefore the end result is corrupted.

Its a bit like this. Imagine an election poll. The statistician only looks at one state. He looks at the mean vote and the standard deviation of that state. He works out using that sample that candidate X has a 80% chance of being elected. Ofcourse the problem here is the the sample he has collected from has been corrupted because it is only one state. For example this state maybe in the deep south which is notoriusly Republican which is not representative of the entire USA.

A Bayesian statistian would look at one state and collect the data. But then refine the probability of candidate X winning by using an underlying assumption about the rest of of the USA, for example that votes are evenly spread with a larger standard deviation. The Bayesian method reduces the probability of X winning to 60% for whatever reason because it accounts for the underlying distribtution of votes.

This is what I am saying about winrates. The OP has just used a sample from one state and I am saying he should incorperate assumed data from the entire population to get a better estimate. This assumption being most players are losers of around -4bb/100 hands I have found (not sure on that BTW and I am still trying to find the SD)

Having these figures is very useful for working out bankroll management strategies, risk of ruin, kelly criterion and the like. You can not put into an forumla an 'I reckon'...... you need a figure.

I am genuinely trying to help not just 'showing off' and I am also interested in this topic because I am writing a paper on these types of techniques.
I respect your thoughts believe me... I didnt mean to go off on you earlier with a rant. My bad, I was having some anger management issues that I was taking out on you... so, sorry about that.

That being said, his sample isn't a specific state... its over a random smattering of hands and you have no idea whether he was running good, running bad, or just average. I would be willing to say that if you are running truly EXTREME good or EXTREME bad, generally you can tell. That being the case you throw the sample out the window, but otherwise you assume its within the normal range of chances and is a fairly representative sample of the population. Any sample is going to have the chance of being not representative of the population, but you kind of need to take that as it is, because its not like he has the ability to truly increase his sample short of playing more. And of course if you do that your ability to determine if you're a "winner" or not goes up (confidence interval)... but generally not fast enough for our purposes. Unfortunately we have to work with what we got, so to speak.

So, in his example, I'd like to think his range is reasonable. If you want to somehow adjust for the overall mean (in that the full population average is -4BB/100) would it be reasonable to just adjust both the high and low end of his range -4BB/100 for the overall population? Of course its an estimate, but its taking his calculated range and adjusting it down conservatively, assuming he was on an absolute great run of cards...

It just seems to me like you are saying "well its not a big enough sample, there is all this white noise called luck, we dont know whether he is or not"... but for a guess I'd say its not bad. Also, doesnt the idea of standard deviation take into account the idea of luck? ie. If he was absolutely lucky during that run, an awesome estimate of his winrate is probably something around -3BB/100, or the low end of his range?

I also need to go back and re-read some of what you wrote, its getting a little advanced for me, admittedly
08-02-2010 , 05:01 PM
Quote:
Originally Posted by RustyBrooks
Did you even read any of this thread? The whole point of this excercise is to determine with what degree of certainty you can place your win rate. No matter how many hands you've played, whether 1 or a billion, there is a measure of uncertainty in your measurement. You can *always* make qualified statements about your win rate.
One of the reasons i started to read 2+2 is that I want to get to the next level as a recreational player. Live 2/5 NLH player who plays between 100 to 300 hours per year and has over the past 4 years had an hrly win rate between \$20-\$28 in 3 of the years. 1 year rate was about \$8.

One way of improving my game i beleieve is take math to the next level, beyond pot odds, implied odds...so hopefully I will learn some things from those of you who have played far more poker then I have and know far more about stats. To this end I have bought the Mathmatics of Poker at the recommondation of a friend and will continue to read Poker theory forums. I am most inetersted to see how one can take the concepts and theories and practically apply to poker. Given my poker results at 2/5 level I can say somewhat confidently that I am an above average recreational 2/5 player. My assumption is that some of the things that are talked about here are things that I do instinctively. Kind of like skiing, I am a very good skier (top 20%), I heard a friend of mine who is an ex olympic skier explain how to turn to a beginner...I said I do not do any of those things and he said you do but do not realize it.

I look forward to continuing posting my thoughts, some will be right and some will be wrong and some will be in that 4th dimension, neither right nor wrong. I have no doubt that I will learn from many of you.
08-02-2010 , 06:47 PM
Quote:
Originally Posted by poiu
It seems you have quite deep understanding of the issues discussed, but this comparison seems flawed, unless you're implying that there is some systematic bias in OP's sample. A just analogue to your election example would be, if he had played only on friday nights with drunk opponents and expected to have a proper estimate of his winrate against typical field during less fishy hours.
Not deep enough though. The reason I am some what knowledgeable is that I love bayes bayes theorem.

