Quick answer: The Kelly Criterion tells you what fraction of your bankroll to stake for maximum long-term growth: f* = (bp − q) / b, where b is net odds, p your win probability and q your loss probability. With a real edge, full Kelly maximizes growth — but because overbetting shrinks growth and estimates are never exact, most professionals stake ¼ to ½ of Kelly instead. For a typical poker or sports edge that means risking roughly 2–10% of your bankroll per play, not 25%+. Compute yours instantly with our Kelly Criterion Calculator.

What Is a Bankroll (and Why Poker Players Need One)?

Your bankroll is the total money you have set aside for playing — separate from rent, savings, and everything else. In games with variance (and poker is nothing but variance), the bankroll is what keeps a losing streak from ending your career:

• Cash game players traditionally hold 20–40 buy-ins for their stakes
• Tournament players need far more — often 100+ buy-ins — because fields are huge and cashes lumpy
• Sports bettors think in units: 1 unit = 1–2% of bankroll

The Kelly Criterion is the mathematical engine underneath all these rules of thumb: it formalizes exactly how big each bet should be given your edge and the odds.

In 1956, a physicist named John Kelly published a paper that would revolutionize gambling and investing. His formula answers a simple question: "What percentage of my bankroll should I bet to grow it as fast as possible without going broke?"

The answer — the Kelly Criterion — is used today by professional poker players, sports bettors, hedge fund managers, and even Warren Buffett.

The Kelly Criterion Formula

$$f^* = \frac{bp - q}{b}$$

Where:

• f* = fraction of bankroll to bet
• b = decimal odds - 1 (the net odds received)
• p = probability of winning
• q = probability of losing (1 - p)

Example: You have a 60% chance of winning a bet at 2.00 decimal odds (even money):

$$f^* = \frac{1 \times 0.60 - 0.40}{1} = \frac{0.20}{1} = 0.20$$

Bet 20% of your bankroll.

Why Kelly Works: The Growth Rate

The Kelly Criterion maximizes the expected logarithm of wealth:

$$G = p \cdot \ln(1 + f \cdot b) + q \cdot \ln(1 - f)$$

This might look complex, but the intuition is simple: Kelly balances growth and survival. Betting too little leaves money on the table. Betting too much risks ruin.

Key insight: Betting more than Kelly reduces long-term growth. This is counterintuitive but mathematically proven.

Practical Example: Poker Tournament

You're in a poker tournament with a $1,000 bankroll. You identify a spot where you have 55% equity at 2.00 odds:

$$f^* = \frac{1 \times 0.55 - 0.45}{1} = 0.10$$

Full Kelly says bet 10% ($100). But in practice, most pros use Half Kelly — bet 5% ($50). This cuts variance in half while sacrificing only 25% of growth.

Kelly in Sports Betting

For sports betting, Kelly is particularly powerful because it accounts for both your edge AND the odds offered:

Example: You estimate a team has a 45% chance of winning at 2.50 odds (so b = 1.50):

$$f^* = \frac{1.50 \times 0.45 - 0.55}{1.50} = \frac{0.125}{1.50} \approx 0.083$$

Bet about 8% of your bankroll. Note how small the stake is even for a genuine edge — this is normal and correct. If your probability estimate is off by even a few points, full Kelly quietly turns from optimal into reckless, which is another reason pros default to half of whatever the formula says.

Walkthrough: Calculating Your Stake with Our Calculator

1. Open the Kelly Criterion Calculator
2. Enter the odds you're getting (decimal format)
3. Enter your estimated win probability — be honest, not optimistic
4. Read the full Kelly output, then apply a fraction multiplier of 0.25–0.5
5. Recalculate whenever your bankroll changes size

Worked example: $500 bankroll, you estimate 55% equity at even money (2.00): full Kelly says (1×0.55 − 0.45)/1 = 10%, i.e. $50. At Half Kelly you stake $25. Lose three in a row? Your bankroll is $437.50, and the next calculation automatically stakes slightly less — that self-correcting behavior is the whole point.

Common Mistakes

1. Overestimating your edge. If you think you have 60% equity but actually have 50%, full Kelly will destroy your bankroll. Always be conservative.

2. Using full Kelly. The variance is brutal. Even with a genuine edge, you'll face long losing streaks. Use Half Kelly or Quarter Kelly.

3. Ignoring bankroll changes. Recalculate after every session. If your bankroll drops 20%, your Kelly bet should drop 20% too.

4. Applying Kelly to correlated bets. Kelly assumes independent bets. Don't apply it to multiple bets on the same game.

Try It Now

Use our Kelly Criterion Calculator to calculate optimal bet sizes for any scenario.

Use the Expected Value Calculator to determine your edge before applying Kelly.

Related Tools & Resources

• Kelly Criterion Calculator — Optimal bet sizing tool
• Expected Value Calculator — Calculate your edge
• Is This Bet +EV? — Quick EV checker
• Bankroll Management Guide — Bankroll strategy
• What is Expected Value (EV)? — EV fundamentals