Riding a Heater

What is Expected Value?

Expected Value (EV) is the average amount you expect to win or lose per bet if you made the same bet an infinite number of times. It's the single most important concept in gambling mathematics.

The Formula

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

Sports Betting EV

Example: Standard -110 Bet

Risk: $110 to win $100
If your true win probability is 53%:
EV = (0.53 × $100) - (0.47 × $110) = $53 - $51.70 = +$1.30 per bet

Example: Underdog at +200

Risk: $100 to win $200
If true win probability is 38%:
EV = (0.38 × $200) - (0.62 × $100) = $76 - $62 = +$14 per bet

Casino Game EV

Roulette (American, betting red)

Win: $100 (probability: 18/38 = 47.37%)
Lose: $100 (probability: 20/38 = 52.63%)
EV = (0.4737 × $100) - (0.5263 × $100) = -$5.26 per $100 bet

Blackjack (basic strategy)

EV ≈ -$0.50 per $100 bet (0.5% house edge)

Craps (pass line + 3-4-5x odds)

EV ≈ -$0.37 per $100 total wagered

Lottery EV

Powerball ($2 ticket, $100M jackpot)

Non-jackpot EV: $0.32
Jackpot EV: $100M × (1/292M) = $0.34
Total EV: $0.66
EV per ticket: -$1.34

The Key Insight

Every gambling decision should be evaluated through the lens of EV:

+EV bets make money long-term (even if they lose short-term)
-EV bets lose money long-term (even if they win short-term)
The goal is to find and exploit +EV opportunities

Why Short-Term Results Don't Matter

A +EV bet can lose. A -EV bet can win. Over 1 bet, anything can happen. Over 10,000 bets, results converge toward the expected value. This is the Law of Large Numbers, and it's why casinos always win — they play enough hands for the math to work.

Practical Applications

Sports betting: Calculate EV before every bet. If it's not +EV, don't bet.
Casino games: Know the house edge. You're paying for entertainment.
Lottery: Understand you're buying a dream, not an investment.
Poker: Every decision should maximize your EV.

Expected Value (EV) Deep Dive: The Foundation of All Gambling Math