🎲 Kelly Sizer

Optimal bet sizing for asymmetric convex bets. Kelly + fractional Kelly + Monte Carlo equity curve.

📖 Formula

Kelly fraction f* = (p·b − q) / b where p=win probability, q=1−p=loss prob, b=net odds (payout/stake on win).
Full Kelly maxes log-wealth but drawdowns are brutal. Most pros use ¼ to ½ Kelly for comfort.

⚙️ Your Bet

Presets:

Win probability (0–1)

Payoff multiple (b)

Fractional Kelly

Bankroll ($)

MC trials

Bets / year

Kelly Fraction

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Your Bet % (frac·Kelly)

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Bet Size $

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Expected Edge / Bet

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CAGR (expected)

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Risk of Ruin (½)

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📈 Monte Carlo Equity Paths (1 year)

Median · 10th pct · individual paths

⚠️ Kelly Rules

If Kelly is negative, don't bet. You have no edge.
Full Kelly peaks log-wealth but 50%+ drawdowns are routine.
Your p and b are ESTIMATES. If you're overconfident on p, half-Kelly saves you.
Kelly assumes you can scale infinitely and re-bet continuously. Real markets constrain both.
For options: b is often asymmetric (bounded loss, unbounded win). Use expected payoff distribution not single scenarios.
Diversify: each bet at fractional Kelly across uncorrelated positions beats single Kelly.