Finding a horse whose price looks generous is only half of the challenge. The other half is deciding how much to stake, and it is the half most people get wrong. A bettor with a genuine edge can still go broke by staking too much, while one with the same edge and a sensible staking plan survives the inevitable bad runs. This guide covers the mathematics of bankroll management, including the Kelly Criterion, and explains why the safest approach is usually a conservative one.
What Is a Bankroll?
Your bankroll is the money set aside specifically for betting, separate from rent, bills and savings. It should be an amount you can afford to lose entirely. Everything in this article assumes that boundary: no staking system makes losing money safe, and none can turn a negative-expectation bet into a positive one.
Variance: Why Losing Streaks Are Normal
Horse racing outcomes are highly variable. Suppose you back horses that win, on average, 20% of the time, which is a realistic strike rate for a selection of medium-priced runners. The chance of losing any single bet is 80%, and the chance of losing ten in a row is 0.8 to the power of 10, or roughly 10.7%. The chance of losing twenty in a row is about 1.2%. Over a few thousand bets, runs like these are not just possible but expected.
If you stake 10% of your bankroll on each of those bets, ten consecutive losses would reduce the bankroll to about 35% of its starting value (0.9 to the power of 10). If you stake 2%, ten losses cost about 18% (0.98 to the power of 10 gives 0.817). The difference between the two is the difference between a rough patch and a wipeout.
Flat Staking
The simplest plan is flat staking: the same stake on every bet, typically 1% to 2% of the starting bankroll. It is easy to follow and easy to track, and it makes results comparable from bet to bet. Its weakness is that it ignores how strong each opportunity is, a bet with a small edge gets the same stake as one with a large edge.
The Kelly Criterion
The Kelly Criterion, published by John L. Kelly Jr. in 1956, is a formula for the stake that maximises the long-term growth rate of a bankroll when you know your edge. For a bet with decimal odds, it is:
f = (b x p - q) / b
where f is the fraction of the bankroll to stake, b is the net odds (decimal odds minus 1), p is your estimated probability of winning and q is 1 minus p.
A Worked Example
A horse is priced at 5.00 (so b = 4, and the market's implied probability is 20%). Your model estimates its true chance at 25%, so p = 0.25 and q = 0.75.
- f = (4 x 0.25 - 0.75) / 4
- f = (1.00 - 0.75) / 4
- f = 0.25 / 4 = 0.0625
Full Kelly says to stake 6.25% of the bankroll. On a 1,000 bankroll, that is 62.50. If your estimated probability had been 20% or lower, the formula gives zero or a negative number, meaning there is no edge and no bet.
Why Full Kelly Is Risky
Kelly is optimal only if your probability estimate is correct. In practice, every estimate carries error, and overestimating your edge causes overbetting, which is far more damaging than underbetting. Full Kelly also produces large swings: it is common to see the bankroll fall by half at some point even when the bettor is right about their edge.
For these reasons, most practitioners use fractional Kelly, typically half or a quarter of the formula's stake. In our example, half Kelly would be 3.1% of the bankroll, and quarter Kelly about 1.6%. Fractional Kelly sacrifices a portion of the theoretical growth rate in exchange for much lower volatility and a built-in buffer against errors in the probability estimate.
Choosing a Staking Plan
| Approach | Strength | Weakness |
|---|---|---|
| Flat stakes (1-2%) | Simple, low risk, easy to audit | Ignores the size of the edge |
| Fractional Kelly | Scales stakes with edge, limits drawdown | Needs a well-calibrated probability estimate |
| Full Kelly | Maximum theoretical growth | Severe swings, punishes estimation errors |
| Chasing losses (Martingale) | Feels intuitive | Exponential risk; can end a bankroll in a short run |
The Problem With Chasing Losses
The Martingale approach, doubling the stake after each loss so that one win recovers everything, is popular and dangerous. It is dangerous because losing streaks grow exponentially: after just six losses in a row, a 10 starting stake has become a 640 stake, with 630 already lost before it. A bettor is limited by both the size of their bankroll and by betting limits, so eventually a streak arrives that cannot be recovered. No pattern of stakes changes the expected value of a bet; it only redistributes the risk.
Calibration: The Hidden Requirement
The Kelly formula assumes your probability estimates are accurate, which raises the question: how do you know? The answer is calibration testing. Collect your estimates and their outcomes over a large sample and check them. Among all the horses you rated at 20% to 25%, did roughly 20% to 25% win? If the horses you rated at 25% actually win only 18% of the time, then your edge does not exist and Kelly would recommend overbetting. Models are typically assessed with measures such as log loss and Brier score, which reward well-calibrated probabilities rather than merely picking winners.
Practical Rules
- Set a bankroll that you can afford to lose completely, and never top it up to chase losses.
- Cap any single stake, for example at 2% to 5% of the bankroll, regardless of what a formula says.
- Prefer fractional Kelly if you use Kelly at all.
- Record every bet, including the odds taken and your estimated probability, so you can check whether you have an edge.
- Decide in advance the loss at which you will stop and review your approach.
Most importantly, remember that a staking plan manages risk, it does not remove it. Betting should be entertainment. If gambling stops being enjoyable, or you find yourself betting more than you planned, seek help from a support organisation in your country.