There is an actual answer to "how much should I bet?" It came out of Bell Labs in 1956, when John L. Kelly Jr. showed that a gambler with a real edge maximizes long-run growth by betting a specific, computable fraction of capital — no more, no less. The paper — "A New Interpretation of Information Rate" (free PDF) — is one of the few pieces of trading-adjacent math with an unimpeachable pedigree. This lesson teaches what it says, and — more importantly — the two ways it bites people who only learn half of it.
The formula, for the simple case
Kelly's insight is that this fraction maximizes the growth rate of wealth over many bets. Bet less and you grow slower; bet more and — this is the counterintuitive part — you also grow slower, because volatility drag eats the extra aggression. Bet double Kelly and your long-run growth is approximately zero; beyond that, ruin becomes near-certain even with a genuine edge. Over-betting a winning system loses money. That single sentence justifies this whole course.
Why professionals bet a fraction of Kelly
Ed Thorp — the man who took Kelly from blackjack to the markets, and whose profile is worth your time — spent decades on the practical problem, and practice converges on fractional Kelly (a half or a quarter of f*), for three honest reasons. First, you don't know your true p and b — you estimated them from a sample (Lesson 2), and Kelly is brutally sensitive to optimistic errors: overestimating your edge means systematically over-betting. Second, full Kelly's drawdowns are savage — extended 50%+ drawdowns are a mathematical feature, not bad luck, and Lesson 1 showed what those cost. Third, real markets aren't independent coin flips — correlated positions, changing regimes, and gap risk all violate the model's assumptions in the dangerous direction. Institutional practice (Pedersen's Efficiently Inefficient is a good source on this from the hedge-fund side) treats Kelly as an upper bound, never a target.
What Kelly teaches even if you never compute it
Notice where the everyday rules land: a 1–2% fixed fraction is, for most realistic retail edges, comfortably below the Kelly fraction — which is exactly where you want to live given estimation error. So the framework's real gifts are directional: bet size should scale with edge (bigger when your advantage is genuinely bigger — Lesson 5 takes this practical); bet size should shrink with uncertainty (new system, new regime, thin sample → smaller); and there is always a size that is too big even when you're right. Kelly is the mathematical spine behind every seasoned trader's instinct that survival and compounding are the same subject.
Assignment
Using your Lesson 2 numbers (win%, payoff ratio), compute your f*. Compare it to what you actually risk. If your risk is above half-Kelly, you are trusting a 20-trade estimate with career-level stakes — re-read Lesson 1. If it's far below, note that too: the gap is your growth left on the table, and closing it responsibly is Lesson 5.