Bankroll Management Calculator — Staking Plan Comparison
Calculate optimal bet sizes using fixed stake, fixed percentage, and Kelly Criterion staking. Protect your bankroll with mathematically sound money management.
Odds format
Saved for all betting calculators
Your total betting bankroll
e.g. -110 or +150
Win Probability: 55%
Your estimated win probability per bet
Choose how to size each bet
Percentage of current bankroll per bet
Recommended Stake
$50.00
Edge per Bet
+10.00%
Stake %
5.00%
Kelly Fraction
10.00%
Kelly Stake
$100.00
| Bets Placed | Projected Bankroll | Change |
|---|---|---|
| After 10 bets | $1,051.14 | +$51.14 |
| After 50 bets | $1,283.23 | +$283.23 |
| After 100 bets | $1,646.67 | +$646.67 |
| After 200 bets | $2,711.52 | +$1,711.52 |
Last reviewed · How we check our calculators
How to Use the Bankroll Management Calculator
The bankroll management calculator helps you determine exactly how much to bet on each wager based on your chosen staking strategy. Enter your starting bankroll, your estimated win probability (drag the slider), the average odds you expect to be betting at (in the odds format you picked), and choose a staking method. As you type, the result shows your recommended stake, edge per bet, and a deterministic projection of how your bankroll grows (or shrinks) over 10, 50, 100, and 200 bets.
The projections use expected value (EV), not random simulation. This shows the mathematical trajectory of each staking plan given your inputs — the actual path will vary due to variance, but the EV projection is the long-run expected outcome.
The Kelly Criterion option auto-calculates the mathematically optimal stake. If your estimated edge is zero or negative, the Kelly recommendation is £0 — in that scenario, the correct action is not to bet.
The Formula
The calculator uses three staking methods, each with a distinct growth formula:
1. Fixed Stake
You bet the same dollar amount every time regardless of bankroll size. The bankroll after n bets is:
- bankroll_n = bankroll + n × stake × edge
where edge = p × (odds − 1) − (1 − p) = (p × odds) − 1
This is linear growth (or loss). With positive edge it grows steadily. The downside: as your bankroll grows, your fixed stake becomes a smaller and smaller percentage, so you never accelerate your growth through compounding.
2. Fixed Percentage
You bet a fixed percentage of your current bankroll on every bet. This compounds:
- bankroll_n = bankroll × (1 + stakePercent/100 × edge)^n
With positive edge this grows exponentially. The risk is symmetrical: a losing run shrinks your bankroll faster than fixed staking. Common choices are 1–5% of bankroll per bet, with most professional bettors using 1–3%.
3. Kelly Criterion
The Kelly fraction is the mathematically optimal percentage of bankroll to bet, given your edge and the odds:
- f* = (b × p − q) / b
- where b = decimal odds − 1 (net odds), p = win probability, q = 1 − p (loss probability)
The Kelly fraction maximises the long-run geometric growth rate of your bankroll. It is also the staking plan that is least likely to lead to ruin, given accurate probability estimates. Like fixed percentage staking, it compounds. The Kelly projection uses the Kelly fraction as the stake percentage in the same formula above.
Edge Per Bet
The edge (expected value per unit staked) determines whether any staking plan can be profitable:
- edge = p × (odds − 1) − (1 − p)
- Positive edge → long-run profitable; negative edge → long-run losing bet
- At even-money odds (2.0) you need greater than 50% win rate to have a positive edge
Practical Examples
Example 1 — Fixed Stake, Positive Edge
Bankroll: $1,000. Fixed stake: $50. Win probability: 55%. Decimal odds: 2.0.
- Edge = 0.55 × 1.0 − 0.45 = 0.10 (10.00% per bet)
- After 10 bets: $1,000 + 10 × $50 × 0.10 = $1,050
- After 100 bets: $1,000 + 100 × $50 × 0.10 = $1,500
- After 200 bets: $1,000 + 200 × $50 × 0.10 = $2,000
Linear growth: steady but slow. Your $50 stake remains the same even as your bankroll doubles.
Example 2 — Fixed 5%, Same Edge
Bankroll: $1,000. 5% fixed percentage. 55% win probability, 2.0 odds.
- Growth per bet = 1 + 0.05 × 0.10 = 1.005
- After 100 bets: $1,000 × (1.005)^100 ≈ $1,647
- After 200 bets: $1,000 × (1.005)^200 ≈ $2,712
Compounding accelerates growth. After 200 bets with percentage staking you have $2,712 versus $2,000 with fixed staking — 35% more.
