Math and RTP

RTP and house edge#

• RTP 97% by default, configurable per room. The house edge is the rest: 3% at the default.
• One parameter. The RTP sets the probability of the event that takes the margin, and the rest of each game is built around it: changing the RTP needs no re-tuning.
• Lockable. An installation can be restricted to a list of RTP values — for example the ones a laboratory certified — and any other value is refused when a room is created or changed.
• The RTP is a property of the model, before rounding and payout caps: both are described below.

The same expected return for every strategy#

In every game the value of an open position is a martingale: at each step, the chance of losing the position is exactly compensated by the expected growth of its multiplier. By the optional stopping theorem, no exit strategy changes the expected return: cashing out at a target, at a given step, with a stop loss, holding to the end, or reacting to what happens in the round. Skill changes the variance, never the expected value.

So the margin is not spread across the round. Each game takes it in one identifiable place.

Where the margin is taken#

Why a spread: in three of the games the event that takes the margin happens at the launch, and a position opened after it cannot pay it. It pays the same margin as a spread on entry instead, and the two routes give the same RTP — a test proves it for each of the three. When the event that takes the margin happens, no cash-out is accepted: the position is lost before anyone can react, which is what makes the 3% exact.

Caps and forced cash-out#

• No position is ever confiscated at a boundary. When a round reaches its ceiling or time limit, open positions are cashed out automatically, at the value reached.
• God Candle's cap (1000x by default) is an exact absorbing barrier: the price can reach it, and the expected return holds all the way up to it.
• Diamond Hands, Big Fish and Hypnofrog stop just below their configured cap: the round, the fish or the ladder stops before the step that would pass it. The maximum multiplier the catalog publishes is the one a position can reach, not the configured cap.
• Maximum win per position (optional, per room): the position is cashed out at the first step whose payout would reach it, and the payout is capped. Its effect on the expected return is at most one step, and only on positions that reach it.
• Maximum exposure per round (optional, per room): a stake that would push the room's worst case above it is refused before the operator's wallet is called. In a room played on several tables the cap holds for each table.

Rounding#

• The multiplier of a settlement is taken to four decimals.
• Payouts are floored to the currency's smallest unit: the cent, in a two-decimal currency.
• Flooring costs up to one smallest unit per cash-out, so its weight depends on the stake. In one God Candle scenario — 40,000 simulated rounds, entry before the launch, take profit at 1.5x — the RTP paid was 96.48% at a 0.50 stake, 97.01% at 10 and 97.04% at 100, against 97.04% unrounded. These figures describe that scenario only; they are not certified values.
• What matters is how many smallest units are staked, not the currency: in a currency without decimals, a 50-unit stake behaves like a 0.50 stake in a two-decimal one.

Volatility#

Measured by simulation: 60,000 rounds per game at the default RTP (Hypnofrog's median round length over 300,000, because it sits on the boundary between two beats). In Big Fish and Hypnofrog every position lives its own life inside the shared round, so their figures are counted per fish and per fly. Simulation results are not certification, and not a guarantee of individual returns.

How it is tested#

• The simulation gate. Every generator is pinned in continuous integration. For every strategy in an adversarial set — exits at targets and at fixed steps, stop losses, take-profit and stop-loss combinations, holding to the end, and strategies that react to the round's events — the RTP measured over 40,000 simulated rounds must fall within tolerance of the configured value, and within four standard errors of it. For all four games the gate also runs at 90%, 95% and 99%, and checks that the share of instant losses follows 1 − RTP: a configuration that reached the generator is one that changes the outcome.
• Frozen vectors. Fixed seeds must keep producing the same rounds. A change that alters what a generator draws must come with a new generator version.
• The laboratory report — the model, its parameters, the tolerances, and the measurements for a given configuration — is shared on request, under NDA.