(Yes, the comparison is not great (it is a hard concept to understand/explain) but it gives the reader an idea of what we mean by the sample and the population and how the sample can be revised with underlying assupmptions about the population)

Quote:
It just seems to me like you are saying "well its not a big enough sample, there is all this white noise called luck, we dont know whether he is or not"... but for a guess I'd say its not bad. Also, doesnt the idea of standard deviation take into account the idea of luck? ie. If he was absolutely lucky during that run, an awesome estimate of his winrate is probably something around -3BB/100, or the low end of his range?
Standard deviation is not a measure of luck. It is measure of dispersion from the mean. That is a common misconception.

Yes the sample is not really big enough to be confident, that is why the range for a 95% confidence the interval is so large.

Basically the bigger your sample the less bayesian techniques will refine it because you will be more confident in the sample itself, ie the standard deviation falls.

In poker standard deviation is calculated using x bb/100hands

This metric is a bit odd for statistics but it is very important that you understand what it means.

(1) SD = Standard Deviation x 100bb/100 (per 100 hands)

(2) SD* = Standard Deviation x* bb/100 (entire sample)

SD* = (SD/(Units of 100 hands played))*(Units of 100 hands)^0.5

SD* = (Standard Deviation divided by units100 hands)*(Units of 100 hands squared roooted)

Units of 100 hands is very important.

EG. 10,000 Hands Played = 10,000/100 = 100 Units of 100 hands

I actually have an example prepared

Player Blue - Winrate = 5bb/100
................... Std Dev = 75bb/100
.................... Hands = 10,000
.......... Units per 100 = 100

Player Red - Winrate = 5bb/100
................... Std Dev = 75bb/100
................... Hands = 100,000
..........Units per 100 = 1000

(Note that winrate and Std Dev are the same but Player Red has more hands)

Applying (2) we can work out their standard deviations for the entire sample.

SD*(RED) = x*/100 Hands = (75/100) * sqrt(100)
............................................... = Standard Deviation 7.5bb/100

SD*(BLUE) = x*/100 Hands = (75/1000) * sqrt(1000)
.................................................= Standard Deviation 2.73bb/100

Notice how the standard deviation for the bigger sample is considerably smaller. This means that the 95% confidence interval is going to have a much smaller range.

This distribution can be plotted in excel using the NORMDIST function.

[IMG] Uploaded with ImageShack.us[/IMG]

[IMG] Uploaded with ImageShack.us[/IMG]

As you can see Red has a much smaller range because his sample size is much bigger. This means that using bayesian techniques on Red will change his distribution less because we are more confident in it than Blue. There is more scope for guassian noise in Blue than there is in red because of the smaller sample size.

That should clear some things up.

(BTW the process I am intending to use to refine winrates using bayes theorem is to integrate between certain range (say 1bb-2bb) and work out the probability of that occuring in the sample, then work out the probability of that same range occuring over the population. This is a bit of a cop out though but my mathematical skills are not good enough to deal with data that is not nicely broken up)

Last edited by turn & fall; 08-02-2010 at 06:55 PM.
08-02-2010 , 07:29 PM
I see you are a big fan of Bayes theorem. That’s fine, I like it too -- in fact I wrote my master’s thesis using it on a hardware reliability testing problem. But Bayes is not an end-all, be-all. As I stated much earlier in this thread, to use Bayes correctly, you need a reasonable prior distribution, in this case of a player’s win rate. You then take a sample and through the Bayesian model, the data in the sample adjusts the prior distribution to give you a posterior distribution, or modified prior.

If you have a bad sample, one that is biased, for example, Bayes will only use bad data to modify the prior, so your example of sampling from only one state doesn’t mean Bayes solves the problem.

I think you would argue that at least the prior is based on the whole population of poker players, which is better than nothing. I’m not so sure. You are suggesting that using the whole population of poker players – hundreds of thousands to millions, perhaps, to adjust the win rate of one player, OP, is somewhat questionable. Now, if you were to get OP’s characteristics, such as age, IQ, game type, poker study time, poker experience, etc. and use that to define the population, then maybe you might do better. I think I can summarize my concern by stating that bad sample + bad prior is probably worse than just bad sample.

As I and others have suggested, OP’s use of classical statistics to get a confidence interval on his win rate is perfectly acceptable. As he gets more data the width of the confidence interval will decrease just as the Bayes posterior will become better and the effects of a bad prior, if it was bad, will be sampled away. The classical method does account for the noise (standard deviation) and sample size (the sqrt(n) in the standard error term), which you seem to imply only Bayes can handle properly.
08-02-2010 , 07:48 PM
Yes that has been one of my worries that the priori distribution will be floored.

I am going quite a lot of datamining to work out what the mean winrate in 6 max games is and the standard deviation of this winrate over the sample.

