What is an RTP and volatility calculator?
An RTP and volatility calculator takes a simple paytable and works out three things: the return to player (RTP), the hit frequency and how much results swing from session to session. RTP is the share of every bet that comes back on average over a very long run. The default paytable returns 96.25%, so the house edge is 3.75%, or 3.75 units on every 100 bet. That is a long-run average, and a short session can finish far from it.
The page uses a teaching paytable of up to five winning outcomes, each with a payout as a multiple of the bet and a “1 in X” chance. It is not any real game. Its purpose is to show that two games with the same RTP can feel completely different, because the volatility, the size of the swings, differs. It also shows why RTP says nothing about what will happen in the next hundred spins.
How do you use the RTP calculator?
- Enter the bet per spin. It starts at 1 unit.
- Enter the number of spins. It starts at 200, and the tool accepts up to 10,000.
- Fill in up to five winning outcomes. For each, enter the payout as a multiple of the bet and how rare it is, as “1 in X”. Use 0 for the payout of an outcome you do not need.
- Check the chances add up. Together they cannot be more than 1 in 1.
- Read the large number. It is the RTP. The panel shows hit frequency, volatility and a typical session range for your number of spins.
Example: The low-volatility paytable below returns 96.25% with a hit frequency of 62.7%. Over 200 spins at 1 unit the expected result is -7.50 units, but the middle 90% of simulated sessions range from -48.50 to +38.00 units.
How is RTP calculated?
RTP is the sum of each payout multiplied by its chance: RTP = sum of (payout x chance). The house edge is 1 – RTP. The hit frequency is the sum of the chances of any outcome that pays more than zero. The standard deviation per spin is the square root of (sum of payout squared x chance – RTP squared), measured in bets. The calculator treats the five outcomes as separate, with every other spin losing the bet.
For a session of N spins the average result is (RTP – 1) x N x bet. The spread comes from a seeded simulation of up to 5,000 sessions, so the same inputs always give the same answer. The volatility bands are this site’s rough guide: under 3 bets low, 3 to 6 medium and over 6 high. They are not an industry standard.
| Step | Working | Result |
|---|---|---|
| Chance x payout, 0.5x | 1/4 x 0.5 | 0.1250 |
| Chance x payout, 1x | 1/5 x 1 | 0.2000 |
| Chance x payout, 2x | 1/8 x 2 | 0.2500 |
| Chance x payout, 5x | 1/25 x 5 | 0.2000 |
| Chance x payout, 15x | 1/80 x 15 | 0.1875 |
| RTP | sum of the five | 0.9625 = 96.25% |
| House edge | 1 – 0.9625 | 3.75% |
Two paytables with the same RTP
Here are two teaching paytables. They both return exactly 96.25%. You can enter either one into the calculator.
| Payout | Chance | Share of RTP |
|---|---|---|
| 0.5x | 1 in 4 | 12.50% |
| 1x | 1 in 5 | 20.00% |
| 2x | 1 in 8 | 25.00% |
| 5x | 1 in 25 | 20.00% |
| 15x | 1 in 80 | 18.75% |
| Total | 96.25% |
| Payout | Chance | Share of RTP |
|---|---|---|
| 1x | 1 in 5 | 20.00% |
| 5x | 1 in 25 | 20.00% |
| 25x | 1 in 125 | 20.00% |
| 100x | 1 in 500 | 20.00% |
| 650x | 1 in 4,000 | 16.25% |
| Total | 96.25% |
Both paytables hand back the same amount in the long run, but the low-volatility one does it with frequent small wins, and the high-volatility one does it with a few big ones. That changes the experience of a session a lot.
| Measure | Low volatility | High volatility |
|---|---|---|
| Return to player (RTP) | 96.25% | 96.25% |
| House edge | 3.75% | 3.75% |
| Hit frequency | 62.7% (1 in 1.6) | 25.0% (1 in 4.0) |
| Standard deviation per spin | 1.91 bets | 11.44 bets |
| Volatility band | Low | High |
| Expected result after 200 spins | -7.50 units | -7.50 units |
| Median session | -9.00 units | -54.00 units |
| Middle 90% of sessions | -48.50 to +38.00 | -124.00 to +212.00 |
| Chance of finishing ahead | 36.1% | 28.4% |
Why do most sessions finish below the average?
