DISTRIBUTIONS

A library of twenty-one named distributions behind one uniform: every sample is the inverse CDF of a seeded draw, so it is reproducible and auditable. Two uses: free sealed draws for anything a game needs random (bot speeds, timings, Ragency targets), and a money mode where the stake pays a multiple sampled from a chosen distribution, clamped and scaled so its mean is exactly the RTP.

21 distributions, one uniform eachfree sealed drawsmoney mode: any shape, exact RTP
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The math

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Live API (browser module)

The engine is published as an ES module that implements the RGS provider contract and rolls locally with crypto.getRandomValues: open, valid-bets, bet, collect, with the observed balance semantics (bet debits the stake, collect credits the win, integer minor units). No server, every round live, and any round replays from its seed. Bet types: BASE.

import { createGame } from 'https://danvid1009.github.io/gnarone-game-math/distributions/api/rgs.js';

const g = createGame({ preset: 'lognormal' });               // presets: lognormal, exponential, uniform, normal-clipped, pareto, poisson, gamma, loglogistic
                                                       // bet types: BASE
const s = g.open();                                    // session, balance 100000, chipLevels [100,200,500,1000,2500,5000,10000]
const r = g.bet({ sessionId: s.sessionId, betAmount: 1000, betType: 'BASE' });   // fresh crypto seed; win in r.totalWinAmount
g.collect({ roundId: r.roundId });                                           // credits the win → { balance }

// Replay any fixture: same seed, same code path, same answer as rounds/007.json
g.bet({ sessionId: s.sessionId, betAmount: 1000, betType: 'BASE', seed: 'fixture-007' });

Presets and static fixtures

Presets: lognormal, exponential, uniform, normal-clipped, pareto, poisson, gamma, loglogistic (default lognormal). Each preset is a frozen configuration and its own folder: the config, derived tables and settlement rule in field.json, plus one hundred pre-drawn rounds from seeds fixture-000 … fixture-099 settled for every bet type. The same seed drives every preset, so round 007 uses the same u everywhere, and the live module reproduces any of them when given the seed.

# presets, their parameters, bet types and realised RTP over the 100 rounds
curl -s https://danvid1009.github.io/gnarone-game-math/distributions/api/index.json

# one preset: parameters, tables (bands / odds / ladder / decks), RN intervals, how to settle
curl -s https://danvid1009.github.io/gnarone-game-math/distributions/api/lognormal/field.json

# one round (000–099): seed, full outcome, settlement for every bet type
curl -s https://danvid1009.github.io/gnarone-game-math/distributions/api/lognormal/rounds/007.json

# all 100 rounds of a preset (stake and win per bet type)
curl -s https://danvid1009.github.io/gnarone-game-math/distributions/api/lognormal/rounds.json

# round 007 played through the real calls: request bodies and every response
curl -s https://danvid1009.github.io/gnarone-game-math/distributions/api/lognormal/sample-request.json
curl -s https://danvid1009.github.io/gnarone-game-math/distributions/api/lognormal/sample-response.json

Settlement rule is spelled out in each preset's field.json under how_to_settle.

Figures

The six money presets: paid-multiple density and the exact mean at the RTP.
The six money presets: paid-multiple density and the exact mean at the RTP.
Quantile functions of the library at their defaults.
Quantile functions of the library at their defaults.

Build it yourself

git clone https://github.com/Danvid1009/gnarone-game-math.git
cd gnarone-game-math/dist-engine
npm test
node bin/build-dist.js --dist lognormal --mu 0 --sigma 0.8 --max 50