Expected Value as a Decision Lens

## The Master Mental Model Expected value (EV) is the single most important mental model for betting decisions. Every other framework ultimately serves to produce a more accurate EV estimate. EV = P(win) × Net profit + P(lose) × Net loss A positive EV bet: expected to profit long-run. A negative EV bet: expected to lose long-run. ## Thinking in Expected Value, Not Outcomes The fundamental mental shift: evaluate every bet not by "will this win?" but by "what is the expected value of this decision?" A bet at 3.00 with a 40% win probability: EV = 0.40 × 2 + 0.60 × (−1) = 0.80 − 0.60 = +0.20 per unit This bet has positive EV. It will lose 60% of the time. The outcome does not determine whether the bet was correct — the EV estimate does. ## Separating Decision Quality from Outcome Once EV thinking is internalised, losing bets no longer feel like failures. A well-reasoned bet with positive EV that loses is a correct decision with an unfavourable outcome. The decision is evaluated on the EV, not the outcome. This separation is psychologically challenging but essential. It prevents the feedback loop where losing bets lead to process changes regardless of whether the analysis was correct. ## Applying EV Consistently Extend EV thinking beyond individual bets: - Should I cash out now? EV of holding vs EV of cash out - Should I add this new market? Expected EV from this market vs opportunity cost - Should I take this large stake? Expected value of 3× stake vs 1× stake given my edge estimate and variance Every significant betting decision can be framed as an EV comparison between alternatives.