Kelly Log Growth
Compare expected logarithmic growth across fractions of a hypothetical repeated binary wager.
Free theory articleCompare expected logarithmic growth across fractions of a hypothetical repeated binary wager.
Concept & interpretation
Select Win probability = 0.75 and Net win odds b = 1. A win multiplies the current size by 1 + f, while a loss multiplies it by 1 - f. Compare the selectable fractions 1/4 and 1/2 using natural logarithms:
Interactive Experiment
The Kelly Log Growth module allows you to explore the concave growth curve by varying the hypothetical win probability, the net win odds, and the staked fraction.
- Set Win probability to 0.75, and Net win odds b to 1. Notice the continuous optimal fraction f* updates to 0.5.
- Select a Staked fraction f of 1. With Win probability still 0.75, Expected Log Growth displays Negative infinity: a loss has positive probability and its multiplier is zero.