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Understanding RTP: Theoretical, Observed and How Many Rounds It Takes

Topic
Probability & myths
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5 min read
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RTP, return to player, is the share of all money bet that a game pays back over a very long run. A 97% RTP means 97 of every 100 units staked return to players in total, not to you in one session. Theoretical RTP comes from the game's design; observed RTP is counted from real rounds.

What does RTP measure?

RTP is total paid out divided by total staked, over a very large number of bets. If players stake 100,000 units in total and the game pays back 97,000, the RTP over those bets is 97%.

Two things follow from that definition:

  • It is an average over everyone. It describes the game, not any one player's session.
  • It needs a long run. Over a handful of rounds the figure jumps around a lot. Over hundreds of thousands it settles.

The other side of the same number is the house edge: 100% minus the RTP. Understanding House Edge covers that side.

What is the difference between theoretical and observed RTP?

Theoretical RTP is what the game is designed to return. It comes from the maths of the game: the rules and the formula that turns a random number into a result. Providers publish it in their game rules. On this site it is always labelled as a provider claim, for example Aviator's stated 97% on the Aviator page or Spaceman's stated 95.5% on the Spaceman page.

Observed RTP is what a count of real rounds actually returned. It is a measurement, so it comes with a sample size and an uncertainty. For a game working as designed, the observed figure moves towards the theoretical one as the count grows.

The two answer different questions. The claim tells you what the game is meant to do. The measurement tells you what it did in the rounds that were counted.

Why does a crash game have an RTP at every cash-out target?

In a slot, the RTP is one number for the game. In a crash game the return depends on when you cash out, so there is a return for each target:

Return at a target = target × chance of reaching that target

Most crash games are designed so that the chance of reaching a multiplier is about the RTP divided by that multiplier. With a 97% design:

Cash-out targetChance the round reaches itReturn at that target
1.5xabout 64.7%about 97%
2xabout 48.5%about 97%
5xabout 19.4%about 97%
10xabout 9.7%about 97%

So, in a typical design, no cash-out target is "better value" than another. Lower targets win more often; higher targets pay more when they win; the long-run return is about the same. The lab measures the return at 1.5x, 2x, 3x, 5x and 10x separately, because a game could in principle be built to treat some targets differently. The multiplier distribution article shows the full shape.

How much does sample size matter?

A great deal, because each round pays either nothing or a multiple of the stake. That makes results noisy, and the noise is larger for higher targets.

Here is how wide the 95% interval around an observed RTP is, for a game with a 97% design, at two cash-out targets. Illustrative numbers, not lab measurements:

Rounds countedReturn at 2x, give or takeReturn at 10x, give or take
1,000about 6.2 pointsabout 18 points
10,000about 2.0 pointsabout 5.8 points
100,000about 0.6 pointsabout 1.8 points

Read the second row this way: after 10,000 rounds, an observed return at 2x of 95.5% is consistent with a 97% design, because 97% is inside the interval. At 10x, even 10,000 rounds leave a wide margin, because wins at 10x are rare.

This is why the lab does not publish a figure from a few hundred rounds, and why a screenshot of someone's last 50 rounds says almost nothing about a game's RTP. It is also why the is it rigged? question is answered with large counts and intervals, not with impressions.

How does the lab publish RTP?

Every measured figure on Clash Watchdog carries three things:

  1. n, the number of rounds counted;
  2. as of, the time of the count;
  3. a 95% interval, the range the true value is likely to fall in.

A figure without all three is treated as a bug. Below the minimum sample of 10,000 rounds, a game page shows how many rounds are still needed instead of a number, and shows the provider's figure labelled as a claim. When a measurement exists, the page shows the claim and the measurement next to each other, so you can see whether the claim falls inside the measured interval. See Evidence Tiers for how the sample size sets what can be said.

What RTP does not tell you

RTP is useful, and it is easy to ask too much of it.

  • It does not predict a round. History describes behaviour. It does not predict the next round, and neither does RTP.
  • It does not tell you the cost of an evening. That depends on how many bets you place and how big they are. A 99% game played fast can cost more per hour than a 96% game played slowly. See Crash Game Economics.
  • It does not protect a betting system. Changing your stake after wins or losses does not change the RTP of any bet. The martingale simulator shows what doubling after a loss does to a bankroll over many sessions.
  • It says nothing about how results are produced. Whether a round can be checked depends on the game's fairness system. Our hash commitment check works for provably fair and hash-committed games only.

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Questions

If a game's RTP is 97%, will I get 97% of my money back?
No. RTP is an average over a very large number of bets by all players. In one session your result can be far above or far below it. RTP describes the game over the long run. It does not tell you what your next round or your next hour will return.
Why does an observed RTP differ from the stated one?
Mostly because of sample size. Each round pays either nothing or a multiple of the stake, so results swing a lot, and a small count of rounds can land well above or below the true value. A difference only means something when it is larger than the 95% interval around the observed figure.
Does my cash-out target change the RTP?
In a typical crash design, very little. The chance of reaching a target falls in proportion to the target, so the return at 1.5x, 2x or 10x comes out about the same. What changes is the variance: high targets win rarely, so their observed return swings much more from sample to sample.
How many rounds does the lab need before publishing an RTP?
At least 10,000 recorded rounds. Every published figure then carries its sample size, the time it was counted and a 95% interval. Below that threshold the page shows the provider's figure, labelled as a claim, and how many rounds are still needed.
Is the RTP printed in a game's rules a measurement?
No. It is the provider's statement about the game's design, a claim. It may well be correct, but it is not the same as a count of real rounds. Clash Watchdog shows the provider's figure as a claim and the lab's figure as a measurement, never mixed.

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