Casino Math Balancer

Mathematical framework for designing balanced, engaging betting mechanics with appropriate risk/reward curves.

Core Metrics

Return to Player (RTP)

RTP = (Total Amount Returned to Players / Total Amount Wagered) × 100

Target ranges by game type:

• Casual/Social: 95-98% RTP (player-friendly)
• Balanced: 92-95% RTP (sustainable)
• High-stakes: 88-92% RTP (house-favorable)

House Edge

House Edge = 100% - RTP

Example: RTP = 96% → House Edge = 4% For every 100 coins wagered, house keeps ~4 coins long-term

Variance Classification

Variance Hit Frequency Max Win Experience

Low

40% 2-10x Steady, small wins

Medium 20-40% 10-50x Balanced excitement

High <20% 50-500x Rare big wins

Meta-Pot System Math (Farming in Purria)

Pot Categories

Pot Probability Range Suggested RTP Notes

Water 45-65% success 96% Most stable

Sun 35-55% success 94% Medium variance

Pest 25-45% success 92% Higher risk/reward

Growth 15-35% success 90% Jackpot-style

Bet Level Calculations

interface BetCalculation { level: 'fold' | 'call' | 'all_in'; amount: number; multiplier: number; potentialWin: number; expectedValue: number; }

function calculateBet( coins: number, level: BetLevel, potSuccess: number, multiplier: number ): BetCalculation { const amounts = { fold: 0, call: Math.floor(coins * 0.1), all_in: coins };

const amount = amounts[level]; const potentialWin = Math.floor(amount * multiplier); const expectedValue = (potSuccess * potentialWin) - ((1 - potSuccess) * amount);

return { level, amount, multiplier, potentialWin, expectedValue }; }

Multiplier Balance Formula

Multiplier = (1 / Win_Probability) × RTP_Target

Example for 40% win rate at 94% RTP: Multiplier = (1 / 0.40) × 0.94 = 2.35x

Payout table:

• Call bet (10%): Win = 2.35x stake
• All-in: Win = 2.35x stake (same multiplier, higher stakes)

Probability Tables

Standard Template

Example: Meta-Pot Resolution

Adjustment needed: Scale payouts by 0.94/1.23 = 0.764 New payouts: 2.29x, 1.38x, 0.38x, 0x → RTP ≈ 94%

Balancing Levers

Tuning Parameters

Lever Effect on Players Effect on Revenue

↑ Base win rate More engagement ↓ House edge

↑ Max multiplier Higher excitement Variance risk

↑ Tier thresholds Harder to win big ↑ House edge

↓ Bet minimums More accessibility ↓ Revenue per bet

Session Economy

Target metrics per session:

• Average session: 10-15 bets
• Net outcome: -5% to +20% of starting bankroll
• "Near miss" rate: 15-20% (engagement driver)
• Big win frequency: 1 in 20-50 sessions

Simulation Validation

Monte Carlo Template

function simulateSession( startingCoins: number, betsPerSession: number, betSize: number, winProb: number, winMultiplier: number ): SimulationResult { let coins = startingCoins; let wins = 0;

for (let i = 0; i < betsPerSession; i++) { coins -= betSize; if (Math.random() < winProb) { coins += betSize * winMultiplier; wins++; } }

return { finalCoins: coins, netChange: coins - startingCoins, winRate: wins / betsPerSession, rtp: (coins + (betsPerSession * betSize) - startingCoins) / (betsPerSession * betSize) }; }

// Run 10,000 sessions to validate RTP converges to target

Red Flags Checklist

Before shipping any betting mechanic:

• RTP calculated and within target range

• Variance classified and appropriate for audience

• No exploitable patterns in RNG

• Maximum loss per session capped

• Win streaks don't exceed 5 without cooldown

• Loss streaks trigger pity mechanics

• Economy doesn't inflate over time

• Math validated via simulation (10k+ runs)

Legal Considerations

For social casino / non-gambling:

• No real-money conversion

• Virtual currency clearly labeled

• Odds disclosure recommended

• Age-gating in place

• "For entertainment only" messaging