Bankroll Variance Simulator: Model Betting Drawdowns and Outcomes
Simulate a betting bankroll across repeated bets
A bankroll variance simulator estimates how widely betting results can differ when odds, win probability and staking rules stay constant. Enter your assumptions to estimate final-bankroll percentiles, drawdown probability and the difference between mean and median outcomes across thousands of simulated paths.
Advanced simulation settings
Simulation result
Default example: 5,000 paths, 100 bets, 2% of current bankroll per bet.
Bankroll percentiles by bet number
Default 100-bet example: 10th percentile 802.49 units, median 1,061.84 units and 90th percentile 1,349.91 units after 5,000 seeded simulations.
What the bankroll variance simulator measures
The model applies the same decimal odds, estimated win probability and staking rule to every bet. Each outcome is simulated as a win or loss from a seeded pseudo-random sequence, then repeated across thousands of paths to estimate a distribution of possible results.
The simulator does not select bets or calculate an optimal stake. It measures path risk under the assumptions entered. A positive expected return can still produce losing sequences, substantial drawdowns and a median result below the arithmetic mean.
Core return formula
For decimal odds O and win probability p, the net return per 1 unit staked has two outcomes: O - 1 on a win and -1 on a loss.
The variance formula describes one identical independent bet. The simulator then compounds those outcomes through the selected bankroll rule.
Percentage-of-bankroll staking
If each bet risks fraction f of the current bankroll, a win multiplies the bankroll by 1 + f(O - 1), while a loss multiplies it by 1 - f. Under the simulator's identical independent-bet assumptions, the arithmetic expected bankroll after n bets is:
This analytical expectation is shown beside the Monte Carlo mean when percentage staking is selected. The two should be close with a large simulation count, but they will not be identical because the Monte Carlo result is a finite random sample.
Worked example: 2% of bankroll at odds 2.00
Assume a starting bankroll of 1,000 units, decimal odds of 2.00, an estimated win probability of 52%, a stake equal to 2% of the current bankroll, and 100 bets.
- Break-even probability at 2.00 is 50%.
- Expected return per 1 unit staked is 0.52 x 2.00 - 1 = +0.04, or +4%.
- The expected bankroll multiplier per bet is 1 + 0.02 x 0.04 = 1.0008.
- Analytical expected bankroll after 100 bets is 1,000 x 1.0008^100 = about 1,083.25 units.
How to read the simulation output
- Mean final bankroll is the arithmetic average across all simulated paths. A small number of strong paths can pull the mean upward.
- Median final bankroll is the middle final outcome: half of simulations end above it and half below it. With proportional staking, gains and losses compound multiplicatively, so the median can sit below the arithmetic mean even when expected return is positive.
- 10th and 90th percentiles describe the central 80% range of final outcomes. They are not best-case and worst-case values.
- Chance of finishing above start counts how many paths end with more bankroll than they began with. Positive expected value does not make this probability 100%.
- Maximum drawdown measures the largest peak-to-trough percentage decline inside each path. It can reveal path risk that the final bankroll alone hides.
- Drawdown alert probability counts paths whose maximum drawdown reaches the threshold you entered. A path can recover and finish profitable after crossing that level.
- Chance of finishing 20%+ below start measures terminal loss rather than an intrapath drawdown. It counts simulations ending at or below 80% of the starting bankroll.
What this simulation does not model
Results depend on the probability, odds and staking assumptions entered. Real betting records rarely contain identical, independent bets, so this is a controlled variance model rather than a forecast of a future account balance.
- Probability error: the simulator treats your entered win probability as correct for every bet. It does not estimate or validate that probability.
- Changing prices: odds are held constant. Real prices, limits and market availability can change from bet to bet.
- Correlation: outcomes are simulated independently. Bets linked to the same match, team, model factor or market condition can have more concentrated risk.
- Pushes and partial settlements: the model uses binary win/loss settlement. It does not model pushes, half wins, half losses, voids, cash-outs or bookmaker-specific settlement rules.
- Fees and constraints: taxes, commission, minimum stakes, maximum stakes, liquidity and account limits are not included.
- Fixed-stake limit: the selected fixed stake cannot exceed the starting bankroll. If later losses leave less than the selected stake, the next simulated stake is capped at the bankroll remaining.
Bankroll variance simulator FAQ
Why can a positive-EV strategy still finish the simulation below the starting bankroll?
Expected value is a long-run average, not a promise for one finite sequence. When the number of bets is limited, random ordering of wins and losses can leave many paths below the starting bankroll even when the expected return per unit is positive.
Why is the median final bankroll different from the mean?
The mean uses every ending value and can be pulled upward by unusually strong paths. The median only identifies the middle ending value. With percentage staking, bankroll changes compound multiplicatively, so the final distribution can become skewed.
What does the simulation seed do?
The seed makes the pseudo-random sample reproducible. Using the same inputs and the same seed produces the same simulated paths in this calculator. Changing the seed gives a different finite sample while keeping the assumptions unchanged.
Should I use fixed stakes or a percentage of current bankroll?
Choose the rule you actually want to study. Fixed stakes keep the nominal amount stable until the bankroll becomes too small. Percentage staking automatically reduces stakes after losses and increases them after gains. The simulator compares path risk under the selected rule; it does not decide which rule is optimal for you.
How many simulations should I run?
More simulations reduce sensitivity to one pseudo-random sample. The default uses 5,000 paths. If different seeds produce noticeably different estimates, increase the simulation count and avoid over-interpreting small percentage differences.