Theoretical return
Theoretical return is the percentage of all stakes a slot is mathematically designed to pay back, calculated by adding up every possible outcome multiplied by its probability. It is the figure UK games show as RTP. Because it is a calculation rather than a record, what actually happens in your session can be very different, especially over a few hundred spins.
By the Best Slots UK team. Last checked .
Key takeaways
- Theoretical return is calculated from the game's maths, not measured from past play.
- It equals the sum of each outcome's payout multiplied by its probability.
- Actual return over a short session can swing tens of points either side of it.
- UK rules require the theoretical RTP to be available before you play.
- Also called
- Theoretical RTP
- Source
- The game's maths model
- Measured over
- Every possible outcome
- Shown in
- The game's help screen
- Opposite of
- Actual or observed return
Theoretical return: a definition
Every slot has a maths model listing every result the game can produce, how likely each one is and what it pays. Multiply each payout by its probability and add the lot together, and you get the average amount returned per pound staked. Expressed as a percentage, that is the theoretical return, which is what the game's RTP figure means.
The word "theoretical" is doing real work. The number describes the design of the game, the way a coin's 50% chance of heads describes the coin. It does not describe what has happened at any casino, and it does not promise what will happen to you. The Gambling Commission's technical standards refer to it as the average theoretical return to player percentage and require it, or the probability of winning, to be easily available before you gamble.
How theoretical return is calculated: a worked example
Real slots have millions of combinations, but the method is the same as for this made-up game with six possible results per spin. Payouts are shown as multiples of the stake.
| Result | Pays (× stake) | Probability | Contribution to return |
|---|---|---|---|
| No win | 0 | 69.96% | 0.000 |
| Small win | 1× | 18% | 0.180 |
| Low win | 2× | 8% | 0.160 |
| Medium win | 5× | 3.5% | 0.175 |
| Feature | 50× | 0.5% | 0.250 |
| Top prize | 500× | 0.04% | 0.200 |
| Total | 100% | 0.965 = 96.5% |
Add up the last column and the game returns 96.5p for every £1 staked, on average, over its entire life. The other 3.5p is the house edge. Notice two things. First, the "small win" pays back only the stake, so about six in ten wins in this model leave you level rather than ahead. Second, the rare feature and top prize together supply nearly half of the whole return, which is typical of a high-volatility design.
Studios do this sum for every reel position, feature path and modifier, usually with specialist software and billions of simulated spins as a check. Our guide on how slot RTP is calculated explains the full process, and how slot maths models work covers the design side.
Theoretical return versus what actually happens
Because big but rare prizes carry so much of the return, actual results only settle near the theoretical figure after a vast number of spins. Using the model above, the typical range of actual return (covering about two sessions in three) shrinks like this as spins pile up:
| Spins played | Typical actual return range | What it means |
|---|---|---|
| 100 | Anywhere from 0% to about 200% | Pure luck dominates |
| 10,000 | About 86% to 107% | Still wide; a long evening's play is nowhere near the average |
| 1,000,000 | About 95.4% to 97.6% | Close to 96.5%, but only across a whole game's player base |
The lesson is that theoretical return describes the game across all players and all time. It is useful for comparing games and versions, but it is not a forecast for your session. A player who staked £200 and got £120 back has an actual return of 60%, and that is entirely consistent with a 96.5% game.
These ranges come from the variance of the made-up model above. Real slots have their own figures, which studios rarely publish.
What is included in a slot's theoretical return
- Every base-game win, including those that pay less than the stake.
- All features, such as free spins rounds, respins and pick bonuses, weighted by how often they trigger.
- Any jackpot contributions built into the game; on a progressive jackpot slot, part of the figure is money most players never see.
- Outcomes that hit the game's max win cap, counted at the capped amount.
It does not include casino bonuses, cashback or loyalty rewards; those are separate promotions with their own terms.
Where you see theoretical return on UK slot sites
In the UK the figure sits in each game's rules or help screen, and some lobbies show it on the game tile too. If a slot has several certified versions, the casino's chosen one is the figure that matters, which is explained under RTP range. Some operators also publish audited actual payout percentages for their whole casino; the guide on slot RTP versus casino payout shows how these differ from a single game's theoretical figure.
Related terms
Hit frequency tells you how often a spin wins anything, while theoretical return tells you how much comes back on average. Variance describes how far real results scatter around the theoretical figure.
18+. Gambling should be entertainment that costs money, not a way to make it. Set a deposit limit before you play: how to set limits. Free, confidential help: National Gambling Helpline 0808 8020 133.
Frequently asked questions
What is theoretical return in slots?
Theoretical return is the long-run percentage of stakes a slot is designed to pay back, worked out from the odds and payout of every possible result. A 96% theoretical return means that, across all players and an enormous number of spins, the game returns about 96p of every £1 staked. It is the same thing UK games show as RTP. It is a property of the game's design, not a record of past payouts. Our RTP explained guide covers the basics.
How is a slot's theoretical return calculated?
By multiplying the payout of every possible outcome by its probability and adding the results together. If a result paying 50 times the stake has a 0.5% chance, it contributes 0.25 to the total. Real slots involve millions of reel combinations and feature paths, so studios use software and huge simulations to confirm the figure, which independent test labs then check. Our guide on how slot RTP is calculated walks through the method.
Why is my actual return so different from the theoretical return?
Because short sessions are dominated by luck. A large part of a slot's return usually comes from rare features and top prizes, so a few hundred spins can land anywhere from nothing back to well over double your stakes. Only over millions of spins do results cluster close to the theoretical figure. Getting less than the RTP in a session is normal and doesn't mean anything is wrong. The variance entry explains why results swing so widely.
Is theoretical return the same as RTP?
Yes, in practice they mean the same. RTP stands for return to player, and the figure published for a slot is its theoretical value. The Gambling Commission's technical standards describe it as the average theoretical return to player percentage. Some people use "actual RTP" for the payout a game has really produced over a period, which is a different, measured number. Our page on slot RTP versus casino payout explains that difference.
Does theoretical return include the jackpot?
It includes any jackpot that is part of the game's own maths. On a progressive jackpot slot, a slice of each stake funds the jackpot, and that slice counts towards the theoretical return even though very few players ever win it. This is why a jackpot game's base play can feel tighter than its RTP suggests. Mega Moolah, for example, is listed at 88.12%, well below most modern slots. See progressive jackpots explained for how the pool works.
Can theoretical return change at a UK casino?
Not while a game is live in its current version. UK technical standards prevent a game's settings from being changed while it is available for play, and they ban adaptive behaviour that alters outcome probabilities during play. A casino can, however, switch to another certified version of the same slot with a different theoretical return at a later date. That's why the help screen at your casino is the figure to trust. See RTP range for more.