BB/100 variations question !

[kinghippo423]

I was wondering this and, even if my question is maybe to general, I hope to get somekind of a answer from you guys.

If I have BB/100 of 6 after 10K hands, what is the range of my actual REAL BB/100 in the long run? Variation of 6? [0,12]

How about 25K hands? 4?
How about 50K hands? 3?
How about 100K hands? 2?

I ask this question to be able to go up a limit with, in theroy, a good confidance factor of beeting the upper limit without playing hundreds thousands hands.

Thanks a lot guys.

[pococurante]

10k hands is a fairly big amount for something like this. You wanted to find out how many BB/100 you normally earn, and you tested yourself 100 times.

Unless you've been getting a lot of good luck during that run, 6 BB/100 will be very close to your "true" average. Probably within 1 or 2 at most would be my guess.

[LarryLaughs]

I'd say that actually 10k is very little. Any upswing or downswing can change the result a lot. During 1000-2000 hands you could get so much "extra" from a good run that your winrate is inflated after 10k hands.

I would prefer to get 50k hands in before making any big assumptions. Anyway, if you do 6 BB/100, I think it is very likely that you are a winning player, but not so clear how much.

[Pokerfarian]

Assuming NLHE since it wasn't stated.
You're up 600BB in total. It's possible, thus, you could be anywhere from deserving -400 to deserving +1600, assuming +-10BI as a sort've "biggest realisticly possible swing", with a strong bias towards to middle. That's anywhere from -4BB/100 to +16BB/100 so you'd definitely need more hands to have an accurate idea of winrate. But your certainly a very strong favourite to be a winning player.

[pococurante]

Hrm, for some reason I thought I read he was playing limit holdem. If it's NLHE then yeah, more hands are definitely needed.

[rufus]

[ QUOTE ]
Hrm, for some reason I thought I read he was playing limit holdem. If it's NLHE then yeah, more hands are definitely needed.

[/ QUOTE ]

If I recall correctly, the variance for limit tends to be higher because you'll get the odds to call to draws much more often.

[sh58]

10k hands is pretty insignificant.

after 50k hands you will probably know whether you are a winner or a loser at that level.

after 100k hands you will know your winrate +- about 3

after 300k hands you will know your winrate +- about 1

these are just estimates.

you can work out your confidence etc. by doing loadsa stats that someone on the forum will know

[jay_shark]

Use this formula :

xbar +- z*(s.d)/sqrt(number of trails)

xbar is your sample win rate through the number of hands you're interested in .

z is the level of confidence you'd like . Typically , we'd like z=2 or about a 95% confidence level .

s.d/sqrt(number of trials) is your sample standard deviation. Each trail consists of 100 hands , so 50k hands would be equivalent to 500 trials .

[pococurante]

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If I recall correctly, the variance for limit tends to be higher because you'll get the odds to call to draws much more often.

[/ QUOTE ]

Doesn't playing more draws mean that you're more likely to complete your hand the expected percentage of the time, reducing variance?

Don't NLHE's occasional large pots, where you can win or lose a buyin or more in one hand, lead to more variance?

I'm not sure that I'm right... if I'm wrong please enlighten me. There's only one thing that I'm sure about, which is that PLO is most luck reliant. It's crazy how often two players are correct to raise and reraise each other all in on the flop, and then a coinflip decides a buyin.

[DrVanNostrin]

[ QUOTE ]
[ QUOTE ]
If I recall correctly, the variance for limit tends to be higher because you'll get the odds to call to draws much more often.

[/ QUOTE ]

Doesn't playing more draws mean that you're more likely to complete your hand the expected percentage of the time, reducing variance?

Don't NLHE's occasional large pots, where you can win or lose a buyin or more in one hand, lead to more variance?

I'm not sure that I'm right... if I'm wrong please enlighten me. There's only one thing that I'm sure about, which is that PLO is most luck reliant. It's crazy how often two players are correct to raise and reraise each other all in on the flop, and then a coinflip decides a buyin.

[/ QUOTE ]
Clearly a NL game with blinds of 1 and 2 will have more variance than a limit game with the same blinds. The key to answering this question is to find a limit game and a NL game where experts have the same win rate, then compare the variances of those games. Of course it's very difficult say what an expert is and what one would expect to make.

Several years ago when there were a bunch of limit books out there and no one knew anything about NL, NL would have been the game with "less variance". Now that NL games are getting tougher that might not be true.

Another useful statistic is the coefficient of variation (this is the standard deviation per 100 divided by win rate per 100). You could think of it as the luck to skill ratio. It should be noted that this number is a function of the number of hands. (By that I mean the coefficient of varation per 100 does not equal the coefficient of varation per 200).