You've got a coin that's biased in your favor, a sports bet with real value, or a stock pick you're confident in — so how much do you actually risk? Bet too little and you leave money on the table. Bet too much, and even a winning edge can wipe you out. This TLDR primer walks through the Kelly Criterion, the formula professional gamblers and quant investors use to answer exactly that question.

Starting from a simple biased coin flip, the book derives the Kelly formula $f^{\ast }=(bp-q)/b$ step by step, showing why maximizing expected log wealth — not expected wealth — is the right goal when you're betting the same bankroll over and over. From there it works through concrete cases: a sports moneyline, a card-counted blackjack hand, and a simulated bankroll growing (and shrinking) under different bet sizes. A full section is devoted to what happens when you over-bet — the volatility explosion and eventual ruin that full Kelly can cause once your estimate of your edge is even slightly wrong — and why real practitioners run half- or quarter-Kelly instead. The final section extends the idea past the casino, into stock portfolios and everyday decisions made under uncertainty.

Written for high school and early-college students who want the math made concrete with numbers, not buried in theory. No filler, no hand-waving — just the derivation, the worked examples, and the intuition you need to explain (or use) the Kelly Criterion with confidence. Parents and tutors looking for a clean explanation of optimal bet sizing math will find this useful too.

Open it, work the examples, and walk into your next stats class or poker night knowing exactly why doubling down is a losing strategy in the long run.