Expected balance is a lower bound, not a floor
The expected balance after wagering, from the expected balance calculator.
- Read as
- The expected balance is the amount a session will end with, and results should land near it.
- Actually
- It is the average over very many repetitions of the same wagering, computed as though the entire requirement gets staked — which is usually more staking than actually happens, so the figure typically sits below the true expectation.
The formula is E[balance] = B − T × h, where T is the amount that must be staked and h is the house edge. It charges the edge against the full required turnover.
Real wagering stops when the balance runs out. A run that busts stops losing, while the formula keeps staking past zero. So actual turnover tends to be smaller than T, and the true expectation is B − h × E[actual turnover], which is generally higher than the published figure.
This is observable rather than asserted. Run the variance explorer with a heavy requirement and the simulated mean sits above the closed-form number, for exactly that reason. The gap is small while the balance comfortably covers the requirement and grows as busting becomes likely.
The alternative — modelling ruin exactly — needs the game’s full payout distribution and the bet size. Neither is published for real games, so the choice was between a stated lower bound and a precise-looking number derived from an invented paytable. This site publishes the bound and says so.
The direction of the error matters. A lower bound understates what remains on average, so it is the conservative side to be wrong on. It is still not a floor: individual sessions end below it routinely, and a balance can reach zero long before the requirement is met.
The method behind this figure
Theoretical expected balance after wagering — expected-balance v1.0.0. Its formula, assumptions and limitations are published in full on the methodology page.
Related: Expected balance calculator, Variance explorer, Methodology, Glossary