# Kelly Criterion How much should you bet when the odds are in your favour? The Kelly criterion gives a precise answer: bet the fraction that maximises long-term wealth growth. Bet too much and you risk ruin. Bet too little and you leave money on the table. --- ## The formula For a simple bet with win probability *p* and odds *b* (net payout per unit wagered): **f* = (bp - q) / b** where *q = 1 - p*. This is the fraction of your capital to bet. If the result is negative, don't bet. **Maximising growth, not expected value.** Kelly doesn't maximise expected returns on a single bet. It maximises the expected logarithmic growth rate of wealth across many bets. Strategies that maximise expected value can have terrible long-term outcomes because a single catastrophic loss wipes you out. **Fractional Kelly.** Full Kelly is volatile. Many practitioners use half-Kelly or quarter-Kelly - sacrificing some growth for lower variance and smaller drawdowns. --- Kelly formalises a principle that runs through the strategy and numbers essays here: survival is the binding constraint, not expected returns. [[Paying for growth]] asks when growth creates value versus consumes capital. Kelly provides the quantitative frame: even when the expected return on a growth investment is positive, over-allocating destroys value because the path includes periods of loss severe enough to threaten the enterprise. The right question isn't "is this a good investment?" but "how much of our capital should we commit?" [[Cash and profit]] makes the same point from the accounting side. Cash is the bankroll. A business that bets its entire cash position on a positive-expected-value project is playing full Kelly or worse - and full Kelly is already more volatile than most operators can stomach. The serial acquirer discipline is fractional Kelly in practice. [[Constellation]] makes many small acquisitions rather than a few large ones. [[Halma]] and [[Lifco]] set strict deal-size limits relative to group cash flow. They're not optimising for the best single bet - they're sizing each bet so that the portfolio compounds over time without risking ruin on any one deal. The [[Ergodic Hypothesis]] explains why this matters at a deeper level. Kelly works because it respects non-ergodicity: you live one path through time, and ruin on that path is permanent regardless of what the ensemble average says.