kelly-stake

kelly-stake

Kelly criterion position sizing and bankroll risk management for betting and trading.

• Zero runtime dependencies — pure, deterministic math.
• No install scripts — nothing runs on npm install.
• TypeScript-first — ships type declarations.
• Guard rails built in: fractional Kelly, bankroll-fraction caps, min/max stake clamps, and never a negative stake.

Install

npm install kelly-stake

Quick start

import { kellyStake, kellyStakeFromReturns } from "kelly-stake";

// Size a bet from a known edge (60% win chance, even money), half-Kelly:
const stake = kellyStake(
  { winProbability: 0.6, payoffRatio: 1 },
  { bankroll: 1000, fraction: 0.5, maxFraction: 0.2 }
);
// -> 100  (raw f*=0.2, half-Kelly=0.1, 10% of 1000)

// Or estimate the edge from realised per-trade returns and size directly:
const returns = [1.0, 1.0, -0.5, -0.5]; // +100%, +100%, -50%, -50%
const next = kellyStakeFromReturns(returns, { bankroll: 1000, fraction: 0.5 });

The formula

f* = p - (1 - p) / b

• p — win probability, 0..1
• b — net payoff ratio (units won per unit staked on a win)

A negative f* means no edge → stake 0. Full Kelly maximises long-run growth but is volatile and unforgiving of estimation error, so prefer fractional Kelly (fraction: 0.5 is common) with a hard maxFraction cap.

API

Function	Purpose
kellyFraction(winProbability, payoffRatio)	Raw Kelly fraction f*, clamped >= 0.
kellyFractionFromDecimalOdds(winProbability, decimalOdds)	Kelly from decimal odds (stake-inclusive payout).
fractionalKelly(kelly, fraction)	Apply a fractional-Kelly multiplier.
kellyStake(bet, options)	Concrete stake with fractional Kelly, caps and clamps.
edgeFromReturns(returns)	Estimate { winProbability, payoffRatio, sampleSize } from realised returns.
kellyStakeFromReturns(returns, options)	Estimate the edge, then size the stake.

StakeOptions

Option	Default	Meaning
bankroll	—	Total bankroll to size against (required).
fraction	1	Fractional-Kelly multiplier, 0..1.
maxFraction	1	Cap on the bankroll fraction per stake, 0..1.
minStake	0	Floor for any non-zero stake.
maxStake	Infinity	Ceiling for any stake.

Disclaimer

The Kelly criterion assumes accurate estimates of win probability and payoff. Real edges are uncertain — under-betting (fractional Kelly) is far safer than over-betting. This library is provided for educational purposes and is not financial advice.

License

MIT