Are 10,000 hands good enough to give you expected variance ?

Also is there an Approximate number to win % that should make a person
competitive/profitable ?
I mean I know if you loss 500 on your losses and win 200 on your wins not even 65% wins cuts it but i am talking in general terms.
I am going to guess IF there ever has been any research on said subject its likely to be in the 59 to 61% range ?

You never get an exact number. You get a best estimate and an error rate. So after 10000 hands if your winrate is 5bb/100 hands there is 65% chance that your real winrate is between 1bb and 9bb. There's about 95% chance that your real winrate in between -3bb and 13bb.

These are made up numbers but mostly accurate 100bb microstakes online play. In live play you probably need more hands to get an accurate estimate but typical winrates are much higher. So you might get something like 8bb-40bb with a 95% probability.

There are some technical points, like you can't really say that your winrate is such and such with 95% percent probability. What you can say is that if your real winrate is 4bb then you would observe a winrate between -3bb and 13bb with a 95% probability. But in practice this distinction usually doesn't matter.

Yes, this can be done in general. You can look up binomial distribution on wikipedia or search for binomial distribution calculators on google. If you won p percent out of n games (i.e. 60% -> p=0.6) then the "standard deviation" is sqrt[p*(1-p)*n]/n. So taking 500 games and a winrate of 0.6 gives

SD = 0.022. If you want a 90% "Confidence Interval" you need to give about 1.65*SD on either side (read up on z-tables, if you want to know where this number comes from). So in this case you could say that the 90% confindence interval for the winrate is [56.4%,63.6%]

Anyway, here's a simple binomial distribution calculator that gives you confidence intervals based on the number of games played (trials) and won (successes)

http://www.danielsoper.com/statcalc/...tor.aspx?id=85

@ambie That link was great.
So Basicaly if i understand it correctly when i plug in 120 and 200
it is indicating there is a 90% chance my win rate will fall between 53 and 65% ?

Still wondering about what win rate should depict a break even to profitable player

A win rate depicting a break even to profitable player looks like zero to some number larger than zero

That's correct, yes. This is assuming we're not doing anything fishy like "banking our wins" or playing longer to break even in a session.

You mean how many games and what winrate guarantees that the real winrate is over 50%? Say with 90% confidence? It's possible to give an exact answer for a given number of games.

I.e. for 100 games it's 59, which I found by plugging numbers into the calculator. How does it change with more games? The answer is that the width of your confidence interval goes as the inverse square root of the sample. I.e. for 100 games it's about 9% on either side. For 400 games it would be half of that, so 4.5% and for 8100 games (9*9*100) it would be 1%.

edit: to clarify how it helps you find the winrate that guarantees being brakeven or better. If you know that the error rate is 4% on either side, you just need a 54% winrate to be sure of being brakeven or better.

This is an approximation but should be good enough for practical purposes. The main takeaway is that if you want to be twice as precise in your estimate you need 4 times as much data.

if you were wining 8% of all the games you played in you would be in the poor house right quick

Thanks that was VERY Helpful.
I also went on to extrapulate that I would be breaking even at Approx a 57% win rate based on my Avg win/loss per game.
I am also pretty sure that 57% is going to hold true for Most Players.
Less you will be losing money You will Probably need to be at or above 59% to turn a consistent profit.

You'll know your variance very well, because it converges quickly. If you're asking about both win rate and variance, the discussion in the thread applies.

You are going to run into some real sampling bias questions in all of this. We see it all of the time on the forum. Nearly all of the people who do this math have won recently, and they're asking how likely it is that they win long term (or beat PLO for 30bb/100 ). As someone who has self selected based on a winning sample, the statistics for confidence intervals tend to give you strange answers -- they always say you're pretty likely to win.

One way to solve this issue would be to do the confidence intervals you want, and then go play 10,000 hands. "I want to be 95% confident that I'm a >X bb/100 winner, how many hands do I need". Then go play the hands, and if you pass the CI test you are 95% sure.

The real answer is just to keep playing. As your samples get big, you'll have more confidence that you're a winner. Keep all results, don't explain away losses. If you're the guy who writes off the sessions "I was tired" or "I knew I shouldn't play that table", your results will never be trustworthy. It is easy to do this, and imo, it is how we have so many day traders in the world.

Where did you get this 10k hands number to be 95% sure your bb/100 hands number should be about constant at.
I am currently at 6.1 bb/100 for 4k hands.
Maybe I am wrong but I am thinking games played might be a better way to gauge ? I am still thinking that winning 57 % of your games should put you about even.....Maybe someone knows ? I am guessing winning players should be about 59 to 61%...world class players are probably above 63%

Are you talking about cashgames?


Sessions won/lost, doesn't mean **** at cashgames and is totally irrelevant. What matters is winnings.

