Work out the stake that maximises long-run bankroll growth. Enter the odds and your estimated probability of winning, and the calculator returns the optimal fraction of your bankroll to stake.
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The Kelly fraction assumes your probability estimate is accurate. Because real estimates are uncertain, fractional Kelly (half or quarter) is widely used to cut volatility.
The Kelly Criterion answers one question: given a known edge, what stake grows your bankroll fastest over the long run without risking ruin? Stake too little and you leave growth on the table; stake too much and variance eventually wipes you out. Kelly is the balance point.
where f* is the fraction of your bankroll to stake, b is the net decimal odds (decimal odds − 1), p is your probability of winning, and q = 1 − p is the probability of losing.
Say the decimal odds are 2.50 (so b = 1.5) and you believe the true win probability is 45% (p = 0.45, q = 0.55). Then f* = (1.5 × 0.45 − 0.55) / 1.5 = (0.675 − 0.55) / 1.5 = 8.3% of your bankroll under full Kelly — or 4.2% under half Kelly.
Full Kelly is only optimal if your probability estimate is exactly right. In reality it never is, and overestimating your edge leads to overbetting, which is punishing. Half and quarter Kelly give up a little theoretical growth for a large reduction in swings and in the chance of a deep drawdown.
A formula that gives the stake size, as a fraction of your bankroll, that maximises the long-run growth rate given the odds and your estimated probability of winning.
Staking half of the fraction full Kelly suggests. It sacrifices a little long-run growth for a large reduction in volatility and risk of ruin, which is why many practitioners prefer it.
When the Kelly fraction is zero or negative, the odds do not compensate for your estimated probability — there is no positive expected value, so the growth-maximising stake is nothing.
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