A single expected-value calculation tells you what happens on average over an infinite number of bets. It never tells you what a realistic 100-bet stretch actually looks like, including the losing streaks that can wipe out an underfunded bankroll long before the “average” ever shows up.
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This calculator runs thousands of independent simulated betting sequences using your odds, win probability, staking method, and bet count, then shows you the full spread of possible outcomes rather than one flattering number.
Instead of just an expected value, you get a median ending bankroll, a realistic best-case and worst-case range, and a concrete risk-of-ruin percentage based on how your specific staking plan behaves under thousands of random sequences.
π How to Use the Monte Carlo Betting Simulator
Enter the odds you’re getting per bet, your honest estimated win probability, and how many bets you plan to place in the sequence you want simulated (a betting season, a specific system’s typical sample size, or any stretch you care about).
Pick a staking strategy that actually matches how you bet in practice β flat stakes, a fixed percentage of your current bankroll, or a fraction of the Kelly Criterion β since the choice changes the risk-of-ruin result dramatically.
Then choose how many simulations to run. More simulations produce a smoother, more reliable distribution, but take longer to compute β 2,000 to 5,000 runs is typically enough to get a stable picture for most bankroll and bet-count combinations.
π’ Calculator Fields Explained
Starting Bankroll – The amount of money you’re beginning the simulated betting sequence with.
Odds Per Bet – The odds you expect to get on each bet in the sequence, assumed constant across every bet for simplicity.
Your Win Probability – Your honest estimated chance of winning each individual bet.
Number of Bets – How many bets make up one simulated sequence β for example, 100 bets might represent a few months of regular action.
Number of Simulations – How many independent random sequences to run. Each one uses the same inputs but a different random outcome for every bet, producing a full distribution of results.
Staking Strategy – Whether each bet’s stake is a flat dollar amount, a fixed percentage of the current bankroll, or a fraction of the full Kelly Criterion stake.
π° Understanding the Results
| Result Field | What It Tells You |
|---|---|
| Median Ending Bankroll | The middle outcome across all simulations β half finished above this, half below. |
| Mean Ending Bankroll | The average ending bankroll, which can be skewed upward by a small number of extreme winning runs. |
| Risk of Ruin | The percentage of simulations where the bankroll dropped to a near-zero threshold before the sequence finished. |
| Chance of Profit | The percentage of simulations that ended with more money than the starting bankroll. |
| Percentile Table | The full spread from worst-case to best-case ending bankroll, letting you see the realistic range instead of just one number. |
| Average Max Drawdown | How far the bankroll typically fell from its peak at some point during a sequence, on average across all runs. |
The median is usually a more honest number to plan around than the mean, since a handful of very lucky runs can pull the average well above what a typical sequence actually looks like.
Comparing the 5th percentile against the 95th percentile gives a far more realistic sense of what could actually happen than any single expected-value figure ever will.
A wide gap between the 5th and 95th percentile is a sign of high variance, even when the median outcome looks perfectly healthy. That gap is exactly what a single EV calculation hides from view.
π Calculation Formulas
Rather than a single closed-form formula, Monte Carlo simulation works by repeating a straightforward per-bet process many thousands of times and studying the resulting spread of outcomes.
| Staking Method | Stake Formula | Behavior |
|---|---|---|
| Flat | Fixed dollar amount every bet | Simple, but doesn’t scale down automatically during a losing streak |
| Percentage of Bankroll | Bankroll Γ chosen % | Naturally shrinks stakes as the bankroll falls, reducing ruin risk |
| Kelly Fraction | Bankroll Γ (full Kelly %) Γ multiplier | Mathematically growth-optimal at full Kelly, smoother at half or quarter Kelly |
Each simulated bet is resolved with a single random draw weighted by your win probability, and the bankroll is updated up or down depending on the odds and stake before moving to the next bet in that sequence.
Running this process thousands of times, each with a fresh set of random outcomes, is what produces the full distribution shown in the results rather than a single deterministic number.
π Practical Examples
Example 1: Flat staking, modest edge. A $1,000 bankroll, 2.00 decimal odds, 55% win probability, flat $20 stakes, over 100 bets typically shows a healthy median gain with a fairly low risk of ruin, since the flat stake never grows large relative to a shrinking bankroll.
Example 2: Aggressive percentage staking. The same edge staked at 10% of bankroll per bet instead of a flat $20 produces a much wider percentile spread β a higher best-case outcome, but also a meaningfully elevated risk of ruin during a normal losing streak.
Doubling your stake size doesn’t just double your expected profit β it typically increases your risk of ruin by a much larger factor, since variance compounds faster than edge does.
Example 3: Half-Kelly staking. Using a 50% Kelly multiplier on the same edge usually produces a median outcome close to full-Kelly staking, but with a noticeably smoother percentile band and a lower risk of ruin β a common reason many serious bettors prefer fractional Kelly over full Kelly in practice.
Half-Kelly staking commonly captures most of full Kelly’s long-run growth while cutting the worst-case drawdowns significantly. That tradeoff is exactly what this simulator is built to show.
π‘ Tips & Best Practices
Run at least 2,000 simulations before trusting the results. Fewer than a few hundred runs can still show noisy percentile figures that shift meaningfully if you re-run the simulation.
Be brutally honest with your win probability input. Overestimating your true edge, even slightly, produces a distribution that looks far rosier than what real-world results will deliver.
Compare flat, percentage, and Kelly-fraction staking on the exact same odds and win probability. The differences in risk of ruin between these three methods are often larger than most bettors expect.
