Reno, 1961: Thorp used card counting to compute his edge, then the Kelly formula to size the bet — doubling his stake in 72 hours, the first time anyone beat a commercial casino with mathematics.
Blackjack is the cleanest Kelly setting: when the shoe is rich in high cards the player has an edge (p>0.5). Counting gives the live win probability p and odds b; Kelly gives the fraction f* to bet. Bigger edge, bigger bet; zero edge, no bet.
Binary Kelly · how much to bettypescript
// f* = (b·p − q)/b, q = 1−p
export function binaryKelly(p: number, b: number): number {
const q = 1 - p;
return (b * p - q) / b;
}
// A 2% edge (p=0.51, b=1) → Kelly bets just 2% of capital. Restraint is what winning looks like.
◆Thorp's rule
"Use Kelly, but half-Kelly or less — because you always overestimate your edge."