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Kelly Criterion: The Mathematical Approach to Optimal Betting

The Kelly Criterion estimates an optimal bet size based on your edge and the odds. Used correctly, it replaces arbitrary staking with a disciplined, probability driven approach.

Understanding the Purpose

Kelly tells you what fraction of your bankroll to wager to maximize long run growth when you have a positive expectation. If you do not have an edge, Kelly will not recommend a bet.

The Kelly Formula

KELLY FORMULA

f = (bp - q) / b

  • f = fraction of bankroll to wager
  • b = net odds (decimal odds minus 1)
  • p = your estimated probability of winning
  • q = probability of losing (1 minus p)

If f equals 0.05, that suggests betting 5% of your bankroll. If f is negative, Kelly suggests not betting.

Important: the output is only as good as your probability estimate. Garbage in, garbage out.

The Importance of p

Your edge comes from estimating p more accurately than the market. Bet Better’s data models provide objective probability estimates you can use for disciplined staking.

Fractional Kelly

Full Kelly can produce large swings. Many bettors reduce variance by using Fractional Kelly, such as half Kelly or quarter Kelly. This keeps the structure of Kelly while lowering drawdowns.

FRACTIONAL KELLY EXAMPLE

Full Kelly result: 6%

Half Kelly stake: 3%

> Lower variance, same disciplined logic.

Pair this with bankroll discipline: Bankroll Management Guide.

FAQ

What is the Kelly Criterion used for?
It estimates an optimal bankroll fraction to stake when you have an edge, aiming to maximize long run growth.
Why do bettors use Fractional Kelly?
Because full Kelly can be volatile. Fractional Kelly reduces variance and drawdowns while keeping a consistent edge based staking approach.
What does a negative Kelly number mean?
It suggests you do not have positive expected value at the offered odds, so Kelly would recommend passing.