Odds Format
Stake Strategy
Results Summary
Median Final Bankroll
Average Final Bankroll
Probability of Profit
Probability of Ruin
Best Case (95th %ile)
Worst Case (5th %ile)
Final Bankroll Distribution
Sample Bankroll Paths
What Is It?
A Monte Carlo simulation uses random sampling to model the probability of different outcomes over many iterations. In betting, it simulates thousands of hypothetical betting seasons to show you the range of possible results ā from best case to worst case ā given your win rate, odds, and stake strategy.
Rather than giving you a single expected outcome, Monte Carlo shows you the full probability distribution: What’s the chance you double your bankroll? What’s the chance of going bust? What does the median outcome look like? This is far more informative than a simple EV calculation for understanding real-world risk.
The tool supports both fixed-stake and percentage-of-bankroll stake strategies, letting you compare how different approaches affect your risk of ruin and long-term growth.
How to Use
1
Enter win rate
Your estimated probability of winning each bet (as a percentage).
2
Enter odds
The average decimal odds of your bets.
3
Enter starting bankroll
Your initial betting fund.
4
Enter bets per season
How many bets you plan to make in one season/cycle.
5
Enter number of simulations
How many seasons to simulate (e.g., 1,000 or 10,000). More simulations = more reliable results.
6
Select stake strategy
Fixed ($X per bet) or Percentage (X% of current bankroll per bet).
7
Click 'Run Simulation'
Wait for results. A progress bar shows completion status.
8
Review results
Median bankroll, average bankroll, probability of profit, probability of ruin, percentile ranges, bankroll distribution chart, and sample path chart.
Formulas & Data Sources
For each simulated season:
Starting bankroll = B0
For each bet (1 to N):
Generate random number r in [0, 1]
If r < win_rate: Win ā bankroll += stake x (odds – 1) Else: Lose ā bankroll -= stake
Fixed strategy: stake = fixed amount Percentage strategy: stake = bankroll x percentage
Median = middle value of all final bankrolls Average = mean of all final bankrolls P(Profit) = % of simulations where final > starting
P(Ruin) = % of simulations where bankroll hit $0
Percentiles: 5th, 25th, 75th, 95th for range insight
No external data is used. All inputs are user-supplied. The simulation uses the browser’s random number generator for sampling. Results are purely probabilistic ā they show what could happen, not what will happen.
Real-World Scenarios
1
Testing a new betting strategy
BeginnerYou believe you can achieve a 54% win rate at average odds of 1.95. Starting bankroll: $1,000. Bets per season: 500. Fixed stake: $20. Run 10,000 simulations.
Median final bankroll = $1,180 | P(profit) = 72% | P(ruin) = 3%
This tells you the strategy is likely profitable but has a non-trivial chance of failure.
2
Comparing fixed vs. percentage staking
IntermediateSame parameters as above, but try 2% of bankroll as the stake strategy. Results: median = $1,210, P(ruin) = 0%. Percentage staking eliminates ruin (you can never hit exactly $0) but may show higher variance in the upper percentiles.
Compare the charts to decide which strategy suits your risk tolerance
3
Understanding losing streaks
AdvancedEven with a 55% win rate, a 10-bet losing streak is surprisingly common over 500 bets. The simulation’s sample paths chart shows this visually ā some paths dip dramatically before recovering.
Helps set realistic expectations and avoid panic during inevitable downswings
Frequently Asked Questions
QHow many simulations should I run?
At minimum 1,000 for rough estimates. 10,000 gives reliable results. Beyond 50,000, improvements are marginal. More simulations take longer to compute.
QWhy does the median differ from the average?
The distribution of final bankrolls is skewed. A few very lucky simulations pull the average up, while the median represents the “typical” outcome. The median is usually a more useful number for decision-making.
QCan I simulate with varying odds and win rates?
This tool uses a single win rate and odds across all bets. For more complex strategies with varying parameters, you would need a custom simulation. However, using average values provides a useful approximation.
QWhat does 'probability of ruin' mean?
It’s the percentage of simulations where your bankroll hit $0 at any point during the season. Even profitable strategies can have non-zero ruin probability if stake sizes are too large relative to bankroll.
QWhy does the same input give slightly different results each time?
Monte Carlo simulations use random sampling, so results vary between runs. This variance decreases as you increase the number of simulations. With 10,000+ runs, results should be very consistent.
