An average is not a typical session
The mean outcome reported by the variance explorer.
- Read as
- The average result describes what usually happens, so a session should look roughly like it.
- Actually
- The mean is pulled upward by rare large wins, so in a high-volatility game most sessions finish below the average and the median is the better description of a typical one.
The model game returns b × k with probability p and nothing otherwise, with k = r ÷ p so that its RTP is exactly r. Lowering p while holding r fixed forces k up: wins become rarer and larger, variance rises, and the average is unchanged.
That is the whole point. Two settings with identical RTP produce completely different distributions, and the average is the statistic least sensitive to the difference.
As p falls, more and more of the total return concentrates in fewer outcomes. The mean stays put while the bulk of the distribution slides below it, so the share of runs finishing under the average grows. Reading the mean as the typical case gets steadily more wrong in exactly the games that feel most volatile.
The explorer reports percentiles for this reason, using nearest-rank so every value shown is one the simulation actually produced. Percentiles are sample estimates and are displayed to the nearest whole coin.
The model is also gentler than reality. Real games have many payout tiers and heavier tails, so a real game at the same RTP and hit frequency spreads more widely than this one. The model understates extremity, which is the safe direction to be wrong in.
The method behind this figure
Variance simulation (model game) — variance-simulation v1.0.0. Its formula, assumptions and limitations are published in full on the methodology page.
Related: Variance explorer, Volatility, Glossary, Methodology