The Kelly Criterion — Optimal Stake Sizing for Profitable Betting

The Stake-Sizing Problem — More Important Than the Tip

Even with a perfect forecasting model, you can lose your entire bankroll through poor money management. It's a paradox most beginners miss: you can be 70% accurate and still go broke, or 55% accurate and steadily profit. The difference is bankroll management.

Picture a 10,000-unit bankroll and 50% stakes per match. First bet wins: 15,000. Second loses: 7,500. Third wins: 11,250. Fourth loses: 5,625. After two wins and two losses (50% accuracy) you've lost 4,375 — almost half the bankroll. That's the "volatility trap", and it's exactly what the Kelly Criterion solves.

Now the same sequence at 5% stakes: start 10,000, after a win 10,500, after a loss 9,975, after a win 10,474, after a loss 9,950. After the same two wins and two losses you've lost just 50 units. The difference is enormous.

What the Kelly Criterion Is — History and Essence

The Kelly Criterion is a formula developed by John Kelly at Bell Labs in 1956. Originally meant to optimise telecom signals, it turned out to be ideal for determining optimal stake size. The legendary mathematician Edward Thorp used Kelly to beat casinos at blackjack and to run a hedge fund — successfully in both cases.

The formula maximises the logarithmic growth of the bankroll: over an infinite series of bets the bankroll grows as fast as possible while the theoretical risk of ruin is zero. It's the optimal balance between aggression and safety.

The formula: Kelly % = (probability × odds - 1) / (odds - 1). The result is the fraction of your current bankroll to stake.

A Worked Example

Our Poisson model gives a 62% probability on Under 2.5; the bookmaker offers 2.00. By the formula: Kelly = (0.62 × 2.00 - 1) / (2.00 - 1) = 0.24, or 24%. Full Kelly says stake 24% of the bankroll. On a 50,000-unit bankroll that's 12,000 on a single bet.

That's aggressive and risky, because the formula assumes a perfectly accurate probability estimate. In reality our 62% might be off — the real probability could be 55% or 68%. That's why, in practice, we use fractional Kelly.

Another example: probability 58%, odds 1.75. Kelly = (0.58 × 1.75 - 1) / (1.75 - 1) = 0.02, or 2%. The formula automatically recommends a small stake because the edge is small. That's the beauty of Kelly — it scales the stake to the strength of the signal.

Fractional Kelly — the BETSKOP Approach

In practice we use 25% of full Kelly. This cuts volatility fourfold while sacrificing only 50% of growth speed — an excellent trade-off. In the first example, 25% of full Kelly (24%) = 6% of bankroll. On a 50,000 bankroll the stake is 3,000 — sensible and psychologically comfortable.

Why 25%? On a small sample (under 100 bets) full Kelly creates extreme volatility — drawdowns of up to 50% are normal. Fractional Kelly smooths those swings. Research shows 25-33% of full Kelly is optimal when the probability estimate is imperfect.

In the BETSKOP system, fractional Kelly runs with guardrails: a minimum stake of 1% of bankroll (for any edge above 5%), a maximum of 5% (even at a 30% edge), and a 0.5% step (1%, 1.5%, 2%… 5%). Every stake recommendation is published with each analysis on the site and in the Telegram channel.

Bankroll Protection Levels

Our system runs three modes. Standard — bankroll stable or rising, stakes per Kelly (25% of full), range 1-5% of bankroll. Defensive — when the bankroll falls 20% from its peak, all stakes are halved and only bets with an edge above 15% are allowed. Pause — when it falls 30% from peak, a full stop for 2-3 days, a review of recent results and a re-check of model parameters.

Comparing Staking Strategies

Flat betting — the same amount each time, e.g. always 1,000 units. Simplicity is the upside, but you miss the chance to bet more on a bigger edge and less on a smaller one.

Fixed percentage of bankroll — e.g. always 3%. Better than flat because it automatically reduces stakes during a drawdown, but it ignores edge — the stake is identical for a 5% and a 20% edge.

The Kelly Criterion — optimises the stake for each specific situation. Big edge = big stake, small edge = small stake. Maximum growth at a given risk level. That's our choice.

Psychology and Discipline — the Hardest Part

Kelly solves the maths, but the hardest part is psychology. Typical errors include raising stakes after a winning run (euphoria — "I'm on a roll!"), raising them after losses (chasing — "this one's bound to land!"), deviating from the system out of "conviction" about a particular match, and betting without edge out of boredom.

An automated system solves this — each stake is calculated strictly by formula, with no subjective tweaks. A bot feels no emotion and never deviates from the maths. That's the core advantage of the mathematical approach, covered in detail in our mathematical vs expert predictions article.

For more on how we find value bets for every stake, see the main article. And for the common mistakes beginners make and how to avoid them, see the separate guide.