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