Kelly Criterion Calculator: Optimal Bet Sizing Formula

A poker buddy of mine—brilliant with numbers, reckless with chips—once went on a full-Kelly tear at a cash game. He'd calculated his edge precisely, sized his bets accordingly, and was up 40% in two hours. Then the deck turned cold. Within thirty minutes, he'd given back every penny and then some. "The math was right," he muttered. "I just didn't survive long enough for it to matter."

That's the paradox of the Kelly Criterion. It's mathematically perfect and practically dangerous. Developed by John Kelly at Bell Labs in 1956, it tells you exactly how much to bet—assuming you have infinite time and unlimited nerve. You don't.

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Kelly Formula

The core equation is deceptively simple:

f* = (bp − q) / b

f is the fraction of your bankroll to bet. b is the odds (net payout per unit wagered). p is win probability. q is loss probability (1 − p).

Say you have a 60% edge paying even money (1:1). Plug it in: f* = (1 × 0.60 − 0.40) / 1 = 0.20. Bet 20% of your bankroll. That's the optimal number—anything more or less and you're leaving long-term growth on the table.

With 55% win probability and 2:1 payouts: f* = (2 × 0.55 − 0.45) / 2 = 0.325. Thirty-two and a half percent. The formula doesn't care about your gut feelings—it just does the math.

Edge: The Non-Negotiable

Kelly is useless without a positive edge. Zero edge? Zero bet. The math says so.

Edge calculation is straightforward:

Edge = (Win Probability × Win Amount) − (Loss Probability × Loss Amount)

60% chance of winning $100, 40% chance of losing $100: Edge = (0.60 × 100) − (0.40 × 100) = $20 per $100 wagered. That's your edge. Kelly then translates it into optimal position sizing, accounting for compounding returns.

No edge, no bet. It's that simple—and that hard.

Full Kelly versus Half Kelly

Full Kelly is the theoretical optimum. It's also a wild ride. A string of losses can vaporize 50% or more of your bankroll before recovery kicks in. Most humans can't stomach that volatility.

Half Kelly—betting half of what the formula prescribes—sacrifices about 25% of growth rate while cutting volatility roughly in half. That's a trade most sane people are happy to make.

Quarter Kelly goes even further: you give up about 56% of growth rate but get an equity curve that looks a lot less like a heart attack monitor.

Here's the real-world rule of thumb: most professional gamblers and institutional investors use 25–50% of full Kelly. They want the growth without the sleepless nights.

Portfolio Application

When you're sizing multiple positions simultaneously, Kelly becomes a matrix equation. It accounts for correlations between positions—because if your bets are correlated, the risk is higher than the sum of its parts.

Practical portfolio Kelly evaluates the entire opportunity set holistically, not each position in isolation. High correlations? Dial back. Uncorrelated bets? Deploy more aggressively.

Continuous Kelly

For investments with continuously distributed returns, the formula simplifies:

f* = μ / σ²

μ is expected return, σ² is variance. With 15% expected return and 30% volatility: f = 0.15 / 0.09 = 1.67. That's 167% of capital—yes, the math says use leverage*. Whether you should is an entirely different question.

The Catch: Why Full Kelly Fails in Practice

Kelly demands precise edge estimates. Nail it, and you're golden. Overestimate, and you're headed for ruin. Underestimate, and you're playing too small to matter.

The formula also assumes infinite time. You have a finite lifespan. It ignores utility—how much pain you can tolerate—and that matters more than most quant types like to admit.

The Pragmatic Path

Fractional Kelly is where theory meets reality. Use 25–50% of the full Kelly number. You'll capture most of the growth. You'll sleep at night. And when the inevitable losing streak hits—and it will hit—you'll survive to bet another day.

The Kelly Criterion isn't a license to bet big. It's a framework for betting right.