#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:
#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
| Strategy | Bet Size | Growth Rate | Volatility |
|---|---|---|---|
| Full Kelly | $3,330 | 100% | High |
| Half Kelly | $1,665 | 75% | Medium |
| Quarter Kelly | $833 | 50% | Low |
| Fixed $1,000 | $1,000 | Varies | Fixed |
#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:
- Calculate edge for each
- Consider correlations
- Allocate fraction of bankroll
- 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.