Poker
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Can anyone help me here?
I have analysed the last 10000 hands I was dealt by betfair. In a heads up situation one would expect the proportion of hands won to average out at 0.5.
Since luck also plays a part there is a standard deviation around the 0.5. Over 10,000 hands I estimate this to be 0.001. Therefore one might expect to average out between 0.498 and 0.502 depending if one is relatively lucky or unlucky.
My average came out at 0.494, some 6 standard deviations from the mean - essentially outside the bounds of probability if my analysis is correct.
Incidentally I ran the statistics on 3000 hands dealt to me under a previous id, and the average there came out at 0.493.
Can anyone provide an explanation for this, or have they run a similar analysis on the hands they have been dealt?
I have analysed the last 10000 hands I was dealt by betfair. In a heads up situation one would expect the proportion of hands won to average out at 0.5.
Since luck also plays a part there is a standard deviation around the 0.5. Over 10,000 hands I estimate this to be 0.001. Therefore one might expect to average out between 0.498 and 0.502 depending if one is relatively lucky or unlucky.
My average came out at 0.494, some 6 standard deviations from the mean - essentially outside the bounds of probability if my analysis is correct.
Incidentally I ran the statistics on 3000 hands dealt to me under a previous id, and the average there came out at 0.493.
Can anyone provide an explanation for this, or have they run a similar analysis on the hands they have been dealt?
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Replies: 42
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you are going to showdown with weak hands, you must be a calling station hth
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Maybe you're just bad at poker?
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Can anyone provide an explanation for this, or have they run a similar analysis on the hands they have been dealt?
I'll answer the first question. You don't understand the maths techniques you are applying. |
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I think you dont understand my question.
I am not talking about playing every hand, just the the theoretical probablility of a given set of hands winning. This has nothing to do with how one plays them in reality. It is independent of skill. I assume you agree with me that if you were dealt AA every time you would have a better chance on average of winning than if you were dealt 23 off suit. What I am saying is that over a large number of hands the theorteical probability of winning preflop should average out to be 0.5. Can you understand that? |
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Yes, all in preflop with you seeing both sets of cards in all cases would give you an average of 0.5. However, you cannot know what cards are involved when your opponent folds preflop unless you are playing with yourself. This means your results will always be biased. The fact that you got within 60 hands out of 10,000 is almost certainly not outside of 6 standard deviations.
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mach 13 Dec 14:23
you are going to showdown with weak hands, you must be a calling station hth Baracus 13 Dec 14:44 Maybe you're just bad at poker? Before you start taking the p1ss out of people, may I advise reading the posts properly so that you don't look like a complete moron Peter Parkers brother 13 Dec 14:49 I'll answer the first question. You don't understand the maths techniques you are applying. This is the correct answer. |
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your ideas about 0.5, standard deviation etc are completely incorrect, that's why your stats appear 'wrong'.
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Also your sample is pitifully small. You need 100k hands absolute minimum to do any sort of meaningful analysis really.
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wykhamist 13 Dec 15:05
What I am saying is that over a large number of hands the theorteical probability of winning preflop should average out to be 0.5. No. The theoretical probability will only average out to 0.5 as the number of hands dealt tends to infinity. |
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The point is: What is a reasonable spread around 0.5 for a given number of hands.
I calculated the sd as follows: Using a grid of hand strengths rainging from 0.8545 (for AA) down to 0.296 for 23 os I calculated the odds for each hand dealt preflop. If you add the results and divide by the number of samples you should come out at 0.5. In my case this was 0.494. If you take the variance of all the outcomes and divide by the number of samples this gives an estimate of the variance in the mean. Taking the square root of this gives the s.d. The variance of the samples is about 0.01, so you can see the variance in the mean should be about 0.01/10000. Take the sqrt of this and you come up with 0.001. Note that this variance is not the same variance which is commonly referred to in poker. That takes into account all the possible flop, turn and river cards. I agree that you would need a far larger sample to look at that, and it also encompasses the decision process regarding when to fold/raise etc. Perhaps a maths graduate could confirm my calculation is correct. To those other posters, who clearly come from Newcastle and failed maths GCSE miserably: Please don't bother to reply. |
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wykhamist
The point is: What is a reasonable spread around 0.5 for a given number of hands. If this is your question - What is a reasonable spread around 0.5 for a given number of random hands. Then your answers may seem valid. But you are not analysing random hands, they will just be showdown hands and these are not random. E.G if I wanted to I could play some HU poker and take the worst 30% of starting hands to showdown and fold the top 70% of hands before showdown. In this case you wouldn't expect each players hands to win 50% of the time. |
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main thing everyone seems to be ignoring seems to be the 10,000 is being used a decent sample size. sorry i play more hands than that over a busy weekend.
run the same calculations over a few million hands to get a better picture. |
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In reply to Peter Parker's Brother:
I am trying to find a model that will tell me if I am getting a fair spread of hole cards, or if the spread I get is in any way biassed. If there is no bias in my hole cards then my average should come out to be 0.5+/- a few standard deviations. With my 10000 samples I found I am 6 s.d's adrift from the mean. This seems to indicate a systematic bias. This has nothing whatsoever to do with what happens at the flop or after, who I am playing against, or what my strategy is. |
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I had AA twice in one MTT once.
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again refer to my above point. you cannot run an analysis like this over 10k hands. i have over a million hands in my HEM and still u dont get a true picutre.