Running the same edge through all three staking methods side by side is one of the fastest ways to understand why professional bettors rarely use flat stakes on a growing bankroll.
Treat the worst-case (5th percentile) outcome as your real planning number, not the median. If that worst-case outcome would be financially painful, your stake size is probably too aggressive for your actual bankroll.
- Re-run the simulation with a slightly lower win probability to stress-test how sensitive your results are to being overconfident about your edge.
- Use a bet count that matches a real time horizon you care about, not an arbitrarily large number just to smooth out variance.
Remember that a low risk-of-ruin result assumes your inputs stay constant for the whole sequence β real edges and odds shift over time, so revisit the simulation periodically rather than trusting one run forever.
β οΈ Common Mistakes to Avoid
Trusting the Mean Instead of the Median
It’s tempting to focus on the average ending bankroll since it’s often the largest, most encouraging number in the results.
The mean ending bankroll can be pulled significantly higher than a typical outcome by a small number of extremely lucky simulated runs, making it a misleading number to plan around.
The median, along with the percentile table, gives a far more realistic picture of what a normal sequence actually looks like.
Running Too Few Simulations
Some bettors run only a handful of simulations and treat the resulting risk-of-ruin figure as precise.
A risk-of-ruin figure calculated from only a few hundred simulations can swing noticeably each time you re-run it, since small sample sizes produce unstable percentile estimates.
Always run at least 2,000 simulations, and consider re-running at 5,000+ if the result matters for a real staking decision.
Overestimating Win Probability
Entering an optimistic win probability, even a few percentage points higher than reality, can make a losing long-term strategy look profitable in the simulation.
Because the entire distribution shifts based on this single input, small overestimates compound across hundreds of simulated bets. A win probability just 3-4 percentage points too optimistic can turn a realistic risk-of-ruin figure into a dangerously understated one.
π― When to Use This Calculator
Use this simulator before committing to a specific staking plan on a real edge you believe you have, whether that edge comes from a betting system, a statistical model, or your own handicapping.
An edge that looks good on paper only matters if your staking plan lets you survive the losing streaks needed to actually realize it.
It’s especially useful for comparing staking strategies side by side, stress-testing an assumed win probability, or deciding how large a bankroll you’d realistically need before running a specific system at scale.
π Related Calculators
Kelly Criterion Calculator, Kelly Growth Calculator, Risk of Ruin Calculator, Expected Value Calculator, Drawdown Calculator, Sharpe Ratio Calculator.
π Glossary
| Term | Definition |
|---|---|
| Monte Carlo Simulation | A technique that repeats a random process many times to study the full range of possible outcomes rather than a single average. |
| Median | The middle value in a sorted list of outcomes β half the results are above it, half below. |
| Percentile | The value below which a given percentage of results fall, e.g. the 5th percentile is worse than 95% of outcomes. |
| Risk of Ruin | The probability that a bankroll drops to a near-zero threshold during a simulated sequence. |
| Flat Staking | Betting the same fixed dollar amount on every wager, regardless of current bankroll. |
| Kelly Fraction | A percentage of the mathematically optimal full Kelly stake, used to reduce variance while retaining most of its growth benefit. |
| Drawdown | The decline in bankroll from its highest point reached so far down to a subsequent lower point. |
| Variance | The degree to which actual results swing around the expected average outcome. |
| Expected Value (EV) | The average result of a bet over an infinite number of repetitions, given a specific edge. |
| Bankroll | The total amount of money set aside specifically for betting activity. |
β Frequently Asked Questions
What is Monte Carlo simulation in betting?
It’s a method that simulates a betting sequence thousands of times using random outcomes weighted by your win probability, then studies the full range of resulting bankrolls instead of relying on a single average figure.
For example, running 100 bets 5,000 separate times produces 5,000 different possible bankroll paths, each shaped by a different random sequence of wins and losses.
How is this different from a simple expected value calculation?
An expected value calculation gives one theoretical average outcome assuming an infinite number of bets. Monte Carlo simulation shows what a realistic, finite sequence of bets actually tends to look like, including the spread of good and bad outcomes.
Two staking plans can share the exact same expected value while having very different risk-of-ruin percentages, which a Monte Carlo simulation reveals and a plain EV calculation cannot.
Why does risk of ruin change so much between staking methods?
Flat staking keeps risking the same dollar amount even as the bankroll shrinks during a losing streak, while percentage and Kelly-based staking automatically reduce stake size as the bankroll falls.
This is why flat staking often shows a higher risk of ruin than percentage staking on the exact same odds and win probability, especially over longer bet sequences.
How many simulations should I run for a reliable result?
At least 2,000 simulations is a reasonable minimum for a fairly stable result; 5,000 or more produces an even smoother, more reliable percentile distribution.
If you re-run the simulation with the same inputs and the risk-of-ruin figure jumps noticeably, that’s a sign you should increase the simulation count.
What ruin threshold does this calculator use?
The simulator treats a bankroll as “ruined” once it falls to 5% of the original starting bankroll, since a bankroll this depleted is functionally unusable for continued betting at any meaningful stake.
You can interpret this conservatively β some bettors would consider themselves ruined at a higher threshold, such as 25% or 50% of their original bankroll, depending on their own risk tolerance.
βοΈ Legal Disclaimer
This calculator is provided for informational and educational purposes only. It simulates hypothetical betting sequences based on the odds, win probability, and staking method you provide, and does not guarantee any real-world betting outcome. Actual results depend on factors this simulator cannot account for, including changing odds, model accuracy, and market conditions. Please gamble responsibly and within your means, and check the legal status of sports betting in your jurisdiction before wagering.
