Interactive growth model

Leverage & Kelly Model

Compare a chosen exposure with the growth-optimal Kelly exposure through time. A favorable expected return can still produce collapsing median wealth and near-certain ruin when exposure is excessive.

f* = [p·g − (1−p)·ℓ] / (g·ℓ)
Current period
0 / 100
Chosen exposure
1.0×
Kelly exposure
1.0×
Mean wealth · chosen
$100.00
Median wealth · chosen
$100.00
Median wealth · Kelly
$100.00
Ruin · chosen
0.00%

Wealth through time

Blue: chosen median. Orange: Kelly median. Dashed: chosen mean.

Chosen-exposure distribution

The upper 1% is clipped so typical outcomes remain visible.

Exposure versus median wealth

The curve uses the same realized win/loss histories at the current period.

Ready: Press Start to compare arithmetic expectation with compound growth.