Independence and a suitable sampling model are required.
Estimate versus truth
A simulated return of 95.9% is not proof that the exact RTP is 95.9%. The estimate moves from run to run.
A confidence interval gives a range produced by a stated procedure, not a probability guarantee about one fixed completed interval.
Why rare prizes are difficult
When a large share of return comes from an event occurring once in millions of trials, short samples can miss it completely.
Analytical enumeration or variance-reduction methods may be more informative than brute-force sampling.
Observed casino results
Player tracking data can be affected by changing wagers, strategies, promotions, stopping, and non-independent sessions. A raw win percentage is not automatically an estimate of the game’s edge.
The model and sampling process must be described before precision is meaningful.
Responsible reporting
Publish the number of trials, estimated standard error or interval, random process, and validation checks.
Do not print more decimal places than the uncertainty supports.
Working checklist
- Report sample size
- Estimate uncertainty
- Check independence
- Treat rare prizes separately
- Round to justified precision
Confidence intervals and sample size, explained. uses rounded teaching examples. Apply a number to a live game only after matching its rules, pay table, strategy and denominator.