Kelly Criterion Position Size

Calculates the mathematically optimal fraction of capital to risk on a trade based on win probability and payout ratio, maximizing long-run growth.

Written by the Vorzep Team

CryptoTradingRisk Management

Kelly Criterion Calculator Optimal Position Sizing

f* = (b · p – q) / b

f* = Kelly fraction (position size) · b = net odds received · p = probability of winning · q = probability of losing (1 – p)

⟹ Solve ⟷ f*, b, p, q

Net Odds (b)

Win Prob (p)

Loss Prob (q)

Kelly Fraction (f*)

Please fix the errors above.

Solve for: Kelly Fraction (f*) Net Odds (b) Win Prob (p) Loss Prob (q)

Presets:

Kelly Fraction —

—

f*: — b: — p: — q: —

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Kelly Position Size Gauge —

Negative EV (< 0) Conservative (0 – 25%) Aggressive (25% – 50%) High Risk (> 50%)

f* = (b · p – q) / b · Kelly Criterion maximizes the expected logarithm of wealth.

f* = (bp - q) / b

Kelly Criterion Position Size

Variables

Symbol	Quantity	Unit
f*	Optimal fraction of capital to risk
b	Net odds received (payout ratio)
p	Probability of winning
q	Probability of losing (1-p)

What it means

The Kelly criterion is a formula for position sizing that maximises the expected growth of capital. It uses the probability of winning (p), the probability of losing (q=1−p), and the odds (b = profit/loss ratio). It is used to determine the optimal fraction of capital to bet. Understanding this helps traders manage risk and maximise long‑term growth. However, many use a fractional Kelly to reduce risk.

Worked example

Kelly Criterion – Two Detailed Examples

Real‑World

Scenario: A trader has a win probability of 55% (p) and a payout ratio of 1.5 (b). The Kelly fraction f* = (bp - q) / b, where q = 1 - p = 0.45. f* = (1.5 × 0.55 - 0.45) / 1.5 = (0.825 - 0.45) / 1.5 = 0.375 / 1.5 = 0.25. This means they should bet 25% of their capital on each trade to maximise long‑term growth. Most traders use a fraction of Kelly to reduce risk.

Parameter	Value
Win Probability (p)	0.55
Payout Ratio (b)	1.5

1q = 1 - 0.55 = 0.45

2f* = (1.5 × 0.55 - 0.45) / 1.5 = (0.825 - 0.45) / 1.5 = 0.25

Result 0.25 ✓ 25% allocation

Scenario: A trade has a 60% win probability and even money payout (b=1). f* = (1 × 0.60 - 0.40) / 1 = 0.20. This suggests betting 20% of capital. However, many traders use half‑Kelly (10%) to reduce risk. The Kelly criterion helps optimise position sizing for long‑term capital growth.

Parameter	Value
p	0.60
b	1.0

1q = 0.40

2f* = (1 × 0.60 - 0.40) / 1 = 0.20

Result 0.20 ✓ 20% Kelly

Insight: The Kelly criterion calculates the optimal fraction of capital to bet to maximise growth. In practice, traders often use a fraction of Kelly (e.g., half) to reduce volatility.

Common mistakes

Kelly criterion: Determines optimal bet size to maximise growth.
b: Net odds (profit per unit stake).
p: Probability of winning.
q: Probability of losing (1−p).
f*: The fraction of capital to wager.
Fractional Kelly: Many use a fraction of the Kelly stake to reduce risk.

Applications

Kelly Criterion position size calculates the optimal fraction of capital to bet on a trade, based on the win probability and win/loss ratio. This maximises the expected growth rate of capital. Traders use it to size positions systematically, balancing risk and reward. While aggressive, it helps avoid ruin. Understanding the Kelly criterion is valuable for disciplined traders and investors.

Determining optimal position size for trading systems
Maximising long‑term capital growth
Risk management and avoiding over‑betting
Evaluating the edge of a trading strategy
Educational understanding of optimal betting