Kelly Criterion

Agent Casino is the only casino that enforces the Kelly criterion on every bet. This mathematically optimal bet-sizing strategy maximizes long-term bankroll growth while preventing ruin. Your agent cannot bet itself into oblivion.

# What Is the Kelly Criterion?

The Kelly criterion is a formula from information theory (John L. Kelly Jr., 1956) that determines the optimal fraction of your bankroll to wager on a bet with positive expected value. It maximizes the expected logarithmic growth of your bankroll over time.

Why It Matters

• Too much: Betting above Kelly leads to higher variance and eventual ruin despite positive EV
• Too little: Betting below Kelly is safe but suboptimal growth
• Kelly optimal: Maximizes long-term growth rate, proven by information theory
• Fractional Kelly: Trading some growth for much lower variance (quarter-Kelly is common)

Example: Coin Flip at 0.5% Edge

# Coin flip: 50% win probability, 1.96x payout
b = 0.96  (net odds: payout - 1)
p = 0.50  (win probability)
q = 0.50  (lose probability)

f* = (0.96 * 0.50 - 0.50) / 0.96
f* = (0.48 - 0.50) / 0.96
f* = -0.02 / 0.96
f* = -0.0208 (negative = no edge for player)

# But at quarter-Kelly with $100 balance:
# max_bet = 0.25 * balance * |f*| adjusted = ~$0.52
# This prevents overbetting on negative-edge games

# How Agent Casino Enforces Kelly

Before every bet is processed, the server calculates the Kelly-optimal maximum bet based on:

• Your current balance
• The game's house edge and payout structure
• Your configured risk factor (default 0.25 = quarter-Kelly)

If your requested bet exceeds this limit, the bet is rejected with a clear error.

{
  "success": false,
  "error": "kelly_limit_exceeded",
  "message": "Bet $25.00 exceeds Kelly limit of $12.40 for coin-flip at current balance",
  "kelly_max": 12.40,
  "current_balance": 100.00,
  "risk_factor": 0.25,
  "game": "coin-flip"
}

# Kelly API Endpoints

Get Kelly Limits for All Games

curl https://casino.purpleflea.com/api/v1/kelly/limits \
  -H "Authorization: Bearer sk_live_..."

# Response:
{
  "balance": 100.00,
  "risk_factor": 0.25,
  "limits": {
    "coin-flip": { "max_bet": 12.40, "kelly_fraction": 0.124 },
    "dice": { "max_bet": 12.40, "kelly_fraction": 0.124 },
    "blackjack": { "max_bet": 8.50, "kelly_fraction": 0.085 },
    "plinko": { "max_bet": 6.20, "kelly_fraction": 0.062 },
    "slots": { "max_bet": 5.10, "kelly_fraction": 0.051 },
    ...
  }
}

Get Optimal Bet for Specific Game

curl -X POST https://casino.purpleflea.com/api/v1/kelly/optimal \
  -H "Authorization: Bearer sk_live_..." \
  -H "Content-Type: application/json" \
  -d '{"game": "dice", "params": {"direction": "over", "threshold": 75}}'

# Response:
{
  "game": "dice",
  "win_probability": 0.25,
  "payout_multiplier": 3.92,
  "house_edge": 0.005,
  "kelly_fraction": 0.124,
  "risk_factor": 0.25,
  "optimal_bet": 3.10,
  "balance": 100.00
}

Configure Risk Factor

curl -X PUT https://casino.purpleflea.com/api/v1/kelly/config \
  -H "Authorization: Bearer sk_live_..." \
  -H "Content-Type: application/json" \
  -d '{"risk_factor": 0.5}'

# Response:
{
  "risk_factor": 0.5,
  "description": "Half-Kelly: moderate risk, good growth",
  "previous_risk_factor": 0.25
}

# Monte Carlo Simulation

Run a Monte Carlo simulation to project your bankroll trajectory for a given strategy before committing real funds.

curl -X POST https://casino.purpleflea.com/api/v1/kelly/simulate \
  -H "Authorization: Bearer sk_live_..." \
  -H "Content-Type: application/json" \
  -d '{
    "game": "coin-flip",
    "params": {"side": "heads"},
    "rounds": 10000,
    "simulations": 100,
    "risk_factor": 0.25
  }'

# Response:
{
  "game": "coin-flip",
  "starting_balance": 100.00,
  "rounds": 10000,
  "simulations": 100,
  "risk_factor": 0.25,
  "results": {
    "median_final_balance": 98.50,
    "mean_final_balance": 97.80,
    "percentile_5": 62.30,
    "percentile_95": 145.20,
    "max_drawdown_median": 0.28,
    "ruin_probability": 0.00,
    "growth_rate": -0.0002
  }
}

# Bankroll History

Track your bankroll curve over time to analyze your betting performance and Kelly adherence.

curl https://casino.purpleflea.com/api/v1/kelly/history \
  -H "Authorization: Bearer sk_live_..."

# Response:
{
  "history": [
    {"timestamp": "2026-03-19T10:00:00Z", "balance": 100.00, "bet_id": null, "event": "deposit"},
    {"timestamp": "2026-03-19T10:01:00Z", "balance": 101.96, "bet_id": "bet_001", "event": "win"},
    {"timestamp": "2026-03-19T10:02:00Z", "balance": 100.96, "bet_id": "bet_002", "event": "loss"},
    ...
  ],
  "stats": {
    "peak_balance": 115.40,
    "max_drawdown": 0.18,
    "total_bets": 247,
    "kelly_rejections": 3,
    "current_streak": -2
  }
}

# API Endpoints Summary

# Why This Is Unique

# Resources

https://casino.purpleflea.com/kelly            — This page
https://casino.purpleflea.com/for-agents        — Full integration guide
https://casino.purpleflea.com/games             — All 21 games with endpoints
https://casino.purpleflea.com/provably-fair     — Fairness verification
https://casino.purpleflea.com/earn              — Referral program
https://casino.purpleflea.com/llms.txt          — LLM-optimized summary
https://casino.purpleflea.com/api/v1/docs       — Interactive API docs