Play around with this and check some samples like 100-200k and see how realiable your 10k hand sample is.

http://pokerdope.com/poker-variance-calculator/

I just book marked that That was a GREAT Link.
Long story short its said I was 58% probable to either stay at or improve from current bb/100 level....I know its aint 80% but its on the right side of 50/50

Nowhere, because I didn't say that. I said you'd know your variance well. You're confusing variance with win rate (expectation or EV). Your EV after 4K hands hasn't converged much, at all.

You're using terms that you don't really understand, and demanding answers to narrow questions. That's fine, as most people are a bit confused by statistics. Maybe Kahn academy would help? Maybe someone else has a simple stats course online that would be better for poker?

If you don't want to learn the math, I think people are randomly saying 50K or 100K samples to "know" your win rate, these days. Your variance will have converged well before that. You use EV and WR as two factors in calculating bankroll. Otherwise, you don't care other than knowing that you are a winner... maybe to brag to friends or explain to your wife that another $100 deposit is a good idea.

You're using the terms in ways that no poker player would. Nobody talks about confidence of staying at or above current win rates, because that makes no sense.

You're not making any sense. Random Card Cycles become cyclical given enough samples.
Thus if your bb/100 is A for X amount of hands. A is NOT likely to vary much IF the sample size is Big enough.
Or Perhaps I should say That A WILL remain within an expected standard deviation if X is large enough.

I hope for your sake that you're saying this to be funny.

This is such an interesting topic to try and quantify via numbers ... lots of factors IMO. And I'm not sure the software available could break them down the way I would want it.

1) Is a win any time? PF, Flop, Turn and River?
1A) Where do you do best with variable bet sizing?
2) Win percentage would change drastically based on playing style.
3) Win percentage by pot size (and street) would be more important to me ...
4) Win percentage playing HU or multi-way ...
5) Why is making a good fold still a loss when you 'lose less'?
6) Win percentage by position, by cold calling, by flatting 3-bets and by limping .. What do they do for our 'game'?

When playing 1-2 I win a huge percentage of pots PF and Flop, but that does no good for your session if you lose $300 in one pot in there. There are sessions that I win 65-75% of the pots that I VPIP. That doesn't project a winning session much less a winning player.

I totally agree that you could be looking at stats like this for guidance, but only to see where you want to make changes to your game. The overall results are completely based on your BR line.

If I look at 10K hands in live poker that equates to about 250 hours and at 10-15 hours per week that's 4-6 months of playing live. I think that would be a decent period of time to judge a player. But if you squeeze that down to a grinder who might do that in a 5 week period of time, then I have trouble with it. That may make little sense to some but that's my viewpoint. Taking time for reflection, different 'daily' life situations, the weather and/or player's personal feeling about poker (and life) at the time of a session create dynamic and the longer a player stretches this 'on the watch/calendar' the better a reflection on his game IMO.

It's a lot easier for most to come back the next Saturday after you were brutally coolered in your previous session than to come back 'after lunch' and go at it again. GL

Really ? Really ? Maybe you need to look up the definition of standard deviation.
If You flip a coin 10k times for sample set A heads will be X times
if You did it 10k More times for sample set B heads will be Y times

And you think X and Y will be much different ? LOL

@answer The most importent number is how you did after 5th street.

Also Poker Genius gives you all kind of stats like sb/100...%played pre flop.
win% by street

Poker is not flipping coins, tone down your incorrect condescension.

If they were cyclical, they wouldn't be random. DUCY?

the troll is strong in garyfelice...shoudnt this go into his containment thread?

Asks about hands needed to get "expected variance" and then lectures people on basic statistics. Nice.

he got a little smart with me 1st.

With statements like that I starting to see why I have been winning...I mean Like really ? Thats My opposition ?

Next time you track 10k hands see if the number of flushes you hit is much different then the second 10k sample.

This Thread started out nice Until a couple of people (who obviously arent nearly as good as they think they are) got smart

Words have meanings. Terms of art have specific meanings.

10k hands isn't enough to derive any useful information, especially considering that you're hopefully a better player at hand 10k than hand 1.

I think you should focus on the fundamentals and let variance do its thing. Since you can't control it, you should just accept it as it is.

I've never been a statistics player and I don't plan on being a statistics player in the future. I don't think there's much use for a recreational player in learning all this ****. If and when you're crushing medium to high stakes and living off of your winnings, then and only then should you be concerned with the statistics because you'll want to know how much you can withdraw on a regular basis while maintaining a safe risk of ruin considering the size of your bankroll and the need to protect it. However, by that time you will have amassed so much money and you will have played so many hands that even a vicious downswing will only affect your winrate slightly. It'll be just a drop in the bucket, so to speak.

Until then, I think you should just accept that every hand is a fair deal and you should try to make the most of your playing experience by having as much fun as possible. That way, when your losses add up to such a substantial amount that the hole you've dug for yourself will be impossible to get out of, you can look back on your poker days as a fun time in life. If instead you focus on winrates, standard deviation, risk of ruin, etc, then you're just going to end up with bad feelings when you lose, but hey, at least you can always blame variance.