Kelly criterion simulator
A positive expected value identifies a favorable bet; it does not determine how much of a bankroll can safely be exposed to it. This simulator applies different staking rules to the same opportunities and the same sequences of wins and losses, isolating the consequences of money management.
The comparison is paired: simulated player 1 receives exactly the same opportunities and outcomes under every strategy, as does simulated player 2, and so forth. Only the amount wagered changes.
Every faint line is one persistent simulated player. A path that reaches the bankruptcy boundary remains visible; failed players are not removed.
Population, not one player: at any given bet, P25 is the bankroll below which 25% of simulated players lie at that moment. A percentile curve can contain different players at different bets and is not an individual history. Minimum and maximum are unstable sample extremes.
Each box describes all final bankrolls: P10–P90 whiskers, P25–P75 box, median line, and mean dot. The default log scale keeps radically different bankrolls readable but compresses their absolute distance; select Bankroll to inspect the full mean–median gap created by exceptional winners.
| Strategy | P10 | Median | Mean | P90 | Ever reached practical bankruptcy | Finished below start | Median maximum drawdown | Maximum wager bound |
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The median describes the typical simulated player. The mean answers a different question and may be dominated by a small number of exceptionally large bankrolls.
This curve is calculated from the configured opportunities rather than from random outcomes. It shows expected logarithmic growth as the stake moves from zero to three times the estimated Kelly fraction. Under accurate probabilities the maximum occurs at full Kelly; estimation error can move the safest growth region toward fractional Kelly.
Interpretation: the simulator illustrates mathematical consequences under stated assumptions. A positive true expected value is imposed by the selected environment; real probability estimates are uncertain, and no staking system can make an incorrect estimate profitable.