Bankroll Basics: Flat Staking vs Kelly (How to Size Your Bets)
Bankroll sizing methods, assumptions and practical risk controls
Fixed-unit flat staking keeps the cash amount unchanged. Percentage staking keeps exposure proportional to the current bankroll. Kelly uses odds and an estimated win probability to calculate an edge-based fraction. With accurate inputs and a simple win-or-loss payoff, full Kelly maximises expected logarithmic bankroll growth, but it can size bets too aggressively when probabilities are optimistic, unstable or correlated.
Fixed-unit flat staking and percentage staking
Flat staking usually means placing the same monetary amount on every qualifying bet. If the unit is 10, each accepted selection receives a stake of 10 until the staking plan is reviewed. The cash exposure remains constant, but the percentage of bankroll changes as the bankroll rises or falls.
Fixed-unit flat staking
- Rule: use the same monetary unit for each accepted bet.
- Advantage: simple records and stable cash exposure.
- Main risk: the unit becomes a larger share of bankroll after a drawdown.
Fixed-percentage staking
Percentage staking uses the same proportion of the current bankroll rather than the same monetary amount. A 1% rule on a bankroll of 1,000 produces a stake of 10. If the bankroll falls to 800, the next stake becomes 8.
- Rule: recalculate the stake from the current bankroll.
- Advantage: exposure contracts automatically during drawdowns.
- Main risk: every accepted bet receives the same percentage even when estimated edges differ.
Kelly staking: edge-based bankroll allocation
Kelly staking uses the available odds and your estimated win probability to calculate a bankroll fraction. Under accurate probability estimates, repeated independent bets and the stated payoff assumptions, full Kelly maximises expected logarithmic bankroll growth. It does not guarantee a profit, prevent losing runs or protect against inaccurate inputs.
Kelly formula for decimal odds
Let O be decimal odds, b = O − 1, p your estimated win probability and q = 1 − p.
b = O − 1
q = 1 − p
The result f* is the full Kelly fraction of bankroll. A negative result means your probability estimate does not show a positive edge at the available price, so the Kelly stake is zero.
Where Kelly risk comes from
- Probability error: an overstated probability produces an overstated stake.
- Variance: a genuine edge can still experience long losing sequences.
- Correlation: several bets may depend on the same model assumption, match or market condition.
- Price movement: an edge calculated at one price may disappear after the odds shorten.
Fractional Kelly and stake caps
Fractional Kelly keeps the direction of the Kelly calculation but uses only part of the full fraction. A larger estimated edge can still receive a larger stake, but exposure is reduced.
A stake cap is different from a Kelly fraction. The fraction reduces every positive Kelly result. The cap limits only results that exceed a chosen maximum. Both controls can be used together.
Worked examples with decimal odds
For a simple single-outcome price, the raw implied probability is approximated as 1 ÷ decimal odds. In multi-outcome markets, bookmaker margin means the displayed probabilities may sum to more than 100%, so proper market comparison may require normalisation.
Example A: a small estimated edge at 2.10
q = 1 − 0.50 = 0.50
f* = (1.10 × 0.50 − 0.50) / 1.10
f* = 0.04545... = 4.55%
The full Kelly stake is substantially larger than the fixed-unit and percentage stakes because the calculation treats the estimated difference between 50.00% and 47.62% as a genuine edge. If that estimate is too optimistic, the stake is too large.
Example B: the estimate does not clear the price
At odds of 2.10, an estimated win probability of 46% is below the raw implied probability of 47.62%.
p = 0.46
q = 0.54
f* = (1.10 × 0.46 − 0.54) / 1.10
f* = −0.0309...
Kelly returns a negative fraction, so the calculated stake is zero. A fixed-unit system could still place the bet mechanically, which is why fixed staking should be combined with a separate selection and price filter.
Example C: a larger estimated edge
Odds of 1.80 imply 55.56%. If your estimated win probability is 62%, full Kelly produces a much larger fraction.
q = 1 − 0.62 = 0.38
f* = (0.80 × 0.62 − 0.38) / 0.80
f* = 0.145 = 14.50%
A 14.50% full Kelly stake is not automatically suitable for real betting. It assumes the 62% estimate is reliable and that the position is not materially correlated with other open bets. Fractional Kelly and a cap can reduce this exposure.
Pushes, partial wins and partial losses
The standard formula above assumes a binary win-or-loss settlement. Markets with pushes, half wins, half losses or several possible payouts require a calculation based on the complete outcome distribution. This applies to some Asian handicaps and Asian totals.
Flat, percentage and Kelly staking compared
| Method | How the stake changes | Main limitation |
|---|---|---|
| Fixed-unit flat | The monetary stake stays unchanged until the unit is reviewed. | Risk as a percentage of bankroll rises after losses and falls after gains. |
| Fixed percentage | The monetary stake rises or falls with the current bankroll. | The percentage does not respond to differences in estimated edge. |
| Kelly criterion | The fraction changes with odds and the estimated probability advantage. | Inaccurate probabilities and ignored correlation can produce excessive exposure. |
A practical staking workflow
- Make the take-or-pass decision first: staking does not turn a poor price into a good bet.
- Use the current available price: recalculate if the odds move materially.
- Separate normal exposure from the maximum cap: they serve different purposes.
- Review combined exposure: reduce stakes when several bets share the same underlying driver.
- Track closing prices and probability calibration: staking quality cannot compensate for weak probability estimates.
Flat, percentage and fractional Kelly calculator
Outputs use the same monetary units entered for bankroll and fixed stake.
This calculator applies the selected staking rules. It does not determine whether your probability estimate is accurate or whether the available price is attractive after bookmaker margin.
Calculator assumptions
- The Kelly calculation assumes a binary win-or-loss settlement.
- The entered probability must be your estimate, not the probability copied from the same odds.
- The Kelly cap applies only to the fractional Kelly result.
- Related bets should not be treated as independent without a correlation adjustment.
FAQ: bankroll and staking methods
What is the difference between flat and percentage staking?
Fixed-unit flat staking keeps the same monetary amount. Percentage staking recalculates the monetary stake as a constant proportion of the current bankroll.
What does the Kelly criterion calculate?
Kelly calculates a bankroll fraction from decimal odds and an estimated win probability. Under its assumptions, full Kelly maximises expected logarithmic bankroll growth over repeated bets.
Why use half Kelly or quarter Kelly?
Probability estimates are uncertain. Fractional Kelly reduces the calculated exposure while retaining the rule that a larger estimated edge can receive a larger stake.
Can full Kelly produce large drawdowns?
Yes. Losing sequences remain possible even when an edge is genuine. Optimistic probabilities, correlated bets and large calculated fractions can make drawdowns substantially deeper.
When should this Kelly calculator not be used?
The simple calculation should not be used unchanged for pushes, partial wins, partial losses, several payout levels or correlated portfolios. Those situations require the complete outcome distribution and combined exposure to be modelled.