Look at the median and the chance of finishing ahead. Both games have an expected result of -7.50 units over 200 spins, but the high-volatility game has a median of -54 units and only a 28.4% chance of finishing ahead. A few huge wins pull the average up, but most sessions never see one. The typical session is therefore worse than the average, and a small number of sessions are far better. The low-volatility game stays near the average, with a median of -9 units and a 36.1% chance of finishing ahead.
Neither game is “better”. A lower volatility means a slower, smaller loss. A higher volatility means a bigger chance of losing more quickly and a small chance of a large win. Because the RTP is the same, the average cost is the same.
Does a higher RTP mean I will win?
No. An RTP of 96.25% still means 3.75 units are kept by the house for every 100 bet, on average. Even a 99% RTP game has a house edge, and the swings in a session are much larger than the edge. RTP is useful for comparing the long-run cost of two games, and for seeing that no game returns more than you bet. It does not predict a session, and a game is not “due” to pay out after a long losing run. The roulette odds and payouts guide shows the same idea for a table game.
What does the calculator leave out?
- Real games. The paytable is a teaching model with up to five outcomes. Real slots have far more.
- Features. Free spins, bonus rounds and multipliers are not modelled.
- Variable bets. It assumes the same bet every spin.
- Published RTP. The RTP of a real game is set and published by the operator or regulator.
- Short samples. Session figures come from a simulation, so they are close but not exact.
- Player skill. Slots offer none. The result of each spin is random.
What mistakes do people make with RTP?
- Treating RTP as a session promise. It is a long-run average over many millions of spins.
- Comparing only RTP. Two games with equal RTP can have very different swings.
- Believing in “due” wins. Each spin is independent.
- Mixing up hit frequency and RTP. A game can hit often and still pay back little.
- Raising the bet to recover losses. It raises the expected loss in step with the bet.
What should you try next?
Enter the high-volatility numbers (1 in 5 for 1x, 1 in 25 for 5x, 1 in 125 for 25x, 1 in 500 for 100x, 1 in 4,000 for 650x) and compare the session range with the default. To see what a session costs on average, use the expected loss calculator, and to see the cost of regular play, use the gambling session cost calculator. To set limits before you play, read the Safer play toolkit.
How to read the result
The large number is the return to player (RTP): the share of each bet that comes back on average over a very long run. The line under it gives the house edge, which is 100% minus the RTP. The panel gives the hit frequency, the standard deviation per spin, a low, medium or high volatility band, the expected result over your spins and the range of simulated sessions, including the median and the chance of finishing ahead. A session can end far from the average.
How it is calculated
RTP = sum of (payout x chance) over the outcomes you enter, and every other spin loses the bet. House edge = 1 - RTP. Hit frequency = sum of the chances of outcomes that pay more than zero. Standard deviation per spin = sqrt(sum of payout^2 x chance - RTP^2), in bets. Expected result = (RTP - 1) x spins x bet. The session range comes from up to 5,000 simulated sessions with a fixed seed.
Worked example
Worked example
Default (low volatility) paytable: 0.5x at 1 in 4, 1x at 1 in 5, 2x at 1 in 8, 5x at 1 in 25, 15x at 1 in 80. RTP = 0.125 + 0.2 + 0.25 + 0.2 + 0.1875 = 0.9625 = 96.25%. House edge 3.75%. Hit frequency 62.7%, standard deviation 1.91 bets. After 200 spins at 1 unit the expected result is -7.50, and the middle 90% of sessions range from -48.50 to +38.00. The high-volatility paytable in the page text has the same RTP but a 1.91 versus 11.44 standard deviation.
Limits
The tool uses a simple paytable of up to five outcomes, so it is a teaching model and not any real game. It does not model free spins, bonus rounds, multipliers, changing bets or progressive prizes. A real game's RTP is set and published by the operator or regulator, and the paytable here is not it. Session ranges come from a seeded simulation, so they are close but not exact, and the volatility bands are this site's rough guide, not an industry standard. Results are averages and are not predictions.