Expected Value: The Complete Guide
Expected value is the single most important concept in gambling mathematics. It tells you exactly how much you can expect to win or lose per bet over time.
The Formula
A Simple Example
You bet $10 on heads. Win $10 if heads, lose $10 if tails.
EV = (0.5 × $10) - (0.5 × $10) = $5 - $5 = $0
This is a "fair" bet with zero expected value.
Why Casinos Always Win
Every casino game is designed to have negative expected value for the player. Roulette, slots, blackjack without card counting—all negative EV. The house edge is simply the negative EV expressed as a percentage of your bet.
Finding Positive EV
Positive expected value exists in a few places: full-pay video poker with perfect strategy, blackjack with card counting, poker against weaker opponents, and promotional situations where casinos offer better-than-usual odds.
Everything else is entertainment, not investment.