Live poker variance: hours, hands and an uncertain win rate

Hours need a hands-per-hour assumption.

Use 100 playing hours at an assumed 30 hands/hour: that is 3,000 modeled hands, or 30 blocks of 100. It is an estimate of volume, not a measured hand count. Edit the pace for your table; breaks should not count as playing hours.

The live variance tool exposes both hours and hands/hour. The same modeled hand volume should give the same outcome whether entered as live hours or online hands.

SD describes spread, not your edge.

BB means one big blind. For this illustration, assume true net edge 10 BB/100 hands and SD 120 BB for a 100-hand result. The SD is an editable example, assumed and not measured. It is not a normal-live benchmark or a preset for every NLHE or PLO game.

Standard deviation describes the model’s spread around its expected result. Depth, straddles, player style, game conditions and rake can change the appropriate input. The tool’s evidence notes distinguish assumptions from source-reported measurements.

Variance adds across independent equal blocks; SD therefore scales with their square root. For N hands and t = N/100:

Expected result = w × t
Total-result SD = s × √t

At 30 hands/hour, the assumed one-hour SD is 65.73 BB: 120 × √0.3. Multiplying 120 directly by hours or hands/hour would use the wrong units.

Read a future outcome band under those assumptions.

For the 100-hour illustration, the model’s expected result is 300 BB and its total-result SD is 657.27 BB. At USD 1/2, the expected profit is USD 600.

Using the normal-distribution model, the 95% final-outcome band is approximately −988.22 to 1,588.22 BB. The modeled chance of finishing below zero is about 32.4%.

That is a hypothetical future-result distribution with a specified true edge and SD. It does not establish that you have the edge. The model assumes independent, stationary increments and fixed stakes; changing games and heavy tails can make real results behave differently.

The band is pointwise: a band at the final horizon is different from a corridor containing an entire path. The tool’s seeded paths are illustrations, not worst-case bounds or bankroll-ruin forecasts.

An observed win rate asks another question.

The future scenario above assumes 10 BB/100 is true. If instead you observed 3 BB/hour over 100 hours, the same assumed hourly SD gives a conditional 95% normal interval of about −9.88 to 15.88 BB/hour for the mean.

To reproduce it in the observed-rate tool, choose live hours, 100 hours played, 3 BB/hour observed net win rate, SD 120 per 100 hands and assumed 30 hands/hour.

That wide interval still includes losing and winning rates under the model. The known-SD normal interval treats SD as supplied; with a guessed SD, this result is conditional on that guess. This tool does not estimate SD or fit a Student-t interval.

NIST explains confidence coverage: a 95% method covers the fixed true mean in about 95% of repeated samples under its assumptions. It does not assign a probability that this player is a winner. Open observed-rate uncertainty separately →

More volume changes the two spreads differently.

Holding the same inputs fixed, 400 hours means four times the hands: expected total result becomes 1,200 BB and total-result SD becomes 1,314.53 BB, twice as large. The standard error of the observed average instead halves.

There is no magic hour count that proves skill. The relevant uncertainty depends on the sample, SD assumption and whether the game stayed comparable. Taking the ordinary SD of unequal-length session win rates does not produce a common 100-hand SD.

Use future variance for assumed swings and observed-rate uncertainty for the sampling question. Record complete sessions, including losses and breaks. The session template or GoodRun’s offline workflow can keep that record consistent.