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House Edge and RTP Maths: Expected Loss, Variance and Short Sessions
House edge and RTP are two views of the same number. Worked examples show expected loss per spin, what variance does and why short sessions rarely match the stated RTP.
By Casino Software Hub Editorial Team · Reviewed by Casino Software Hub Editorial Team · Published Oct 30, 2026 · Updated Oct 30, 2026 · 3 min read
Key takeaways
- RTP plus house edge equals 100%. A 96% RTP means a 4% house edge.
- Expected loss is total amount staked times house edge. It is an average, not a forecast.
- Variance makes short sessions swing far more than the edge, so the result of a session says little about the RTP.
Two names for one number
Return to player (RTP) is the share of all stakes a game pays back on average over a very large number of rounds. House edge is the remainder. If RTP is 96%, house edge is 4%. These are theoretical figures calculated from the game’s maths, and studios publish them per game. See how to read RTP, volatility and max win.
Expected loss
Expected loss per round is the stake multiplied by the house edge. With a 96% RTP game and a stake of 1.00 per spin, the expected loss is 0.04 per spin.
- 100 spins: 100 × 0.04 = 4.00
- 1,000 spins: 1,000 × 0.04 = 40.00
- 10,000 spins: 10,000 × 0.04 = 400.00
Expected loss grows in direct proportion to the total amount staked, which includes winnings that are played again. That is why faster games accumulate it faster.
What variance does
The expected value is an average. Individual spins vary around it, and the spread is measured by standard deviation. For illustration, assume a volatile slot where one spin of 1.00 has a standard deviation of 3.00. The standard deviation of the net result over n spins is 3 × √n, because independent spins add variances, not deviations.
- 100 spins: 3 × 10 = 30
- 1,000 spins: 3 × √1,000 ≈ 95
- 10,000 spins: 3 × 100 = 300
The figure of 3.00 is an assumption for the example. Real values differ by game and are not always published.
Why short sessions diverge
Compare the expected loss with the spread. After 100 spins the expected loss is 4 and the standard deviation is 30, so the average is small next to the swing. Using a normal approximation, the probability of finishing a 100-spin session ahead is roughly 45%. After 1,000 spins it is roughly 34%. After 10,000 spins it is roughly 9%.
| Spins | Expected loss | Std. deviation | Approx. chance of being ahead |
|---|---|---|---|
| 100 | 4 | 30 | about 45% |
| 1,000 | 40 | 95 | about 34% |
| 10,000 | 400 | 300 | about 9% |
The edge grows in proportion to the number of spins, while the spread grows only with its square root. Over a long time the edge dominates. Over a short time it is hidden. Real slot payouts are skewed, with a few large wins and many small losses, so the normal approximation is rough, especially for high-volatility games.
What this does not mean
A lucky short session does not show that a game’s RTP is higher than stated, and a bad one does not show it is lower. Past results do not change the odds of the next spin. For the mechanics that create high or low volatility see slot mechanics. Tools for limiting spend are on our responsible gambling page.
This article is information, not advice to gamble. You must be 18 or older.
FAQ
What is the relationship between RTP and house edge?
They add up to 100%. A game with 96% RTP has a 4% house edge: on average, 4 units of every 100 staked are kept by the operator over a very large number of rounds.
Does 96% RTP mean I get 96 back from my session?
No. RTP is a long-run average over a very large number of rounds. In a short session the result is dominated by variance and can be far above or below the average.
What does variance or volatility measure?
It measures how widely individual results spread around the average. High-volatility games pay rarely but sometimes in large amounts, so results differ more from the RTP in the short term.