Example 3 — Kelly Criterion
Bankroll: $1,000. 55% win probability, 2.0 decimal odds.
- b = 2.0 − 1 = 1.0; p = 0.55; q = 0.45
- Kelly fraction: f* = (1.0 × 0.55 − 0.45) / 1.0 = 0.10 (10%)
- Kelly stake: 10% × $1,000 = $100
- Growth per bet = 1 + 0.10 × 0.10 = 1.01
- After 100 bets: $1,000 × (1.01)^100 ≈ $2,705
Full Kelly bets aggressively and grows fast, but produces high variance. Most professionals use half Kelly ($50 in this case) to reduce volatility while capturing most of the long-run growth benefit.
Pros and Cons of Each Method
| Method | Pros | Cons |
|---|---|---|
| Fixed Stake | Simple, predictable, easy to track | No compounding; stake becomes tiny relative to bankroll |
| Fixed % | Compounds growth; scales with bankroll automatically | Losing runs shrink stake quickly; requires discipline |
| Kelly | Maximises long-run growth; theoretically optimal | Requires accurate probability estimates; high variance at full Kelly |
More Money-Management Tools
Position sizing only works as a system. Check the same plan from every angle:
- Anti-Martingale Calculator — Pyramid Winners — Calculate the anti-martingale position sizing strategy.
- Martingale Calculator — Calculate martingale position sizes for crypto and forex trading.
- Kelly Criterion Calculator — Calculate the mathematically optimal bet size using the Kelly Criterion formula.
- Masaniello Calculator — Plan a Masaniello staking series: set a bankroll, the number of bets and the wins you expect, and get each stake as results come in, the target and the full stake plan.
- Drawdown Calculator — Calculate the percentage gain needed to recover from a drawdown.
- Risk Reward Calculator — Calculate the risk/reward ratio for any trade in seconds.
New to sizing rules? Read the guide Money Management & Position Sizing: Martingale, Anti-Martingale, Kelly and Risk of Ruin — formulas, worked examples and risk-of-ruin numbers for every method.
Frequently Asked Questions
Bankroll management is the practice of sizing your bets relative to your total betting funds (bankroll) to maximise long-run growth while minimising the risk of ruin. Poor bankroll management — betting too large a percentage per bet — is the leading cause of going broke even among bettors with a genuine edge. The three most common approaches are fixed stake (same dollar amount every bet), fixed percentage (same % of bankroll every bet), and Kelly Criterion (mathematically optimal % based on your edge and odds).
The Kelly Criterion is a formula that calculates the exact percentage of your bankroll to bet in order to maximise the long-run geometric growth rate. It was developed by John L. Kelly Jr. at Bell Labs in 1956. The formula is: f* = (b×p − q) / b, where b is the net odds (decimal odds minus 1), p is your win probability, and q is 1−p. When f* is positive you have an edge and should bet. When f* is zero or negative, the correct bet is zero — there is no mathematical basis for wagering.
Very accurate for full Kelly, less so for conservative staking plans. The Kelly Criterion is sensitive to probability estimates — overestimating your edge by just 5 percentage points can cause significant over-betting. This is why most professionals use half Kelly or quarter Kelly rather than full Kelly. Fixed percentage staking is more forgiving of estimation error because it caps your risk at a fixed fraction regardless of your claimed edge. If you are uncertain about your true win rate, use a smaller percentage (1–2%) and track your actual results over at least 500 bets before increasing.
Professional sports bettors typically bet 1–3% of bankroll per bet under a fixed percentage system. Very aggressive bettors with high confidence in their edge might use up to 5%. Anything above 5% per bet is generally considered high risk — even a short losing run at 10% per bet can reduce your bankroll by 65% (ten consecutive losses: 0.90^10 = 0.35). The Kelly Criterion provides a theoretically optimal answer given your edge, but most practitioners use half or quarter Kelly to account for uncertainty in their probability estimates.
The projections use deterministic expected value (EV) calculations, not random Monte Carlo simulation. For fixed staking, each bet adds stake × edge to the bankroll. For percentage and Kelly staking, the bankroll compounds by (1 + stake% × edge) each bet. These are the mathematical expected outcomes — your actual results will differ due to variance, and over short horizons (fewer than 100 bets) variance dominates. The EV projections show the long-run trajectory. Use them to compare staking plans, not to predict exact outcomes.
Sources
- J. L. Kelly Jr., A New Interpretation of Information Rate (Bell System Technical Journal, 1956)
- Edward O. Thorp, The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market (Handbook of Asset and Liability Management, Elsevier, 2006)
- Compound interest (Wikipedia)
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