A bettor with a real 55% winner at plus money can still go broke betting too big, and can miss much of the edge by betting too small. The size of the stake decides how fast a bankroll grows or how fast it disappears, which matters more than most bettors give it credit for.
Enter a bankroll, the odds on the bet, and a win probability, and the result shows the full Kelly stake, the half and quarter versions most bettors actually use, and the edge those odds and that probability produce. That number is the difference between a stake that compounds an edge and one that guesses at it.
Start with the bankroll, the full amount being risked across bets, not just what is set aside for this one wager. Enter the odds on the bet in the format the sportsbook posts them, plus or minus American odds. Finish with a win probability, the bettor’s own honest estimate of how often the bet hits, not the number implied by the odds themselves.
The result returns four numbers: the full Kelly stake as a percentage of bankroll and in dollars, the half Kelly dollar amount, the quarter Kelly dollar amount, and the edge those inputs produce. A bettor reads the edge first to see whether there is one at all, then picks the stake size that matches how much variance they can stand.
Kelly sizing runs on one formula: the fraction of bankroll to bet equals (b times p minus q) divided by b. Here b is the decimal odds minus 1, p is the win probability, and q is 1 minus p, the probability of losing. The formula never goes below zero, because there is no such thing as a negative bet. No edge means no stake.
On the default inputs, a $1,000 bankroll faces +100 odds with a win probability of 55%. Odds of +100 pay even money, so b equals 1. Plug in p of 0.55 and q of 0.45: (1 times 0.55 minus 0.45) divided by 1 equals 0.10, or 10%. That 10% is both the Kelly fraction and the edge at these odds, and on a $1,000 bankroll it works out to a full Kelly stake of $100.00, a half Kelly stake of $50.00, and a quarter Kelly stake of $25.00.
Kelly sizing is built to maximize long-run bankroll growth, but only if the win probability entered is accurate. Since no bettor’s probability estimate is perfect, betting the full Kelly stake magnifies the cost of being wrong, and a string of bad estimates at full Kelly can cut a bankroll in half or worse. Betting half or quarter Kelly gives up some growth in exchange for a much smoother ride, which is why most bettors who use this method size down rather than take the full number.
The most common mistake is treating the sportsbook’s implied probability as the bettor’s own probability, which produces a Kelly fraction of zero every time since there is no edge left to bet. The second is ignoring bankroll changes and staking the same dollar amount race after race instead of recalculating the percentage against the current bankroll. A bettor trying to grow a bankroll rather than gamble on a single outcome treats the Kelly number as a ceiling, not a target, and sizes down from it based on how confident the win probability really is.
Why does Kelly ever return zero? Kelly returns zero whenever the win probability entered is equal to or lower than what the odds already imply, meaning there is no edge to size a bet against. Zero is the correct answer in that case, not a flaw in the math.
Should a bettor ever bet full Kelly? Full Kelly is the stake that grows a bankroll fastest if the win probability is exactly right, but win probabilities are estimates, not certainties, so most bettors who use this method bet half or quarter Kelly to cut the swings that come with being wrong.
Where does the win probability come from? It comes from the bettor’s own handicapping, not from the odds on the ticket. Using the odds’ implied probability as the input for Kelly is circular and always returns a stake of zero.
Does a bigger bankroll change the Kelly percentage? No. The Kelly fraction depends only on the odds and the win probability, and the bankroll is what converts that fraction into a dollar amount. A larger bankroll changes the dollar stake, not the percentage.