/kelly 0.45 0.55 10000              Market price, your prob, bankroll
/kelly "Trump 2028" 0.55 --bank 10k Calculate for specific market
/kelly --half 0.45 0.55 10000       Half Kelly (safer)
/kelly --quarter 0.45 0.55 10000    Quarter Kelly (conservative)

Position Sizing

/size 10000 --risk 2%               Size for 2% risk per trade
/size 10000 --max-position 25%      Max 25% in single position
/size portfolio --rebalance         Rebalance to target weights

Edge Calculation

/edge 0.45 0.55                     Calculate edge (prob - price)
/edge "Trump 2028" --estimate 0.55  Edge vs market price

TypeScript API Reference

Create Sizing Calculator

import { createSizingCalculator } from 'clodds/sizing';

const sizing = createSizingCalculator({
  // Bankroll
  bankroll: 10000,

  // Kelly fraction (1 = full, 0.5 = half)
  kellyFraction: 0.5,

  // Limits
  maxPositionPercent: 25,
  maxTotalExposure: 80,
});

Basic Kelly

// Binary outcome (YES/NO market)
const size = sizing.kelly({
  marketPrice: 0.45,        // Current price
  estimatedProb: 0.55,      // Your probability estimate
  bankroll: 10000,
});

console.log(`Optimal bet: $${size.optimalSize}`);
console.log(`Edge: ${size.edge}%`);
console.log(`Kelly %: ${size.kellyPercent}%`);
console.log(`Expected value: $${size.expectedValue}`);

Fractional Kelly

// Half Kelly (recommended for most traders)
const halfKelly = sizing.kelly({
  marketPrice: 0.45,
  estimatedProb: 0.55,
  bankroll: 10000,
  fraction: 0.5,  // Half Kelly
});

// Quarter Kelly (very conservative)
const quarterKelly = sizing.kelly({
  marketPrice: 0.45,
  estimatedProb: 0.55,
  bankroll: 10000,
  fraction: 0.25,
});

console.log(`Full Kelly: $${sizing.kelly({...}).optimalSize}`);
console.log(`Half Kelly: $${halfKelly.optimalSize}`);
console.log(`Quarter Kelly: $${quarterKelly.optimalSize}`);

Multi-Outcome Kelly

// For markets with 3+ outcomes
const multiKelly = sizing.kellyMultiOutcome({
  outcomes: [
    { name: 'Trump', price: 0.35, estimatedProb: 0.40 },
    { name: 'DeSantis', price: 0.25, estimatedProb: 0.20 },
    { name: 'Haley', price: 0.15, estimatedProb: 0.15 },
    { name: 'Other', price: 0.25, estimatedProb: 0.25 },
  ],
  bankroll: 10000,
  fraction: 0.5,
});

for (const alloc of multiKelly.allocations) {
  console.log(`${alloc.name}: $${alloc.size} (${alloc.percent}%)`);
}

Portfolio-Level Kelly

// Optimal allocation across multiple markets
const portfolio = sizing.kellyPortfolio({
  positions: [
    { market: 'Trump 2028', price: 0.45, prob: 0.55 },
    { market: 'Fed Rate Cut', price: 0.60, prob: 0.70 },
    { market: 'BTC > 100k', price: 0.30, prob: 0.40 },
  ],
  bankroll: 10000,
  correlations: correlationMatrix,  // Optional
  fraction: 0.5,
});

console.log('Optimal Portfolio:');
for (const pos of portfolio.positions) {
  console.log(`  ${pos.market}: $${pos.size}`);
}
console.log(`Total exposure: ${portfolio.totalExposure}%`);

Confidence-Adjusted Sizing

// Reduce size when less confident
const size = sizing.kellyWithConfidence({
  marketPrice: 0.45,
  estimatedProb: 0.55,
  confidence: 0.7,  // 70% confident in estimate
  bankroll: 10000,
});

// Size is reduced proportionally to confidence
console.log(`Confidence-adjusted size: $${size.optimalSize}`);

Edge Calculation

// Calculate edge
const edge = sizing.calculateEdge({
  marketPrice: 0.45,
  estimatedProb: 0.55,
});

console.log(`Edge: ${edge.edgePercent}%`);
console.log(`EV per dollar: $${edge.evPerDollar}`);
console.log(`Implied odds: ${edge.impliedOdds}`);
console.log(`True odds: ${edge.trueOdds}`);

Risk-Based Sizing

// Size based on risk per trade
const size = sizing.riskBased({
  bankroll: 10000,
  riskPercent: 2,     // Risk 2% per trade
  stopLossPercent: 10, // 10% stop loss
});

console.log(`Position size: $${size.positionSize}`);
console.log(`Max loss: $${size.maxLoss}`);

Kelly Fractions

Fraction	Risk Level	Use Case
Full (1.0)	Aggressive	Mathematical optimum, high variance
Half (0.5)	Moderate	Most traders, good balance
Quarter (0.25)	Conservative	New traders, uncertain edges
Tenth (0.1)	Very Safe	Learning, small edges

Edge Requirements

Edge	Recommendation
< 2%	Don't trade
2-5%	Small size (quarter Kelly)
5-10%	Normal size (half Kelly)
10%+	Larger size, verify edge

Formulas

Kelly Formula

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

Where:
f* = fraction of bankroll to bet
p = probability of winning
q = probability of losing (1 - p)
b = odds received (1/price - 1)

Edge Formula

Edge = Estimated Prob - Market Price
EV = Edge * Bet Size

Best Practices

Use fractional Kelly — Full Kelly has too much variance
Be conservative on edge — Overconfidence kills accounts
Account for correlation — Don't over-expose to same theme
Set max position — Never more than 25% in one market
Reassess regularly — Edge changes as prices move