The Kelly Criterion for Gambling

The Kelly Criterion is the mathematically optimal strategy for sizing bets to maximize long-term growth of your bankroll.

Developed by John Kelly at Bell Labs in 1956, it's used by professional gamblers, investors, and anyone managing risk under uncertainty.

But here's the catch: For most casino gambling, it tells you something you might not want to hear.

What the Kelly Criterion Is

The Formula

Kelly fraction = (bp - q) / b

Where:

• b = odds received on the bet (net odds, decimal - 1)
• p = probability of winning
• q = probability of losing (1 - p)

The result: Percentage of your bankroll to bet

Simple Example

Coin flip with edge:

• You bet $1, win $2 (1:1 odds), so b = 1
• Coin is weighted: 60% heads (your pick)
• p = 0.60, q = 0.40

Kelly = (1 × 0.60 - 0.40) / 1 = 0.20 = 20%

Optimal bet: 20% of your bankroll on each flip.

What It Optimizes

Kelly maximizes the expected geometric growth rate of your bankroll.

In plain English: It makes your money grow as fast as possible over time while avoiding ruin.

Not what it does:

• Guarantee wins
• Work for negative expectation bets
• Eliminate short-term volatility

Kelly Criterion for Casino Games

The Problem

Most casino games have negative expected value. You don't have an edge.

When p × b < q, Kelly is negative or zero.

This means: Don't bet.

Let's Calculate

Roulette (single zero):

• Bet on red: win 1x (b = 1)
• p = 18/37 = 0.486
• q = 19/37 = 0.514

Kelly = (1 × 0.486 - 0.514) / 1 = -0.028

Interpretation: Optimal bet is -2.8% of bankroll. Since you can't bet negative, Kelly says: don't bet at all.

Blackjack (basic strategy):

• House edge ~0.5%
• p ≈ 0.495, q ≈ 0.505 (simplified)

Kelly = (1 × 0.495 - 0.505) / 1 = -0.01

Interpretation: Still negative. Don't bet.

Where Kelly Works

Positive expectation situations:

• Counting cards in blackjack (when count is favorable)
• Some sports betting with information edge
• Poker (skill-based)
• Certain promotional/bonus situations

For most casino gambling, Kelly's answer is: $0

Why People Still Gamble

If Kelly says don't bet, why does anyone play?

Entertainment Value

Gambling is entertainment. People pay for entertainment.

Kelly optimizes money growth, not enjoyment.

If you're gambling for fun:

• Kelly doesn't apply
• Set entertainment budget
• Accept losses as cost of entertainment

Utility vs. Expected Value

Kelly maximizes expected log wealth. But:

• $10 loss doesn't hurt same as $100 gain helps
• Risk tolerance varies
• Non-monetary factors matter

Rational gambling can exist if utility of entertainment exceeds disutility of expected loss.

When You Have an Edge

Kelly becomes valuable when you actually have positive expectation:

• Card counting
• Sports betting with analysis edge
• Poker
• Arbitrage situations

For a deeper look at when you actually have an edge, see our advantage play guide.

Practical Kelly for Positive EV Situations

When It Applies

If you're in a positive expectation situation:

Step 1: Confirm you have an edge

• Be honest about your edge
• Most people overestimate
• Statistical verification needed

Step 2: Calculate Kelly bet

• Use the formula
• Be conservative with edge estimates

Step 3: Consider fractional Kelly

• Full Kelly is aggressive
• Half Kelly or quarter Kelly reduces volatility

Fractional Kelly

Why use less than full Kelly:

• Edge estimates are uncertain
• Variance is still high at full Kelly
• Emotional comfort matters
• Mistakes happen

Common approaches:

• Half Kelly (50%): More conservative, still strong growth
• Quarter Kelly (25%): Very conservative, much smoother
• Depends on certainty of edge estimate

Example: Sports Betting

You believe:

• True probability of Team A winning: 55%
• Odds offered: +110 (bet $100 to win $110)
• b = 1.10, p = 0.55, q = 0.45

Kelly = (1.10 × 0.55 - 0.45) / 1.10 = 0.14 = 14%

But consider:

• How confident are you in 55%?
• If true probability is 52%, Kelly = 6.5%
• If true probability is 50%, Kelly = 0%

Better approach: Use half Kelly (7%) to account for uncertainty.

