Expected Value Explained in 2 Minutes

Expected Value Explained in 2 Minutes

Expected Value (EV) is the secret weapon that separates professional gamblers from recreational players. It's a simple calculation that tells you exactly how much you can expect to win or lose on any bet over time.

The Formula

EV = (Probability of Winning × Amount Won) - (Probability of Losing × Amount Lost)

That's it. Let's see it in action.

Example 1: Coin Flip Bet

Your friend offers you a bet: Flip a coin. Heads, you win $10. Tails, you lose $10.

- Probability of winning: 50% (0.5)

- Amount won: $10

- Probability of losing: 50% (0.5)

- Amount lost: $10

EV = (0.5 × $10) - (0.5 × $10) = $5 - $5 = $0

This is a neutral bet. Over time, you break even. Not good, not bad.

Example 2: Roulette Red/Black

Betting $10 on red in American roulette:

- Probability of winning: 18/38 (47.37%)

- Amount won: $10

- Probability of losing: 20/38 (52.63%)

- Amount lost: $10

EV = (0.4737 × $10) - (0.5263 × $10) = $4.74 - $5.26 = -$0.52

You lose an average of $0.52 per bet. Do this 1,000 times and you'll lose about $520. This is the house edge in action.

Example 3: A Good Bet

Your friend is drunk and offers you this: Flip a coin. Heads, you win $20. Tails, you lose $10.

EV = (0.5 × $20) - (0.5 × $10) = $10 - $5 = +$5

This is a positive EV bet! On average, you make $5 every flip. You should take this bet all day long.

Why This Matters

Every casino game has negative expected value for the player. That's how casinos make money. The games aren't rigged - they're just mathematically designed so the EV is negative for you and positive for them.

Understanding EV helps you:

- Identify which casino games are "less bad" (blackjack vs. slots)

- Spot sucker bets (insurance in blackjack, tie bets in baccarat)

- Know when to walk away (when any bet has negative EV and you're playing for fun with a budget)

The Golden Rule

If the expected value is negative, you're paying for entertainment, not investing. There's nothing wrong with that - just know the difference. Positive EV opportunities are rare and should be exploited when found.

Use our simulator to calculate expected value for different betting strategies. You'll quickly see why the house always wins in the long run.