The Kelly Criterion is a formula for deciding how much of your bankroll to stake on a bet, given the odds on offer and your own estimate of the true probability of the outcome. It was developed by John Kelly at Bell Labs in 1956 for a completely different problem — noisy telephone lines — but bettors and investors adopted it because it answers the exact question staking plans dodge: not “should I bet this?” but “how much should I bet if I’m right about my edge?”

The logic is that betting a fixed amount every time ignores how big your edge actually is, while betting a fixed percentage of your bankroll regardless of edge risks overstaking on marginal value and understaking on strong value. Kelly ties stake size directly to edge: the bigger your perceived advantage over the market price, the larger the fraction of your bankroll you commit, and when you have no edge at all the formula tells you to stake nothing. It also compounds correctly — you’re betting a percentage of a bankroll that grows or shrinks with each result, not a flat dollar figure that ignores your current position.

The formula, in decimal-odds terms, is: f* = (bp − q) / b, where b is the decimal odds minus 1 (the profit per dollar staked if you win), p is your estimated true probability of winning, and q is 1 − p. The output, f*, is the fraction of your bankroll to stake. If f* comes out negative, the market price is worse than your assessed probability and Kelly says don’t bet.

The catch is that everything depends on p, and nobody knows the true probability of Arsenal beating Bayern Munich — you only have an estimate. Overestimate your edge even slightly and full Kelly will oversize your stakes and produce brutal bankroll swings. This is why almost every serious practitioner bets a fraction of full Kelly rather than the raw number.

Example

Suppose your bankroll is $8,400. Arsenal are away to Bayern Munich in the Champions League, priced at 2.50 to win the match. Your own model, built from recent form, injuries and expected-goals data, puts Arsenal’s true winning chance at 46%, versus the 40% implied by 2.50 (1 ÷ 2.50). You believe you have a genuine 6-point edge.

Convert the odds to b: 2.50 − 1 = 1.50.

Plug into the formula: f* = (bp − q) / b = (1.50 × 0.46 − 0.54) / 1.50 = (0.69 − 0.54) / 1.50 = 0.15 / 1.50 = 0.10

Full Kelly says stake 10% of your bankroll: 0.10 × $8,400 = $840.

If Arsenal win, you collect $840 × 2.50 = $2,100, a profit of $1,260, and your bankroll becomes $9,660. If they lose, you’re down to $7,560. Because your edge estimate could easily be wrong by a few points either way, most bettors would run this at half Kelly — 5% of bankroll, or $420 — accepting slower growth in exchange for far smaller drawdowns if the model is over-optimistic.

Key Points

  • Fraction, not certainty: f* only means what it says if your probability estimate is accurate. Treat the output as a ceiling, not a target — half or quarter Kelly is standard practice precisely because real-world edges are estimates, not facts.
  • No edge, no bet: If your calculated true probability is below the market’s implied probability, f* is zero or negative. Kelly’s real discipline is stopping you from betting markets where you have no demonstrated advantage, which is most of them.
  • Recalculate the bankroll each time, not the stake: Kelly staking is dynamic — the 10% or 5% fraction should be applied to your current bankroll before every bet, not to the number you started the month with. This is what makes it compound, and also why a losing streak automatically shrinks your stakes rather than digging a fixed-stake hole.
  • Small errors in probability cause large errors in stake: because p sits inside a formula that’s compared against 1 − p, moving your estimate from 46% to 50% on the same 2.50 price roughly doubles the recommended stake. Be honest about how precise your model really is before trusting the raw output.
  • It’s built for repeatable edges, not one-off punts: Kelly assumes you can make this kind of positive-expectation bet many times over. Applying it to a single Grand National outsider you fancy once a year is statistically meaningless — it’s a bankroll-growth tool for bettors with a genuine, repeatable pricing edge, such as closing-line beaters in football or tennis markets.
  • Correlated bets break the model: Kelly assumes each bet’s outcome is independent. Stacking several same-day accumulator-style edges on correlated events, like backing a title favorite’s build-up markets across a Formula 1 race weekend, means your real risk is far higher than the formula assumes if you size each leg separately.