Maths and RTP
RTP is a measured number, not a promise.
Return to player is the share of stakes a game pays back over a very long run. We compute it, publish how we computed it, and make every single round verifiable from its seeds.
What RTP means, and what it does not
An RTP of 97% means that over millions of rounds a game pays back 97 of every 100 units staked. It says nothing about the next round or the next session: short runs swing far above and below it. That is why we publish volatility and the payout distribution next to the RTP, not instead of it.
RTP by simulation
Where a game has a closed-form answer, we compute its RTP exactly. Games with movement, collisions and chains of events have none, so we compute their RTP by simulation: we run the game’s own deterministic code over a very large number of seeded rounds and measure what it pays.
A simulated RTP is published with its sample: the number of rounds, how the seeds were chosen and a confidence interval. Because each round is a pure function of its seeds and the game version, anyone with the same version and seeds can rerun the simulation and get the same numbers.
What the maths passport states
- RTP, and whether it is exact or simulated, with the sample size and confidence interval.
- The real maximum win and its probability per round, not a theoretical cap.
- Hit frequency: how often a round returns any win at all.
- The payout distribution, so volatility is shown rather than described with a word.
- The game version the numbers belong to.
Provably fair: each round, not just the average
RTP describes the average; provably fair covers the single round. Before play, the server commits to a secret seed by showing its SHA-256 hash. The outcome is derived with HMAC-SHA256 from that seed, the player’s client seed and a nonce. After the seed is revealed, the player can recompute every round and see that it was neither chosen nor changed after the bet.
Provably fair does not prove the RTP: a fair draw from a stingy game is still fair. That is why the two go together: the passport states what the game pays on average, and the seeds prove that each round followed the rules.
Numbers belong to a version
Changing a game’s maths creates a new version with a new simulation and a new passport. An operator always knows which version is live and what it pays.
Questions and answers
What is RTP in a casino game?
Return to player: the share of all stakes that a game pays back to players over a very long run. A 96% RTP means that 96 of every 100 units staked come back as wins on average; the rest is the house edge.
How is RTP calculated by simulation?
The game’s own code is run over a very large number of seeded rounds, and the total paid is divided by the total staked. The result is stated with the number of rounds and a confidence interval, and it can be reproduced from the same seeds and game version.
What is hit frequency?
How often a round returns any win at all. Two games with the same RTP can feel very different: one pays small amounts often, the other pays rarely but more.
What is the real maximum win?
The largest multiplier the game can actually produce, together with how rare it is. A cap that no round ever reaches says little; we publish the largest win the game really produces and its probability.
Does provably fair guarantee the RTP?
No. It proves that each round was decided by seeds committed in advance and not changed after the bet. The RTP comes from the game’s maths, which is why it is published separately in the passport.
Can a player verify a round?
Yes. After the server seed is revealed, the player can check that its SHA-256 hash matches the commitment shown before play and recompute the outcome from the seeds and the nonce. In simulated games the whole round can be replayed from the same inputs.