Kelly Criterion Bet Sizing: How to Calculate Your Optimal Stake

May 7, 2026 · HedgeSlider Team

The Problem Kelly Criterion Solves

You have a bankroll of $2,000. You think the Celtics are being undervalued at +105 moneyline — your model says they should be closer to -110. You want to bet, but how much?

Too small and you leave money on the table when you are right. Too large and one losing streak wipes out a big chunk of your bankroll even if your edge is real. The Kelly Criterion is a mathematical formula that answers this question exactly: given your edge and your bankroll, what is the single bet size that maximizes long-term growth?

It does not require trust in a model or an opinion. It requires two inputs — your estimated win probability and the offered odds — and it produces one output: the fraction of your bankroll to stake.

The Kelly Formula

For a standard two-outcome bet (win or lose), the Kelly Criterion is:

f = (bp - q) / b*

Where:

In words: multiply your net odds by your win probability, subtract your loss probability, then divide by the net odds.

If the result is positive, you have an edge and should bet. If the result is zero or negative, you have no edge (or negative edge) and should not bet.

Worked Example 1: Simple Moneyline Bet

Setup:

Step 1: Convert the American odds to decimal. +105 American → (105/100) + 1 = 2.05 decimal

Step 2: Calculate the net odds (b). b = 2.05 - 1 = 1.05

Step 3: Set your probabilities.

Step 4: Apply the Kelly formula. f* = (bp - q) / b = (1.05 × 0.55 - 0.45) / 1.05 = (0.5775 - 0.45) / 1.05 = 0.1275 / 1.05 = 0.1214

Step 5: Apply to your bankroll. $2,000 × 0.1214 = $242.86

The Kelly Criterion says bet approximately $243 on the Celtics.

At 55% win probability with +105 odds, you have a genuine edge, and betting $243 on a $2,000 bankroll maximizes your long-run growth rate.

To verify this quickly, use HedgeSlider's Kelly Calculator. Enter 55% win probability and +105 odds, and it returns the same 12.1% stake recommendation.

What "Edge" Actually Means

The Kelly formula only works correctly if your estimated win probability is accurate. This is harder than it sounds.

The sportsbook's moneyline implies a probability. For +105 (decimal 2.05), the sportsbook's implied probability is:

Implied probability = 1 / 2.05 = 48.8%

Your estimated win probability (55%) exceeds the sportsbook's implied probability (48.8%) by about 6.2 percentage points. That gap is your edge.

No edge = no positive Kelly stake. If your estimated probability is 48% but the line implies 48.8%, the Kelly formula returns a negative number, which means do not bet. The formula is explicit: you need genuine belief that you have an advantage, not just that you like the team.

Common mistake: Bettors use the Kelly formula but plug in the sportsbook's implied probability as their estimate. That produces f* = 0 always, because the book's odds already reflect their probability estimate. Kelly only works when your probability differs from the book's probability — and when your estimate is right more often than not.

Worked Example 2: Spread Bet at -110

Spread bets are the most common situation in US sports betting. Most close near -110, which gives the bettor a 52.4% implied win probability. To have a Kelly-positive bet, you need to believe you are winning more than 52.4% of the time.

Setup:

Step 1: Convert -110 to decimal. -110 American → 100/110 + 1 = 0.909 + 1 = 1.909 decimal

Step 2: Calculate net odds. b = 1.909 - 1 = 0.909

Step 3: Apply the formula. f* = (0.909 × 0.57 - 0.43) / 0.909 = (0.518 - 0.43) / 0.909 = 0.088 / 0.909 = 0.0968

Step 4: Apply to bankroll. $1,500 × 0.0968 = $145.20

Bet approximately $145 on Eagles -3.5.

Notice that even though you believe you win 57% of these bets (a very solid edge for spread betting), the Kelly recommendation is still only about 9.7% of your bankroll. This is intentional — Kelly is conservative when the net odds are close to even money (-110 odds pay less than you risk).

Fractional Kelly: The Real-World Approach

Full Kelly has an important weakness. If your estimated probability is even slightly wrong — by a few percentage points in either direction — the results can swing dramatically. At full Kelly, an overestimated edge can lead to bet sizes that create significant drawdowns even when you eventually come out ahead.

This is why most professional sports bettors use fractional Kelly — betting a fraction (commonly half or quarter) of what the full Kelly formula recommends.