My initital guess is winrate of -4bb/100 and a SD 8bb/100 (just a guess with the minimal data I have)

However it really depending on how 'bad' your priori distribution is. And TBF it cannot be that bad because we know pretty accurately what the average winrate is in HEM. The error in calculating the SD of the population is my worry. ATM my solution is basically just to overestimate so that the priori distribution has less clout in changing the 'real' distribution.

Quote:
which you seem to imply only Bayes can handle properly.
Classical stats cannot clean up guassian noise though. The just assume a constant system rather than the reality of a dynamic one?
08-03-2010 , 01:59 AM
I get what you're saying in that the average BB/100 of a player is -4 or whatever you said it is. However, that is the average BB/100 for players that are simply Poker players. Nothing else is taken into account.

This average includes players that play drunk, don't care about the stakes they are playing at, don't know the odds of winning, soft play their friends, tip too much after winning, go all-in at the end of the night, call for whatever is rest in their opponent's stack just because \$X isn't that much more anyway *screw it, I'll reload in a second*, go on tilt, don't use good game selection, etc.

I mean, you don't really know who I am, so if I met you and shook your hand and said "Hi, I play Poker," then you could immediately assume that I am likely to be someone who fits right in the middle of the -4 BB/100 area with a SD of 8 BB/10. As you continued to talk to me, if I told you that I play for fun, you would probably assume I lost more than 4 BB/100, and if I sounded like I knew what I was talking about and started saying things like polarizing ranges, betting for a reason, reading players, playing my position, etc..then you'd probably assume I fell into a different category of Poker player.

Maybe that was long winded, but my main point is this:

[x] The average BB/100 of a Poker player is -4.
[ ] The average BB/100 of a Poker player that plays drunk is -4.
[ ] The average BB/100 of a Poker player that frequests the 2+2 strategy forum is -4.

I also realize that you said this was a HEM stat. Live games are different than online Poker as well. I can have more advantages in a live game than an online game. Not to mention the average BB/100 of an online Player, even a good player, will be much lower even if that player is good because the good players will care more about volume than BB/100 because a higher volume will give them a higher win rate. There is no way to multi-table live game play so I'm pretty sure that players make a higher BB/100 in live play than they do online (although online players make more BB/100 across all of the tables they are playing at in that hour, but the individual table BB/100s drop).

Last edited by fourfades; 08-03-2010 at 02:12 AM.
08-03-2010 , 04:52 AM
Good FourFades you are getting the idea. What if the priori distributioin is a load of crap.

What you are saying about being a 2+2er and being smart is correct. It would mean that you are more likely to be a winning player. However there is no way for me to quantify this at the moment.

Imagine for a moment that the only data I have is your winrate and SD, and the winrates of a population of your game. I do not know anything about you other than that.

(Your argument about only using data from players who are similar to you is an interesting one and may actually make better priori distributin.
08-03-2010 , 08:35 AM
Quote:
Originally Posted by fourfades
This average includes players that play drunk, don't care about the stakes they are playing at, don't know the odds of winning, soft play their friends, tip too much after winning, go all-in at the end of the night, call for whatever is rest in their opponent's stack just because \$X isn't that much more anyway *screw it, I'll reload in a second*, go on tilt, don't use good game selection, etc.
Well, it's the average for any closed group of players even if they are all world class. The "average" winrate by definition is 0 minus rake. He is estimating that at micro stakes the rake is about 4bb/100. I think for 6max micro that's probably about right. There aren't any other considerations going into that number.
08-03-2010 , 09:03 AM
Quote:
Originally Posted by spadebidder
Well, it's the average for any closed group of players even if they are all world class. The "average" winrate by definition is 0 minus rake. He is estimating that at micro stakes the rake is about 4bb/100. I think for 6max micro that's probably about right. There aren't any other considerations going into that number.
Yup.

However he may be right that we could use a more refined priori distribution. For example we could use a sample of winrates from players who have similar VPIP stats to him.

But yes I was intending to just use the entire population because of the main reason I do not have enough data so really refined priori distributions.
08-03-2010 , 10:22 AM
Hey all, I've been following this thread, I'm extremely interested in some of the math behind this, and I am very experienced in mathematics, but I haven't had probability/statistics training in a little while now, so bear with me.

I thought that Bayes' Theorem related a conditional probability to the conditional probability of the reversed situation (eg how P(A|B) relates to P(B|A)). In this case we can say our A is the OP's winrate, and our B is the winrates of the population of poker players. I'm assuming we just need to calculate P(A|B), not relate it to P(B|A)? And that doesn't require BT?

Just: P(A|B) = P(A ^ B) / P(B) or something like that? (^ = intersection)

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