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How much can a bankroll grow if your edge is real, and how rough is the ride? Enter your bankroll, the number of bets, the price you pay and your own probability: the planner gives the expected log growth per bet, the median and the 10th–90th percentile ending bankroll from 2,000 simulated runs, and the chance of falling to half the bankroll along the way, with full, half and quarter Kelly one click away. Example: $1,000 over 100 bets bought at 40¢ that you think win 46% of the time. The Kelly stake is 10%; at half Kelly the median run ends at $1,745 and one run in ten ends below $831.
2,000 simulated runs with a fixed seed, each staking the same share of its current bankroll on independent bets, before fees. The result is only as good as your probability: if your edge is smaller than you think, growth is lower and the swings are worse.
$1,000, 100 bets at 40¢, your probability 46%: the Kelly stake is (46 − 40) ÷ (100 − 40) = 10% of the bankroll. The same 2,000 runs for each stake size:
| Stake per bet | Log growth per bet | Median ending bankroll | 10th – 90th percentile | Falls to half at some point |
|---|---|---|---|---|
| 2.5% quarter Kelly | +0.33% | $1,386 | $955 – $2,012 | 0.2% |
| 5% half Kelly | +0.56% | $1,745 | $831 – $3,664 | 5.2% |
| 10% full Kelly | +0.74% | $2,095 | $481 – $9,119 | 33.1% |
| 20% double Kelly | +0.02% | $1,019 | $55 – $18,766 | 73.4% |
Half Kelly keeps 75% of full Kelly's growth per bet while the chance of falling to half drops from 33.1% to 5.2%. Double Kelly takes more risk for less growth: +0.02% a bet against +0.74% at full Kelly.
Each bet stakes a share f of the current bankroll on a contract bought at price c. A win multiplies the bankroll by 1 + f × (1/c − 1); a loss multiplies it by 1 − f. With your probability q, the expected log growth per bet is q × ln(1 + f × (1/c − 1)) + (1 − q) × ln(1 − f). Over n bets the typical (median) bankroll grows by a factor of about en × growth. Growth is highest at the Kelly stake, (q − c) ÷ (1 − c), and staking much more than that lowers it.
The percentiles come from a simulation: 2,000 runs of n bets with a fixed random seed, sorted by their final bankroll. The 10th percentile is the run one tenth of the way up, the median the middle one and the 90th percentile the one nine tenths of the way up. A run counts toward the last figure if its bankroll touches half the start at any point, even if it recovers.
Related tools: the Kelly calculator for the stake on a single bet, the risk of ruin calculator for the chance of hitting a floor you choose, and the expected value calculator for the edge itself. The idea is explained under Kelly criterion in the glossary.
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Work out the expected log growth per bet, q × ln(1 + f × (1/c − 1)) + (1 − q) × ln(1 − f), where q is your probability, c the price and f the share of the bankroll you stake. Over n bets the typical bankroll grows by about e^(n × growth). In the example above, half Kelly grows 0.56% a bet.
Full Kelly maximizes long-run growth only if your probability is right. Smaller stakes give up some growth for much smaller swings: in the example, half Kelly keeps 75% of full Kelly's growth per bet while the chance of falling to half the bankroll drops from 33.1% to 5.2%.
Sort the 2,000 simulated ending bankrolls: one run in ten ends below the 10th percentile and one in ten above the 90th. The range between them is the ordinary spread of outcomes for these inputs, not a worst or best case.
Yes. The runs use a fixed random seed, so the same inputs always give the same numbers, on this page and in the calculator. Change an input to see a different set of runs.
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