How many hours of live poker do you need to know your real win rate

Your hourly rate is an estimate

A live player's hourly rate is simple to calculate: total profit divided by total hours. If you are up $1,500 over 100 hours, you have won $15 an hour so far. What that number cannot tell you on its own is how close it is to your true rate, the one you would see over an enormous number of hours at the same game against the same kind of opponents.

Poker results swing hard relative to the edge, so the gap between observed and true rate stays wide for a long time. PokerCharts, which publishes poker variance tools, describes the first 100 hours of live results as almost entirely noise and says the error band is still very wide between 100 and 500 hours. The way to put a number on that width is a confidence interval.

How to calculate the margin of error

The NIST/SEMATECH e-Handbook of Statistical Methods gives the confidence interval for a mean as the sample mean plus or minus t × s ÷ √N, where s is the sample standard deviation and N is the sample size. For a 95 percent interval with a large sample, NIST's table of t critical values gives 1.960 at infinite degrees of freedom and 1.984 at 100, so 1.96 is a fair multiplier once you have a few hundred hours.

For poker, use hours as the unit. Your hourly rate is the mean, s is your standard deviation per hour and N is the number of hours. You can estimate the standard deviation from your session records: for each session, compare the result with what your average rate predicts for its length, square the difference, divide by the hours, average those values and take the square root.

If you do not have enough sessions yet, PokerCharts' figures give a starting point. It estimates a standard deviation of roughly 80 to 100 bb/100 for full-ring no-limit hold'em and a live pace of 20 to 30 hands an hour, using 25 in its own conversions. At 90 bb/100 and 25 hands an hour, the standard deviation is 90 × √(25 ÷ 100), or 45 big blinds an hour. At $2/$5 that is about $225 an hour.

What the numbers look like

Take a player whose records show $15 an hour with a $225 hourly standard deviation. After 100 hours the standard error is $22.50, and the 95 percent interval runs from about −$29 to +$59 an hour. The data cannot yet distinguish a solid winner from a losing player.

After 400 hours the standard error halves to $11.25 and the interval narrows to about −$7 to +$37. After 1,000 hours it is roughly +$1 to +$29, the first point at which the lower end sits above zero. After 1,600 hours it is about +$4 to +$26, still a wide band around $15.

Notice the pattern. Going from 100 to 400 hours, four times the playing time, only halved the uncertainty. PokerCharts puts it plainly: to cut your error band in half you need four times as many hands, and the NIST handbook notes the same effect for any mean, since the interval narrows through the √N term. In big blinds, 1,000 hours at 45 big blinds an hour still leaves a margin of about ±2.8 big blinds an hour.

NIST also explains what the 95 percent means: if many samples were collected and an interval computed for each, in the long run about 95 percent of those intervals would contain the true mean. It is a statement about the method, not a guarantee about your particular interval.

How many hours before a winner looks like a winner

You can turn the formula around. The lower end of the interval reaches zero when the hours equal (1.96 × standard deviation ÷ hourly rate)². With a $225 standard deviation, a $15 an hour winner needs about 860 hours before the 95 percent interval stays above zero. A $30 an hour winner needs about 220 hours. A $7.50 an hour winner needs about 3,460 hours.

The win rate is squared in the denominator, so halving the edge quadruples the hours. That is why a small edge at a live game can take years of weekend sessions to confirm, and why PokerCharts treats 500 to 1,000 hours, roughly 12,500 to 25,000 hands, as the range where stronger evidence of a real edge starts to appear, and 1,000 hours or more as the most honest read you can get from results alone.

Common mistakes when reading your win rate

Mixing stakes. Dollars an hour at $1/$2 and at $2/$5 are not the same measurement. Either keep separate figures for each stake or convert everything to big blinds before averaging.

Judging after a heater or a downswing. A great month moves the average a lot when the total is only a few dozen sessions. With a $225 standard deviation, 60 hours of play leaves a margin of about ±$57 an hour, which is wider than most live win rates.

Skipping the bad nights or the short sessions. Every hour belongs in the denominator and every loss in the total. A log that is missing the ugly evenings will flatter the rate and shrink the apparent spread at the same time.

Treating the rate as fixed. PrimeDope points out that a real win rate changes as your skill improves, the player pool changes and you tilt. A long record measures the past games you played, not the next ones. RollGauge keeps the hourly rate and BB/100 for every session you log and lets you filter by game, period and venue, so one stake or one room can be checked on its own instead of blended into everything else.

This guide explains bankroll arithmetic. It is not financial advice and does not suggest that poker is a reliable way to make money. If gambling is causing problems for you or someone close to you, the National Council on Problem Gambling's helpline, 1-800-MY-RESET (1-800-697-3738), is confidential and open 24/7 by call, text or chat.

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