Statistical Models Interactive

Monte Carlo Simulation

Use random sampling to understand complex systems. Simulate thousands of scenarios to estimate probabilities, risks, and expected outcomes.

📊 Why Monte Carlo?

🎲

Random Sampling

Generate many random scenarios

📈

Distribution

See full range of possible outcomes

📊

Risk Metrics

Calculate VaR, bust rate, percentiles

Simulation Parameters

100 5000

40 60

50 200

20 100

📊 Simulation Results

Mean Outcome $1469

Std Dev $690

5th / 95th %ile $400 / $2600

Bust Rate 1.2%

Profit Rate 69.1%

Sample Bankroll Paths

Each line is one possible future. Wide spread = high variance.

Final Outcome Distribution

Min: $-400

Median: $1400

Max: $4000

🎰 Monte Carlo in Betting

Bankroll Risk

Simulate ruin probability under different bet sizing

Parlay Pricing

Simulate correlated outcomes to price multi-leg bets

Season Sims

Project win totals and playoff odds

Player Props

Simulate game flow to project stats

R Code Equivalent

# Monte Carlo betting simulation
monte_carlo_betting <- function(n_sims, win_prob, bet_size, n_bets, bankroll = 1000) { 
  outcomes <- replicate(n_sims, { 
    wins <- rbinom(n_bets, 1, win_prob)
    profit <- sum(ifelse(wins == 1, bet_size, -bet_size))
    bankroll + profit
  })
  
  list(
    mean = mean(outcomes),
    sd = sd(outcomes),
    median = median(outcomes),
    p5 = quantile(outcomes, 0.05),
    p95 = quantile(outcomes, 0.95),
    bust_rate = mean(outcomes <= 0),
    profit_rate = mean(outcomes > bankroll)
  )
}

result <- monte_carlo_betting(1000, 0.55, 100, 50)
cat(sprintf("Mean: $%.0f, Bust: %.1f%%, Profit: %.1f%%\n", 
    result$mean, result$bust_rate * 100, result$profit_rate * 100))

✅ Key Takeaways

• Monte Carlo: simulate many random scenarios
• Get full distribution, not just expected value
• Essential for risk metrics (VaR, bust rate)

• More simulations = more accurate estimates
• Can model correlations and path dependence
• Variance matters as much as mean