Staking Plan Simulator
Monte Carlo simulation engine. Test any staking strategy across thousands of simulated betting sequences. See your expected bankroll path, bust probability, maximum drawdown, and optimal stake size.
How Monte Carlo Works
1. Random Walk
Each simulation runs 500 bets. For each bet: win with probability 55% (receiving 1.95× stake) or lose (stake = 0). Stake is recalculated as 2.5% of remaining bankroll each bet.
2. Thousands of Trials
We run 10000 independent trials to build a robust distribution. Each trial is a different sequence of random outcomes — capturing the full range of luck (both good and bad) possible in real betting.
3. Statistical Summary
Median = typical outcome. Bust rate = % of trials where bankroll hit $0. Drawdown = largest peak-to-trough decline. Compare strategies by their risk/reward profile.
Flat vs Percentage vs Kelly vs Martingale: The Math
Flat (level) staking bets the same fixed amount on every wager — say $50 per bet from a $1,000 bankroll. Its appeal is simplicity and low variance: profit tracking is trivial, and a run of wins never inflates your exposure. Its weakness is that exposure never deflates either. Losses erode the bankroll linearly, one full unit at a time, so a long enough streak busts a flat bettor completely. Flat staking also fails to compound: as the bankroll grows, each bet becomes a smaller and smaller fraction of it, leaving growth on the table.
Percentage staking — what this simulator models — recalculates the stake as a fixed fraction f of the current bankroll before every bet. This creates two powerful properties: wins compound geometrically, and losses self-brake. After n consecutive losses at fraction f, the bankroll is multiplied by (1 − f)ⁿ rather than reduced by n fixed units, so the roll shrinks toward zero asymptotically instead of crossing it. The practical cost is that recovering from a drawdown takes longer, because your stakes are smallest exactly when you are furthest behind.
The Kelly criterion is percentage staking with the fraction chosen mathematically: f* = (p × b − q) / b, where p is win probability, q = 1 − p, and b is decimal odds minus 1. Kelly maximizes the expected logarithmic growth rate g = p·ln(1 + f·b) + q·ln(1 − f); staking more than f* actually reduces long-run growth while adding risk. Full Kelly is famously volatile, which is why most practitioners run this simulator at half or quarter Kelly — for a 55% win rate at odds 2.00, f* = 10%, so half Kelly is the 5% preset above.
Martingale doubles the stake after every loss so that the first win recovers everything plus one unit. The catch is exponential stake growth: after n losses the next bet is s × 2ⁿ, and the total committed across the run is s × (2ⁿ⁺¹ − 1). Doubling never changes expected value — your long-run result is still your edge times total turnover — it merely trades many small wins for rare enormous losses. Because every real bankroll and every bookmaker limit is finite, the catastrophic run eventually arrives and takes the accumulated small wins with it.
To size the fraction before you simulate it, use the Kelly Criterion Calculator; to see the analytic bust probability behind the simulated bust rate, check the Risk of Ruin Calculator.
Staking Plan Formulas
Flat: stake = s (constant)
bust after (bankroll ÷ s) net losing units
Percentage: stake = f × current bankroll
after n straight losses: bankroll × (1 − f)ⁿ
Kelly: f* = (p × b − q) / b
growth rate: g = p·ln(1 + f·b) + q·ln(1 − f)
Martingale: stake after n losses = s × 2ⁿ
total risked in the run = s × (2ⁿ⁺¹ − 1)Worked Examples
$1,000 bankroll, 5% sizing, ten straight losses. Flat $50 per bet loses $500 — exactly half the roll. Percentage staking leaves 1,000 × 0.95¹⁰ ≈ $599, a 40% drawdown instead of 50%, because each losing stake shrinks with the roll. The gap widens with the streak: 20 straight losses bust the flat bettor entirely, while the percentage bettor still holds ≈ $358.
Start at $10 on even-money odds and double after every loss. After 8 straight losses you have burned $2,550 and must place a $2,560 bet — $5,110 committed to chase a $10 net profit. At a 50% win rate an 8-loss streak has probability 0.5⁸ = 1/256 ≈ 0.4% per run, so it shows up on average once every 256 doubling runs — well before the small wins can pay for it once a bankroll or table limit cuts the progression short.
Frequently Asked Questions
Which staking plan is best for sports betting?
For bettors with a genuine edge, percentage-of-bankroll staking at a fractional-Kelly level (commonly half or quarter Kelly) offers the best balance of growth and survival. Flat staking is a reasonable, simpler alternative with lower variance. Progression systems like Martingale do not create an edge — they only concentrate risk into rare catastrophic losses.
Does the Martingale system work?
No. Martingale changes the shape of your results — many small wins punctuated by rare huge losses — but not their expected value. Stakes grow as 2^n after n losses, so a modest losing streak demands enormous bets that collide with bankroll or bookmaker limits. With a negative edge, ruin is a mathematical certainty over time; with a positive edge, flat or Kelly staking grows faster with far less risk.
What is the difference between flat and percentage staking?
Flat staking bets a constant amount, so exposure stays fixed as the bankroll changes; a long losing streak reduces the roll linearly and can bust it. Percentage staking recalculates the stake as a share of the current bankroll, so stakes shrink during drawdowns and compound during upswings — after n straight losses at fraction f you retain (1 − f)^n of the roll instead of losing n fixed units.
What stake percentage should I use in the simulator?
Start with your Kelly fraction: f* = (p × b − q) ÷ b, where p is your win probability and b is decimal odds minus 1. Then test half and quarter of that value. Compare bust rate and median drawdown across runs — most bettors find that 1–3% of bankroll keeps bust risk near zero while preserving most of the growth.
Why is the median final bankroll lower than the mean?
Compounded betting outcomes are right-skewed: a small number of extremely lucky simulation paths pull the mean upward, while the median reflects the typical path. When the gap between mean and median is very large, the strategy relies on rare jackpot runs — the median is the more honest planning number.
How many Monte Carlo runs do I need for reliable results?
The default 10,000 trials gives stable estimates of bust rate and median outcome for most setups. Increase toward 100,000 if you are measuring rare events such as bust rates under 1%. Results will vary slightly between runs because the simulation is genuinely random — that variation is itself a useful reminder of how noisy real betting is.