after how many hands is win rate statistically significant?

[steveyz]

I've been playing 3/6 at Party for 5000 hands or so. After how many hands could I be confident that my BB/hr winrate is "accurate" (say within 10%) ... 5000 definitely doesn't seem enough. How about 20k? 30k? 50k? 100k? more?

[balkii]

This should go in the probability forum, I think. But I can answer your question. the standard error of your winrate is


Standard Deviation per 100 hands / Square Root (# of hands/100).

+/- 1 standard error gives 68% confidence.
+/- 2 standard errors gives 95%
+/- 3 standard errors gives 99%


Really you need about 80K hands.

[Brian]

Hi steveyz,

Unfortunately, it is almost impossible to ever determine exactly what your win rate is. This is because to have any sort of idea what your hourly rate is, you need at least around 100k hands at the minimum. But, once you have gotten 100k hands into your Poker Tracker, you are probably significantly better than when you first started. However, you can probably get a roughly accurate idea after you have 100k hands.

-Brian

[MarkD]

Expanding on the above posters numbers and logic.

If I've played 80,000 hands and my SD is 14 BB / 100 hands then I am 95% sure my WR is within 1BB of what my stats say it is.

2xSD/sqrt(80000/100) = 0.99

So if my win rate is 5 BB/100 hands then I know, with a 95% certainty, that it is actually between 4-6 BB/100 hands.

[MikeyObviously]

well...those other guys are definatly correct on precision estimates on your exact win rate. However...if your just wondering IF your a winning player...5-10k hands should tell you that

[MarkD]

Ummm... not really.

At around 5k these are some realistic numbers.

WR = 4 bb/100 hands
SD = 15 bb/100 hands
therefor your 95% error would be
E(wr) = 4.24 bb/100 hands.

Hence you could be a loser. Your WR can fluctuate largely within a 10k sample of hands. That's only like 250 hours of casino play. Most people have historically said it takes around 2000 hours for your WR to converge so...

[steveyz]

I guess I am a winning player then :-). But I was actually wondering how accurate my current BB/100 hands rate (about 6 right now) is, in case I ever need to turn semi-pro (I'm a grad student, so playing 15/hr a week could definitely double my measly stipend, and delay my Ph.D. by a year perhaps ;-) And as a side note, I must say that PokerTracker is great. Definitely help me fix a few holes in my game.

[steveyz]

2000 hours huh? That's full time for a whole year. But as someone mentioned, my win rate would probably have increased a bit after I put in that much time at the tables.

[MarkD]

The 2000 hour marker is at a casino getting 40 hands per hour.

Essentially 80,000 hands, which if you are online playing 3 tables and getting 150 hands per hour is actually around 533 hours.

[Webster]

If you are winning 6BB per 100 hands at one table and keep it up, you are one of the best in the world.

Does that answer your question?

[shandrakor]

Depends on the limit he's playing at. .50/1, I see no reason why he couldn't maintain a 4-6BB/100 rate forever

[Webster]

OK - lets see you try /images/graemlins/smirk.gif

[Bob T.]

There are a lot of players that could probably maintain that win rate at .50/1.00 as long as they can maintain their interest in that game.

[steveyz]

I just checked again and my actual win rate is 5.20 BB/100 with a Stdev of 15.27 BB/100 .... given a sample size of slightly more than 5000 hands, I am supposedly 95% confident my real win rate is 5.20 +/- 4.32 BBs. I guess that's a pretty wide range.