Wondering across how many hands/hours of play one would establish their vppip? I'm thinking as a minimum around 10,000 hands would be close within maybe 5-7.5% standard deviation.?

Thanks alot.

Statistically establishing a VPIP using a series of hands is really just a series of binomial trials, with a “success” probability (p) equal to your VPIP expressed as a decimal and a “failure” probability q = 1-p. Mathematically is is well established that the expected number of successes for N trials is Np and the standard deviation of this value is sqrt(Npq).

Assuming that p=0.3 then (you can repeat this for your actual value), with N=10000 we expect 3000 hands played with a standard deviation of about 45.8. Using 2 standard deviations gives a confidence interval of 95%, three gives a 99% CI. So if you got 30% for a VPIP after 10K hands the 95% CI would be 2908-3092 hands played or 29.08 to 30.92%. If you wanted 99% confidence the interval would be 2863-3137 hands played or 28.63-31.37%.

So yes, 10K hands should give you a pretty decent idea of your VPIP.

Thank you for putting that into English at the end there.

You've been given the answer for establishing the vpip of someone where you do not have any information other than did they vpip. For yourself if you have a set of hands you will vpip with no raise you can establish your maximum vpip at 0 hands. It will vary by game how close you come to this; in a true limp fest you will come close. If someone is raising 20BBs blind every hand it will be much smaller. If you do not have this set of hands or are more interested in actual vpip than the maximum roughly 1000 hands provides a good measurement assuming you can accurately recall whether you have had average luck in your starting hands. The more information you have the smaller the needed sample.

Thanks guys.. really appreciate it.

If it took 10,000 hands to get a good estimate of a player's VPIP, then HUDs would be useless.

Spoiler warning; HUDs are not useless.

Adding to this - suppose we are playing on 8 tables, we see a player who we don't recognize, they're only on one table, and we saw them showdown 84o from UTG in the only hand we've seen them play.

Do I need to see 1k+ hands in order to figure out that this guy isn't one of the 12 VPIP nits you see at the zoom tables?

The question is degrees of precision. Yes you maybe could justifiably assume that the player you describe has a VPIP >12 (most likely, but maybe he misclicked that particular hand and caught a good flop - beware of making conclusions based on a sample size of 1). That doesn’t tell you much about what his VPIP actually is numerically. Maybe he just likes 84 and thinks that is his “lucky hand” and plays a really tight range other wise. Maybe he likes to get caught playing a crap starting hand in any given session to make opponents think he is an idiot. You can’t conclude anything quantitatively from that one hand.

And the number of hands you need depends on how accurate you want your estimate to be. Generally speaking the accuracy depends on the inverse square root of the number of hands. In simpler terms, if we know the accuracy to 1% (which my prior post shows that it takes about 10k hands to get), if we decided that 2% is sufficient, then we need 1/4 of the number of hands, or in this case about 2500. If 3% is good enough then about 1100 hands would do. In the other direction if we wanted twice the accuracy - 0.5% - we need 4x as many hands or 40K.

HUDs are useful, but beware the use of stats for small numbers of hands. If you have 100 hands on a villain and a VPIP of 40, that could reasonably be anywhere from 30-50% for his actual VPIP.

Play 100 hands. If your VPIP is over 20, you are playing WAY too many hands. LOL

My only point is that it's valuable to take a bayesian approach rather than a frequentist one. The fact that it's an unknown single-tabling and I'm shown 84o is enough for me to start deviating. With all these factors taken together our posterior for their VPIP distribution is going to look a lot different than what a confidence interval would suggest.

The crux of OP's question was answered well enough, I'm just adding some additional factors to the discussion. The rote confidence interval calculation doesn't tell the whole story of how a good player would make use of the data that they have available to them.

When a Bayesian and a Frequentist argue, bet on the Bayesian.

(How many times does the Frequentist have to lose before they admit that they are wrong? )