Common fractional Kelly approaches:

Kelly Fraction Full Kelly Stake ($243) Real Stake Recommended for
Full Kelly (1.0x) $243 $243 High-confidence, verified edge
Half Kelly (0.5x) $243 × 0.5 $122 Most bettors, most situations
Quarter Kelly (0.25x) $243 × 0.25 $61 High variance props, new models
Tenth Kelly (0.1x) $243 × 0.1 $24 Futures, long-shot bets

Why fractional Kelly? The math shows that betting half Kelly produces approximately 75% of the long-run growth rate of full Kelly — but with dramatically less volatility. The cost of the reduced stake is small; the benefit of smoother returns and reduced emotional stress is significant.

The practical rule: start with half Kelly (0.5x) unless you have strong reasons to trust your probability estimate. If you are using a well-validated model with a long track record, consider moving toward full Kelly. If you are making judgment calls, stay at half or quarter Kelly.

When Kelly Produces a Stake You Should Ignore

Kelly math is only as good as your probability inputs. There are situations where you should override the formula entirely:

When your estimated probability is unreliable. If you are making a gut-call estimate ("I think there's maybe a 55% chance..."), fractional Kelly helps. But if you are truly guessing, no amount of formula application adds value. Either build a better probability model or pass on the bet.

When the Kelly stake exceeds your comfort level. The math says you should bet $243 on a $2,000 bankroll. If betting 12% of your bankroll gives you anxiety, bet less. Kelly maximizes long-run mathematical growth, not your ability to stick to a system. A smaller stake you can execute without second-guessing is better than a correct Kelly stake you deviate from under pressure.

When the bet is a future or prop. Long-shot futures (team to win championship at +1500) can produce very high Kelly stakes on seemingly small edges. At longer odds, a small probability estimation error has an outsized effect on the recommended stake. Use tenth Kelly or less for futures, regardless of the formula output.

When you are building a multi-bet portfolio. Kelly was derived for a single bet in isolation. If you are betting multiple games simultaneously, the simple Kelly formula overstates your true optimal stake because you are spreading risk across correlated events. A rough fix: sum your individual Kelly stakes and if the total exceeds 25% of your bankroll, scale all stakes down proportionally.

Tracking Your Kelly Bets Over Time

The Kelly Criterion is not useful for a single bet. It is useful over hundreds of bets — because it maximizes the rate at which your bankroll compounds when your probability estimates are accurate.

To know if your probability estimates are accurate, you need to track your results. The minimum data points to record for every Kelly bet:

  1. Your estimated win probability (p)
  2. The sportsbook's implied probability (the "market price")
  3. The Kelly stake and fraction you used
  4. The outcome (win/loss)

Over time, compare your estimated probabilities to your actual win rates. If you bet 60% on 50 plays and won 35 of them (70%), your model is underestimating your edge. If you won only 28 of 50 (56%), your model is overestimating.

HedgeSlider's Bet Tracker is the right tool for this — it logs outcomes and lets you see your closing line value (CLV) and win rate against your estimated probabilities over time. The combination of Kelly sizing (knowing how much to bet) and CLV tracking (knowing whether your edge is real) is how systematic bettors actually make money over the long run.

Connecting Kelly to Bankroll Management

Kelly bet sizing is one part of a broader bankroll management framework. A few rules that keep Kelly working in practice:

Recalculate after each significant bankroll change. Kelly stakes are a percentage of your current bankroll — not a fixed dollar amount. If your $2,000 bankroll grows to $2,400, the same 12% Kelly stake is now $288, not $243. If it drops to $1,600, the stake drops to $194. Adjust after every 5-10% change in bankroll size.

Do not withdraw Kelly stakes mid-streak. Kelly's mathematical properties assume you are always staking a percentage of your current bankroll. Withdrawing money during a good run and then continuing to stake as if your bankroll is unchanged breaks the compounding math.

Keep a separate "betting bankroll." The Kelly formula should apply to money explicitly set aside for sports betting — not your total savings. Mixing your betting bankroll with other funds makes it impossible to apply the formula correctly and creates bad incentives around chasing losses.

HedgeSlider's Bankroll Manager helps track your current bankroll, visualize your Kelly stakes as your bankroll changes, and project growth curves under different edge assumptions.

Key Takeaways