Game mathematics and uncertainty

Status: general explanations · Checked: 2026-11-09 · Source: SRC-MATH-001 (mathematical definitions) · Jurisdiction: general

Return to player (RTP)

RTP is the share of total amounts wagered that a specific game configuration is designed to return to players over a very large number of plays. An RTP of 96% does not mean you will get $96 back from $100 wagered. It is a long-run average across all players and plays; any individual session can return far more or far less, including zero.

House edge

House edge = 1 − RTP for the same configuration. At 96% RTP, the edge is 4%: an expected average cost of $4 per $100 wagered over the long run. “Expected” is an average, not a schedule — short sessions are dominated by chance.

Variance and volatility

Variance describes how widely outcomes swing. A low-variance game pays smaller amounts more often; a high-variance game pays less often, sometimes much larger. Same RTP, very different risk of a fast, large loss. RTP alone never describes that risk.

Independence and the gambler's fallacy

Each spin or hand in a properly functioning random game is independent: a run of losses does not make a win “due”, and a run of wins does not make a loss “due”. Past results change neither the RTP nor the next outcome's probability.

What remains unconfirmed

The RTP of any specific game at any specific operator is not stated on this page, because configurations differ by game version and operator setting and require a reviewed provider or operator source. Anyone quoting you a single RTP without naming the game, version, and configuration is leaving out the part that matters.