What is the Kelly criterion?

Kelly gives the optimal fraction of bankroll to risk when edge and payoff odds are known: f* = (p × b − q) / b, where p is win probability, q = 1 − p, and b is reward-to-risk.

Why use half Kelly or quarter Kelly?

Full Kelly maximises theoretical growth but is volatile and sensitive to estimation error. Half and quarter Kelly reduce drawdown risk while keeping much of the benefit.

Why is f* vs win rate a straight line?

With fixed b, f* = p − (1 − p)/b — linear in p. The curved relationship appears when you vary reward-to-risk instead.

What does negative Kelly mean?

When p × b − q ≤ 0 there is no edge. Kelly suggests zero or negative sizing — do not increase risk.

Kelly Position Sizing Calculator — Full, Half & Quarter Kelly

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Kelly formula

f* = (p × b − q) / b

p = win probability · q = 1 − p · b = reward-to-risk (₹ won per ₹1 risked on a winning trade). f* is the fraction of bankroll the model suggests risking.

Quick scenarios

Win probability: 55%

1%99%

Reward-to-risk (b): 1.50

0.25×5×

Bankroll for stake sizing (₹)

Or enter b directly

p (win)

55.0%

q (loss)

45.0%

Edge (p × b − q)

+0.375

Full Kelly (f*)

25.00%

Stake: ₹2.50 L of ₹10.00 L

Half Kelly (f* ÷ 2)

12.50%

Stake: ₹1.25 L · smoother drawdowns

Quarter Kelly (f* ÷ 4)

6.25%

Stake: ₹62,500 · conservative sizing

Kelly fractions at a glance

Full KellyHalf KellyQuarter Kelly

f* vs win rate (b = 1.50 fixed)

This is a straight line, not a bug. With b held constant, f* = (p × b − q) / b simplifies to a linear function of p — slope (b + 1) / b, intercept −1 / b.

f* lineDots = full / half / quarter at 55% win rate

f* vs reward-to-risk (win rate = 55% fixed)

Here f* curves: f* = p − (1 − p) / b, rising toward your win rate as payoff improves but never exceeding it.

f* curveDashed line = your 1.50× reward-to-risk

Your numbers plugged in

f* = (0.55 × 1.50 − 0.45) / 1.50 = 0.2500 (25.00% of bankroll)

Why half Kelly?

Full Kelly maximises long-run growth in theory but assumes you know p and b exactly. Half Kelly sacrifices some growth for materially lower volatility and drawdown risk.

What is b?

If you risk ₹1 and make ₹2 on a win (and lose ₹1 on a loss), b = 2. Average win ÷ average loss over many trades is a practical way to estimate b.

Not a mandate

Sequences of losses, estimation error, and correlated bets break the tidy maths. Use Kelly as a sanity check on position size — not as permission to lever up.

Kelly sizing is a mathematical model, not a trading mandate. Win rates and payoffs are estimates; real distributions have tails, correlation, and drawdowns. Half or quarter Kelly is often used in practice. Illustrative only — not investment advice.

Kelly position sizing explained

Kelly converts win rate and payoff ratio into a suggested risk fraction. Traders and allocators often haircut full Kelly because real edges are uncertain.

The formula

f* = (p × b − q) / b. Example: 55% win rate and 1:1 payoff (b = 1) → f* = 0.10, i.e. risk 10% of bankroll per bet in the model.

Half Kelly in practice

If full Kelly is 20%, half Kelly is 10% — materially smoother equity curve in simulation, with less growth sacrificed than you might expect.

Illustrative only — not investment advice. Past scenarios do not guarantee future results. Consult a qualified professional before investing.