Expected Value and the Kelly Criterion

Overview

Two questions decide most repeated bets: is this bet good? (EV) and how big? (Kelly). Most professional ruin comes from positive-EV bets sized wrong. EV = p · W − q · L. If EV ≤ 0, do not bet. Kelly f* = (bp − q) / b maximizes long-term geometric growth (Kelly, Bell Labs, 1956). Full Kelly requires casino-grade certainty; default to half- or quarter-Kelly for estimated edges.

Neighbors: first-principles · occams-razor · second-order-thinking · inversion · regret-minimization (for non-repeating life decisions).

When to Use

• Decision repeats many times — capital allocation, position sizing, VC portfolio, ad spend, A/B test budget
• How big to bet matters as much as whether to bet; you have a measurable or estimable edge
• Someone says: "expected value," "EV," "Kelly," "optimal bet size," "how much should we put on this?"
• Sizing bets in a boom with power-law payoffs and possible ruin — how much to allocate to AI startups / GPU-compute capex / AI-exposed equities given frothy AI valuations, uncertain AI adoption, and correlated bets

When NOT to use: one-shot life decisions → regret-minimization; negative-EV bets (don't bet); unestimable probabilities; correlated bets without portfolio adjustment.

Coaching Novices (Adaptive Front Door)