Kelly Criterion

#Definition

The Kelly Criterion is a bankroll sizing rule that maximizes long-run growth when you have a known edge; can be scaled (e.g., half‑Kelly).

#The Formula

For a binary bet with win probability p and odds b:1:

Kelly % = (bp - q) / b

Where:

• p = probability of winning
• q = probability of losing (1 - p)
• b = odds received (payout ÷ stake)

#Prediction Market Version

For prediction markets where contracts pay $1:

Kelly % = (p - price) / (1 - price)

Where:

• p = your estimated probability
• price = current Yes contract price

#Example

Market: "Will it rain tomorrow?"

• Market price: $0.40 (40%)
• Your estimate: 60% (p = 0.60)
• Edge: 0.60 - 0.40 = 0.20 (20%)

Kelly calculation:

Kelly % = (0.60 - 0.40) / (1 - 0.40)
Kelly % = 0.20 / 0.60
Kelly % = 0.333 (33.3%)

Action: Bet 33.3% of your bankroll

Quick Kelly Calculator: Edge / Odds = Kelly %. For binary markets (Odds = 1/Price - 1): (Probability - Price) / (1 - Price)

#Why Kelly Works

#Maximizes Growth

• Optimal between too aggressive and too conservative
• Grows bankroll fastest in long run
• Mathematically proven optimal

#Prevents Ruin

• Never bets entire bankroll
• Scales with edge and confidence
• Built-in risk management

#Compound Growth

• Winners compound
• Losers don't destroy bankroll
• Long-term wealth maximization

#Kelly Fractions

#Full Kelly (1.0x)

• Most aggressive
• Maximum growth rate
• Highest volatility
• Can feel scary

#Half Kelly (0.5x)

• Most popular
• 75% of full Kelly growth
• Much lower volatility
• Better sleep at night

#Quarter Kelly (0.25x)

• Conservative
• ~50% of full Kelly growth
• Very stable
• Good for beginners

#Example Comparison

Scenario: 60% edge, $10,000 bankroll

#Practical Application

#Step 1: Estimate Probability

Your independent analysis:

True probability = 65%

#Step 2: Check Market Price

Current Yes price:

Market price = $0.45 (45%)

#Step 3: Calculate Edge

Edge = 0.65 - 0.45 = 0.20 (20% edge)

#Step 4: Calculate Kelly

Kelly % = (0.65 - 0.45) / (1 - 0.45)
Kelly % = 0.20 / 0.55
Kelly % = 0.364 (36.4%)

#Step 5: Apply Fraction

Using Half Kelly:

Half Kelly = 0.364 / 2 = 0.182 (18.2%)

#Step 6: Size Position

With $10,000 bankroll:

Bet = $10,000 × 0.182 = $1,820

#Common Mistakes

#Overestimating Edge

• Thinking you have 20% edge when really 5%
• Results in overbetting
• Solution: Be conservative with estimates

#Ignoring Correlation

• Kelly assumes independent bets
• Correlated markets need adjustment
• Solution: Reduce size for correlated positions

#Using Full Kelly

• Too aggressive for most
• High drawdowns
• Solution: Use fractional Kelly

#Not Updating

• Edge changes as prices move
• Need to recalculate
• Solution: Dynamic position sizing

#When Kelly Doesn't Apply

#Unknown Probabilities

• Can't calculate edge accurately
• Garbage in, garbage out
• Alternative: Conservative sizing

#Few Bets

• Kelly optimizes long-run
• Short-term variance high
• Alternative: Fixed sizing for one-offs

#Liquidity Constraints

• Can't easily exit
• Position limits
• Alternative: Reduce to fit constraints

#Emotional Tolerance

• Can't handle volatility
• Stress affects decisions
• Alternative: Use smaller fraction

#Kelly for Multiple Markets

#Portfolio Kelly

When trading multiple markets:

1. Calculate edge for each
2. Consider correlations
3. Allocate fraction of bankroll
4. Rebalance as edges change

#Correlation Adjustment

• Reduce Kelly fraction for correlated bets
• Sum of positions should be less than Kelly
• More diversification = closer to full Kelly

#Advanced: Growth vs Risk

#Growth Rate Formula

Growth Rate = r × (1 - σ²/2r²)

Where:

• r = edge × bet fraction
• σ = standard deviation

#Optimal Trade-off

• Full Kelly maximizes growth
• Half Kelly = 75% growth, 50% variance
• Sweet spot for most traders

#Historical Performance

#Simulations Show

• Kelly outperforms fixed sizing
• Half-Kelly beats Full Kelly risk-adjusted
• Quarter-Kelly stable but slower
• Over-Kelly leads to ruin eventually

#Kelly Growth Curve

#Fractional Kelly: The Safer Approach

Because full Kelly betting is extremely volatile (and can wipe you out if your edge is slightly overestimated), most professional traders use Fractional Kelly.

• Half Kelly: Bet 50% of what the formula says.
• Quarter Kelly: Bet 25% of what the formula says.

This drastically reduces volatility while still providing significant geometric growth.

Warning: Never bet more than Full Kelly. Betting more than the Kelly amount actually decreases your long-term growth rate while increasing risk.

#Related Terms

• Expected Value
• Risk Management
• Position Limits