Kelly Criterion Mistakes

Mistake 1: Using Kelly Without Edge

Wrong: "Kelly says bet 10% of my bankroll on roulette"

Reality: Kelly says bet 0% on roulette (negative EV)

Kelly only works for positive expectation bets.

Mistake 2: Overestimating Your Edge

Common in:

• Sports betting (thinking you know better)
• Poker (overconfidence)
• Any situation requiring judgment

Result: Betting more than optimal, increasing risk of ruin

Fix: Use fractional Kelly, be humble about edge estimates

Mistake 3: Ignoring Variance

Full Kelly:

• Maximizes growth rate
• But has high variance
• Drawdowns of 50%+ are common

If you can't handle drawdowns:

• Use fractional Kelly
• Accept slower growth for smoother ride

Mistake 4: Applying to Correlated Bets

Kelly assumes: Bets are independent

Problem: Multiple bets on same game, related markets, etc.

Result: Over-betting when bets are correlated

Mistake 5: Not Recalculating

Kelly requires: Recalculating after each bet based on new bankroll

Wrong: "I calculated Kelly yesterday, same bet today"

Right: After win/loss, recalculate based on new bankroll

For Affiliates: Why This Matters

Educating Your Audience

Understanding Kelly helps you:

• Explain bankroll management honestly
• Discuss why "systems" don't beat house edge
• Build credibility with sophisticated players
• Create educational content

Content Opportunity

Write about:

• Why betting systems don't work
• How bankroll management helps (entertainment budget)
• When Kelly actually applies (advantage play)
• Mathematical honesty builds trust

The Trust Factor

Players appreciate honesty:

• "Most casino games have house edge—Kelly says don't bet"
• "But if you're playing for entertainment, here's how to budget"
• "Here's when math CAN help" (advantage situations)

This builds more trust than fake "winning systems." Learn about the common mistakes casino affiliates make to avoid damaging your credibility.

Practical Bankroll Management

Since Kelly says "don't bet" for most gambling, what should recreational players do?

Entertainment Budget Approach

Instead of Kelly:

1. Set entertainment budget (what you can afford to lose)
2. Divide into sessions
3. Size bets to maximize entertainment time
4. Accept losses as cost of entertainment

Example:

• Monthly entertainment budget: $200
• Four casino trips: $50 each
• Bet sizing: Whatever makes sessions enjoyable
• When $50 is gone, stop

Session Length Strategy

Goal: Maximize play time for entertainment

Smaller bets = longer sessions:

• $1 slots vs $10 slots
• $5 blackjack vs $25 blackjack
• More entertainment per dollar

Not Kelly, but practical for entertainment gambling.

Loss Limits

Set in advance:

• Maximum loss per session
• Maximum loss per month
• Stop when limit reached
• No exceptions

This isn't Kelly optimization—it's harm reduction.

Advanced: Kelly for Advantage Players

Card Counting

Where Kelly actually applies:

When counting cards, you have variable edge:

• High count: positive edge, Kelly says bet more
• Low count: negative edge, Kelly says bet minimum (or nothing)

Bet spreading:

• Minimum bet at negative/neutral counts
• Increase bet proportional to edge
• Maximum at highest edges

Sports Betting with Edge

If you have genuine edge:

• Model true probabilities
• Compare to market odds
• Calculate Kelly
• Use fractional Kelly for safety

Requirement: Verifiable long-term edge (most people don't have this)

Poker

Bankroll management in poker:

• Kelly-like thinking applies
• But variance is extreme
• 20-50 buy-ins recommended
• Fractional approaches common

Conclusion

The Kelly Criterion is:

• Mathematically optimal for positive expectation bets
• A tool for professional gamblers and advantage players
• NOT a magic formula for beating casino games

For recreational gambling:

• Kelly says don't bet (negative expectation)
• Use entertainment budget approach instead
• Set limits, accept cost of entertainment

For advantage situations:

• Kelly provides optimal bet sizing framework
• Use fractional Kelly for safety
• Verify edge before applying

For affiliates:

• Understanding Kelly builds credibility
• Honest math education builds trust
• This knowledge differentiates you from "guaranteed system" promoters

The Kelly Criterion's greatest insight for most gamblers: The math says stop. If you continue anyway, at least be honest about why.

For more on how gambling math works, see our complete guide to provably fair gambling. Understanding concepts like RTP and why betting systems like Martingale fail will help you make informed decisions about when and how much to bet.