As has already been stated above by someone else- you would get exactly .5 based on infinity hands. until you can look at infinity hands there is no point running this type of analysis. incidentaly on my million hands holecards are within +/- 5% of what they should be for every hand. each hand is random dont forget so just because you have AA this time it doesnt alter the odds on you getting AA the next hand. |
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also you figure of .494 doesnt transfer to 6 points beyond the normal deviation.
where there is a random elelement included in any calculation the stadard devaition is +/- 5%. you figure actually relates to well below this deviation. |
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I have analysed the last 10000 hands I was dealt by betfair. In a heads up situation one would expect the proportion of hands won to average out at 0.5.
I am trying to find a model that will tell me if I am getting a fair spread of hole cards, or if the spread I get is in any way biased. You seemed to have changed what you are trying to do?? I'm confused now. 10k sample will be plenty to draw conclusions on the first one, it will be pretty small for the second question but you could still work with it. |
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If there is no bias in my hole cards then my average should come out to be 0.5+/- a few standard deviations.
Not sure where you get this from but if you want to attract some more serious answers I'd suggest setting out all your calcs. |
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I make money at Poker, thats fair enuf for me,.... now after reading through all of this my head hurts,..... please advice ?!?!
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Additional note: You might allready have figured out that i am coming from the Footy Forum :)
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I have a 1st class BSc in Mathematics,(dont necessarily mean im a maths god, just good at exams, once exam is done i release all info and restart the cramming) and i cant be bothered to do anyworkouts.
However there is one solid proof that can be made from this thread and that is that you are 5hit at poker and looking for an excuse rather than remedy. |
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disagree peter that 10k sample size is enough to compare anything in poker.
i have run -100 buyins behind ev over 4000 hands so how can 10k hands prove anything. its called variance for a reason and to get any colcusions on any for of statistical analysis i would say a million hands is the absolute bare minimum to level out some of the variance. |
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if u want to look at 10k hands you shouldve been dealt aces 46 times. if u have been dealt them just 20 times or 70 times it proves nothing.
its like looking at yesterdays premiership results (freak results) then saying you could work out next weeks results based on such a small sample size. nice fishing u got me for a while there. |
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The whole point is that I have taken into account the sample size in my computation of the error in the mean. Therefore don't keep going on about the sample size!
This is not about finding an excuse for losing money at poker. I make money consistently. I would have thought people would be interested to to see a mathematical test to see how random the cards are that they are getting dealt. After all, you see enough posts on here complaining about the software being fixed in some way. Not one single poster has come back with any mathematics in reply - just petty little digs from people who had no idea what I was talking about. |
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disagree peter that 10k sample size is enough to compare anything in poker.
Sure its too small for most things in poker but ok for a "which starting hand is better mine or his" scenario |
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Not one single poster has come back with any mathematics in reply
This is because there is no comprehensible maths in your question. |
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It is quite obvious your maths is wrong. You are saying the 95% confidence interval is something like 4980 to 5020 over 10K hands.
Anybody who has studied stats or played poker for more than 5 minutes can see that is way too small and hence there is an error in your calc. regards |
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In calculating the odds for each hand I ran a monte-carlo simulation over 500,000 hands. Since there were 10,000 hands that is a total of 5 billion theoretical showdowns.
I showed showed that the S.d should be 0.001 about the mean of 0.5 given the sample size. If I am 0.006 adrift of the mean then I am miles outside the 95% confidence level. |
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All you have is a 10k sample, you can't extrapolate that to 5bn. Any error that is in this system is in the parameters you gave it.
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BOOBS HAS SPOKEN.
NOW LET IT REST IF YOU KNOW WHAT'S GOOD FOR YOU |
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BOOBS IS GOD!
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ok toss a coin 100 times. it comes down heads 58 tails 42. now if i use that sample size and multiply it to get a million coin tosses omg i must have a bias coin.
stop trying to bring a mathmatical argument on here until you have a suitable sample size to run a decent analysis on. 10k hands is not even a few days hands. I can run bad or good for a week so why should 10, 20 or even 50k hands be any use for any analysis? i can show you a 10k sample size in my HEM where I have run at 130bb/100. I can also show you the opposite- cant you understand this as a simple synamic of poker? |
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simple dynamic*
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You been on the sauce .. hic... ariston?
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Jeez I just give up. I have said already that I am not using my 10K samples to deduce anything about the system as a whole, or about whether I am playing well or badly.
I was using it to see if there was bias in the hole cards I was getting dealt. I have been thinking more about this, and it may be that in a HU situation the coin toss analogy might be right, since before the hole cards are dealt, one has a 50% chance of winning the hand. If that is correct then you can model the probabilities using a simple binomial distribution. If you toss a coin 10K times the cumulative probability of winning 5940 times or less is 0.117. While this is indeed very unlucky it does not necessarily imply a bias. As always any serious non-abusive replies welcomed. |
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lol how on earth can you take into account the sample size in your computations?!
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Um Mavis In a binomial distribution it is one of the variables.
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ok if you want to do this on a binomial distribution method you have to consider there are 169 different starting hands. also count in the fact that some of those starting hands are more likely to appear than others. there is a simple calculation for the minimum sample size which would be needed to allow for the random element to even out
in fact no im not biting anymore- bit enough already. next you gonna start a thread asking if anyone is anywhere close to solving the Beal Conjecture. you seem like you know plenty about math so you know where your argument is flawed and its too late to be drawn into a serious discussion on this type of thing. |
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Jeezers, this is all a bit above me. Feel quite thick.
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