Tools

Quarter, Half, Full Kelly

Why fractional Kelly. Bankroll-growth simulation and drawdown comparison.

What is the Kelly criterion?

John Kelly Jr.'s 1956 paper A New Interpretation of Information Rate derived the optimal bet size for repeated wagers with known probabilities. The result is striking in its simplicity: bet a fraction of your bankroll proportional to your edge, divided by the odds.

Bet too small and your bankroll grows slowly. Bet too large and you compound losses faster than gains. The Kelly fraction sits at the inflection point — the unique bet size that maximizes expected log-growth, which is equivalent to maximizing geometric mean wealth over many bets.

Read the full methodology →

Why fractional Kelly?

Full Kelly is mathematically optimal only when you know the true probability with certainty. In practice, every fair-value model has noise. If you over-estimate your edge by even 30%, full Kelly leads to severe overbetting — and overbetting at Kelly is asymmetrically painful, because expected log-growth is concave around the optimum.

MacLean & Ziemba (1992) made this explicit: Growth Versus Security in Dynamic Investment Analysis showed that fractional Kelly trades a small reduction in expected growth for an outsized reduction in drawdown variance. The closer your edge estimate is to noise, the more aggressively you should fractionalize.

Quarter-Kelly is the conservative-but-not-paranoid default in professional sports betting and quant trading. It captures roughly 75% of the expected log-growth of full Kelly while cutting drawdown risk by approximately a factor of 4.

Bankroll growth — 1,000 bets at 55% / even money

Median trajectory (solid) and 5th-percentile drawdown (dashed) across 200 simulated trials. Y-axis is log-scaled.

0.10x1x10x100x02505007501000bets
Full Kelly
Median final
273.2x
5th-pct drawdown
0.99x
Half Kelly
Median final
57.6x
5th-pct drawdown
3.49x
Quarter Kelly
Median final
10.4x
5th-pct drawdown
2.55x

Simulation: 1,000 sequential bets at fair probability 55%, even-money payout (decimal 2.0). 200 trials per fraction, mulberry32-seeded for reproducibility. The medians show order-of- magnitude differences, but pay attention to the dashed 5th-percentile lines — Full Kelly's worst-case path drops below half Kelly's by an order of magnitude.

Which should you use?

  • Quarter-Kelly — the BaseCase default. Right when your edge estimate carries any meaningful uncertainty (which is approximately always).
  • Half-Kelly — defensible when you have very high confidence in your edge estimate (e.g., a market-validated arbitrage or sharp cross-book confirmation).
  • Full Kelly — almost never appropriate for retail bettors. Primarily useful as a theoretical anchor and as the input to fractionalize.

BaseCase additionally caps Kelly per-game (not per-bet) to prevent correlated overexposure when multiple +EV opportunities exist on the same event. The Edge Finder displays both raw quarter-Kelly and the post-cap value.

Try it live

Plug in your own edge and odds. Toggle between Full, Half, and Quarter to see the trade-off in stake size:

Inputs

%

Your or BaseCase's de-vigged estimate

$
Kelly fraction

BaseCase defaults to quarter-Kelly for variance reduction.

Results

Quarter-Kelly stake
$352.27
3.52% of bankroll
Full Kelly fraction
14.09%
Theoretical maximum
Expected value
+15.50%
Per dollar wagered
Edge
+7.38 pp