How to calculate return to player (RTP)
By dividing the win and turnover figures generated from a game you can determine the actual RTP.
For example, if after one month of play a game, designed with a 91.68% RTP, has accrued £1,200,000 of turnover and £1,085,000 in wins the RTP can be calculated as follows:
1,085,000 / 1,200,000 = .9042
Therefore this game has achieved an actual RTP of 90.42%, which is below the designed RTP.
Importantly however the volatility of the game must also be considered as it will inform the allowable tolerance above or below the theoretical RTP. The tolerance will be wider when only a limited amount of play has been measured, but as the volume of play increases the tolerance will decrease.
After a significant amount of plays the actual RTP should be very close or equal to the theoretical RTP. To continue with the above example, if the game had a volatility (standard deviation) of 5.6 then the acceptable upper and lower tolerance will be as below:
| Number of games played | Range +/- | % from the mean† |
|---|---|---|
| 50,000 | +/- | 4.90862 |
| 100,000 | +/- | 3.47092 |
| 200,000 | +/- | 2.45431 |
| 300,000 | +/- | 2.00393 |
| 400,000 | +/- | 1.73546 |
| 500,000 | +/- | 1.55224 |
| 600,000 | +/- | 1.41700 |
| 700,000 | +/- | 1.31188 |
| 800,000 | +/- | 1.22715 |
| 900,000 | +/- | 1.15697 |
| 1,000,000 | +/- | 1.09760 |
† This deviation from the mean is calculated with a 95% confidence interval (opens in new tab). This would mean a non defective game might still fall outside range approximately 1 in 20 tests. A higher confidence interval can be selected to reduce the chance of false alarms however caution should be exercised so as not to create tolerances that are too wide. The confidence interval should not exceed 99%, this would mean a non-defective game might fall outside range approximately only 1 in 100 tests. One measurement failure does not confirm the game/RNG is faulty, however sequential failures or a number of failures over a given frequency of measurements might.
So if 400,000 games had been played to accrue turnover and win figures of the example then the allowable tolerance will be 1.75 above or below 91.68. The game could return between 89.93% and 93.43% and still be considered to be performing as expected.
The game’s designers will have calculated the exact theoretical RTP as well as the game’s volatility (these figures will also be reviewed as part of the required external testing). These are the figures against which the actual performance should be measured.
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What volume of play should be achieved before measuring the actual RTP?
Last updated: 25 January 2021
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