The classic Kelly formula assumes you place one bet at a time, and that you know its result before placing the next. In reality, a value bettor often has several bets open at the same time: ten matches on Saturday afternoon, several markets on the same match… In that case, the simple formula no longer applies directly.
Case 1: simultaneous independent bets
If the bets are independent (different matches), you need to maximise expected growth across every possible combination of results:
where equals if bet wins and if it loses.
For small EVs and a moderate number of bets, adding up the individual Kelly stakes remains an acceptable approximation. But the error grows quickly with the EV and the number of bets.
Case 2: mutually exclusive bets (same match)
Betting on two outcomes of the same match (for example Team A win and draw): only one of them can win. The bets partially hedge each other, and the optimum is calculated over the match's outcomes. It can be optimal to stake on an outcome with slightly positive value only because you're already staking on another.
Case 3: correlated bets
The most dangerous case. Examples:
- Team A win and over 2.5 goals in the same match.
- Team A win and Team A to be champions at the end of the season.
- Several bets that rest on the same model error (for example a misjudgement of a team's form).
Correlated bets win and lose together. Treating them as independent means underestimating the risk and staking far too much.
In practice
- For independent bets and modest EVs: individual fractional Kelly + a total exposure cap (for example 20 to 30% of the bankroll).
- For bets on the same match: either take only one (the most +EV), or optimise numerically across the outcomes.
- For correlated bets: cut stakes sharply, or model the correlation (Monte Carlo simulation of joint results + numerical optimisation).