Cash games, win rate

[ahsfl]

How many hands until your win rate is considered sustained? Does this also vary by level?

[pzhon]

There shouldn't be a set number of hands at which point your win rate is considered sustained. What you can say is that your confidence interval tightens about your observed win rate.

A rough 95% confidence interval is your observed win rate +- 2 standard deviations. The standard deviation of your win rate after n * 100 hands is SD/squareroot(n), where SD is your standard deviation per 100 hands. For example, if your standard deviation in limit is a typical 15 BB/100, and you played 5000 hands, n=50, and the standard deviation of your win rate is about 15/sqrt(50) ~ 2 BB/100. If your observed win rate is 1 BB/100, then your 95% confidence interval would be 1+-4 BB/100, from -3 BB/100 to +5 BB/100. Quadrupling the number of hands shrinks the confidence interval by a factor of 2.

In NL, the standard deviation depends more on your playing style. Typical values might be 85 big blinds/100 in full ring, and 95 big blinds/100 shorthanded, but some styles will produce much lower or much higher standard deviations.

[Dove]

Well said pzhon.

[ahsfl]

ok, sorry, I topped out at algebra I so this is very confusing to me. Could you or someone else try to break this down a little bit more to me? Also for playing style assume LAG and I play NL.

[Logitech]

Might as well wait for pzhon to do that.

[fadedstar]

play 10k hands, see if your busto, rinse and repeat.

honnestly, stick to a level you can afford and be patient. log in at least 20k hands and evaluate.

[pzhon]

The idea of a confidence interval is well worth learning.

When you add together the outcomes of many hands, the result is close to a normal distribution, a bell corve. Just over 95% of the normal distribution is within 2 standard deviations of the mean. About 95% of the time, your observed result will be within 2 standard deviations of your true win rate. That's not a certainty, but you can say it is "quite likely."

Computing a confidence interval is simple algebra, evaluating a formula. The standard deviation of your win rate aftern n * 100 hands is (SD per 100)/sqrt(n). If you play with a LAG style, 6-max, you might have a standard deviation per 100 hands of 120-150 big blinds; let's assume it is 150.

After 10,000 hands, the standard deviation of your win rate would be 150/sqrt(100) = 15 big blinds/100. If your observed win rate was 20 big blinds/100, then you can say it is quite likely that your win rate is between 20-30 and 20+30 big blinds/100. As you play more hands, the confidence interval gradually shrinks due to the 1/sqrt(n) factor.

If your win rate is high, you probably are not as concerned about knowing your win rate as precisely as if your win rate is low. The difference between winning 18 versus 22 big blinds/100 is not as important as the difference between winning 2 versus 6 big blinds/100.

[checktowin]

thats a good winrate imo

[excession]

you can also get closer to your 'true' win rate by using your expected win rate from PokerEV > your actual one from PT.

By no means does PokerEV account for all luck - it can only calculate when the hand went to SD and ignores getting coolered (e.g. things like KK running into a short-stack AA pre-flop)- but the number given will certainly be closer to your true win rate than the naked PT numbers..