Game mathematics: RTP, house edge and volatility
96% RTP does not mean you get €96 back from a €100 deposit. RTP, or the theoretical return-to-player percentage, describes a game's long-term average, not the outcome of your individual session. Change the inputs and compare the average, the variation and one random outcome.
TÄRING editorial team · Content checked
RTP and house edge calculator
See the theoretical average loss for the stakes you enter.
The calculation result will appear here.
RTP, house edge and volatility at a glance
Key points
What is RTP?RTP shows the share of money staked that is paid back to players on average over a long period.
What is the house edge?It is the share of stakes that the game operator retains on average over a long period. For example, 96% RTP means a 4% house edge.
What is volatility?It describes how much outcomes can vary. A greater chance of finishing ahead can come with a larger loss when things go badly.
Chance owes you nothingPrevious bad luck does not increase the chance of success on the next independent trial.
How to use: RTP and house edge
- Choose the input method. Enter a stake and number of rounds, or enter total stakes directly. Holding +/− changes the number progressively faster. One round means one stake, such as one spin. Selecting “Total stakes” automatically converts stake × number of rounds into a total.
- Enter the RTP of the specific game. For example, €1 × 100 rounds at 96% gives an average loss of €4. The calculation updates automatically; use a decimal point.
- The result shows an average, not your actual outcome. It also does not show how much money you need to start playing. “Reset example” restores €1, 100 rounds and 96%.
A payout is not the same as profit
€1 stake → €0.40 payout → €0.60 loss. A previous payout can be staked again, so total stakes can exceed the deposit.
What does this mean for wagering requirements?
If 35× applies to a €100 basis and stakes count in full, the required turnover is €3500. At 96% RTP, the mathematical average loss on that turnover is €3500 × 4% = €140.
The example assumes that every stake has the same RTP. It does not show how much money you will actually have left after wagering. The calculation does not add a bonus to your funds or account for running out of money or bonus restrictions. How do you calculate wagering requirements? You can find the turnover with the wagering calculator.
Playing longer does not guarantee you will recover losses. If RTP stays the same and is below 100%, average loss in euros increases with total stakes. Get help limiting your gambling.
Finding RTP, playing history and formulas
Find RTP in the game's help, rules or paytable. Games with the same name may have versions with different RTPs. Payout frequency is not RTP.
Payouts ÷ stakes × 100 in your playing history shows only your return so far. €80 in payouts and €100 in stakes gives an 80% return, but does not establish the game's theoretical RTP or predict the next outcome.
Total stakes = stake × number of rounds. House edge = 100% − RTP. Average loss = total stakes × house edge / 100. Average total payouts = total stakes × RTP / 100.
The calculation excludes bonuses, fees and player decisions. Blackjack figures depend on the rules and how it is played; poker rake and sports-market margin are not the RTP used by this tool.
Same RTP, different volatility
Both illustrative models have 96% RTP and a €1 stake per round.
A More frequent small payouts
The stake per round is €1. A 48% chance of a payout of €2; otherwise €0.
Lower variation · 0.48 × €2 = €0.96 average payout.B Less frequent larger payouts
The stake per round is €1. A 4.8% chance of a payout of €20; otherwise €0.
Higher variation · 0.048 × €20 = €0.96 average payout.These are two simplified illustrative models, not real slots. The same RTP does not determine the probability of finishing ahead.
One random example
The exact calculation above shows probabilities. The chart shows one possible sequence of outcomes, not a forecast.
The zero line means payouts so far cover stakes so far; it is not a starting balance. Every round is completed; running out of money is not modelled. The average line is not a level that an individual outcome must return to. The scale may change between examples but remains fixed during each example.
The comparison will appear here.
How to use: comparison and random example
- Choose the number of rounds. The number field, slider and example buttons change both models together. Hold +/− to change the value quickly. Exact probabilities and the size of losses appear next to the input.
- Run the simulation. Lines A and B show the result after each €1 stake. Above zero is a profit; below zero is a loss. You can pause the example or show the final result immediately. “Without animation” shows the final result as soon as you start.
- One random example can differ from the average. Each new run draws a new sequence; the result can also repeat. A single sequence does not have to return 96%. Changing the number of rounds cancels the previous example.
- Consider both the chance of finishing ahead and the size of losses. The exact table covers every possible final outcome. Average loss in losing runs includes only runs that finish at a loss; it is not the maximum loss. Every round in the model is completed.
What does RTP alone not tell you?
RTP alone does not tell you how often a game pays out or how likely you are to finish ahead. You also need the possible payouts and their probabilities. Here, greater volatility means greater variation, not a better average outcome.
Model formulas and limits
Rounds are independent. The number of payouts K follows a binomial distribution: P(K = k) = C(n, k) × pᵏ × (1 − p)ⁿ⁻ᵏ. Result after stakes = k × payout − n. Mean = −0.04 × n. Standard deviation = payout × √(n × p × (1 − p)).
Average loss in losing runs = the probability-weighted sum of the absolute values of all negative outcomes ÷ the probability of finishing at a loss.
For the exact table we calculate every possible final outcome. For a random example each round is drawn separately in each model; one example does not determine the table percentages.
The 5th–95th percentile interval is selected so that, under the model, the result falls within it with at least 90% probability. The endpoints are included.
Running out of money and the required starting balance are not modelled. Every selected round is completed; a different stopping rule would change the results.
Is the next result already “due”?
Previous bad luck does not change the probability of the next independent trial.
The calculation result will appear here.
How to use: independent trials
- Choose an event and its probability. The probability of one side of a fair coin is 50%. The 1% example is an invented event, not a real game's figure.
- Enter the number of future trials. 50% and 3 trials gives an 87.5% probability of at least one occurrence. “Reset example” restores 1% and 100 trials.
- The calculation covers only trials still ahead. For a fair coin, the probability of the chosen side on the next toss remains 50%, even if it did not appear on the previous three tosses. Do not include past tosses in the number of future trials. Enter the event probability, not RTP.
“Once in a hundred on average” is not a schedule
A 1% event does not occur at all in about 36.6% of sequences of 100 independent trials. Its probability on the next trial is still 1%.
This applies to independent trials with an unchanged probability. If earlier events change the probability of the next outcome — for example, removing cards from a deck — this assumption no longer holds.
Formula and precision
With event probability p per trial and n trials, the probability of no occurrences is (1 − p)ⁿ and the probability of at least one occurrence is 1 − (1 − p)ⁿ. In the calculation, 1% = 0.01. Probabilities very close to 0% or 100% appear as, for example, “below 0.01%” or “above 99.99%”, rather than exactly 0% or 100%.
Sources and calculation limits
UK Gambling Commission: guidance on RTP and house edge, and on theoretical versus measured return. These explain the concepts, not Estonian legal requirements.
Illustrative models and calculations: TÄRING. They do not predict wins or provide betting recommendations. Inputs and calculations stay in your browser.