The Kelly criterion and fractional Kelly

The 1-2% rule is a robust default. The Kelly criterion is a more precise tool that asks: given my edge, what fraction of capital maximises long-run growth? It is powerful — and dangerous if used literally.

The formula

For a bet that wins amount b per unit risked, with win probability p (and loss probability q = 1 - p):

Kelly fraction f = (b x p - q) / b

Read b as your reward-to-risk ratio — win US$2 for every US$1 risked means b = 2.

A worked example

Win probability p = 0.55   (you win 55% of trades)
Loss probability q = 0.45
Reward-to-risk b   = 2      (winners pay twice what losers cost)

f = (2 x 0.55 - 0.45) / 2
  = (1.10 - 0.45) / 2
  = 0.65 / 2
  = 0.325

Full Kelly says risk 32.5% of the account on this trade. That number should alarm you — and it should.

Why nobody trades full Kelly

Full Kelly maximises theoretical growth but produces savage drawdowns — swings of 50% or more are normal — and it assumes you know p and b exactly. You never do. Overestimate your edge even slightly and full Kelly tips you straight toward ruin. It is mathematically optimal and practically reckless.

Fractional Kelly

The standard fix is to trade a fraction of Kelly — commonly a half or a quarter:

Half Kelly  = 0.325 / 2 = 0.1625  (about 16%)
Quarter Kelly = 0.325 / 4 = 0.081  (about 8%)

Even quarter Kelly here (8%) is far above the 1-2% rule — which tells you how optimistic the inputs were, or how conservative the fixed-fractional rule is by design. Use Kelly to understand that bigger edges justify bigger size, then size well below what it suggests. The 1-2% rule is, in effect, deep-fractional Kelly with a wide safety margin baked in.