Slots Provably Fair and Payout Formula

Overview

A slots result uses three multipliers from the game stream: m1, m2, and m3. Lower red multipliers contribute more score; higher multipliers contribute less score; and values at or above 1.98x contribute zero.

• Each multiplier is converted into a bounded score using spinScore(m).
• The average normalized score drives bonusMultiplier(m1, m2, m3).
• Special case jackpot: if m1 = 1, m2 = 1, and m3 = 1, payout multiplier is exactly 2000x.
• Final payout is buyAmount * bonusMultiplier(...).

Full Formula (TypeScript)

const K_NON_JACKPOT = 1.128962195018067;
const JACKPOT_111 = 2000;

export function spinScore(m: number): number {
  if (m >= 1.98) return 0;
  if (m >= 1.6) return 0.85 * Math.sqrt(Math.max(0, (1.98 - m) / 0.38));
  if (m >= 1.35) return 0.85 + 0.15 * ((1.6 - m) / 0.25);
  if (m >= 1.15) return 1 + (1.35 - m) / 0.2;
  if (m >= 1.05) return 2 + 2 * ((1.15 - m) / 0.1);
  return Math.min(6, 4 + 2 * ((1.05 - m) / 0.05));
}

export function bonusMultiplier(m1: number, m2: number, m3: number): number {
  if (m1 === 1 && m2 === 1 && m3 === 1) return JACKPOT_111;

  const t = (spinScore(m1) + spinScore(m2) + spinScore(m3)) / 18;
  const raw = 229.11 * (0.7 * t ** 4 + 0.3 * t ** 8);
  return K_NON_JACKPOT * (raw ** 0.38 + 0.0022 * raw ** 2.5);
}

export const payout = (buyAmount: number, m1: number, m2: number, m3: number) =>
  buyAmount * bonusMultiplier(m1, m2, m3);

Spin Score Bands

Multiplier Range	spinScore(m)
m ≥ 1.98	0
1.6 ≤ m < 1.98	0.85 × sqrt((1.98 - m) / 0.38)
1.35 ≤ m < 1.6	0.85 + 0.15 × ((1.6 - m) / 0.25)
1.15 ≤ m < 1.35	1 + (1.35 - m) / 0.2
1.05 ≤ m < 1.15	2 + 2 × ((1.15 - m) / 0.1)
m < 1.05	min(6, 4 + 2 × ((1.05 - m) / 0.05))

Higher score means better slots outcome contribution.

Example Multipliers

Multi 1	Multi 2	Multi 3	Approx. Payout Multiplier
1x	1x	1x	2,000.00x
1x	1x	1.3x	55.93x
1.1x	1.1x	1.1x	3.58x
1x	1.3x	2x	2.05x
1x	2x	2x	1.48x
1.3x	1.3x	1.3x	0.72x
1.7x	1.7x	1.7x	0.32x
2x	2x	2x	0x

Provably Fair Notes

Slots calculations are deterministic once m1, m2, and m3 are fixed. The formula does not use hidden per-user parameters or manual overrides.

As with Redbot base betting, fairness assumptions depend on the integrity and timing of the underlying bustabit game outcomes.

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