You have an edge — now how much do you bet? Too little and you barely grow; too much and one bad run wipes you out. The KELLY CRITERION gives the exact fraction that maximizes long-run growth: f* = edge / odds. Bet more than Kelly and growth actually FALLS while risk soars; bet the negative-edge side and Kelly says bet nothing. Slide your edge and read the optimal stake.
The Kelly criterion maximizes the expected LOGARITHM of wealth (hence long-run growth rate). For a bet at odds b-to-1 with win probability p (q=1−p), the optimal fraction is f* = (bp − q)/b = p − q/b; on even money (b=1) that is 2p−1, the edge itself. If the edge is ≤ 0, f* ≤ 0 → bet nothing. Betting more than f* lowers growth and raises ruin risk (over-betting is punished harder than under-betting). A fail-loud self-check throws unless p=0.6 at even odds gives f*=0.2 and p=0.4 gives 0. ◆ real probability, node-verified.
Full Kelly maximizes growth but tolerates wild swings; many practitioners bet ‘half-Kelly’ for smoother rides. It assumes a known, fixed edge — misestimate the edge and you over-bet, which Kelly punishes sharply.