Expected Value: The Only Gambling Math You Actually Need

Every gambling decision comes down to one number: expected value. Learn to compute it and you can evaluate any bet — casino, sportsbook, or a coin flip with a friend — without anyone’s opinion.

What expected value is

Expected value (EV) is the average result of a bet if you could repeat it forever. Multiply each outcome by its probability, add them up, and you have the long-run price of the wager.

Take a single-number bet in double-zero roulette. You win 35-to-1, but there are 38 pockets:

• Win: (1/38) × 35 = +0.921 units
• Lose: (37/38) × 1 = −0.974 units

EV = 0.921 − 0.974 = −0.053 units per unit bet, or −5.3%. Every $100 you put on a number costs you $5.26 on average. Not sometimes. On average, always.

The ten-second method

For any casino bet:

1. List every outcome and its true probability.
2. Multiply each payout by its probability.
3. Subtract what you risked times the probability of losing it.

If the answer is negative — and in a casino it always is — that percentage is the house edge. The house doesn’t need luck; it needs volume.

Why negative EV games still fill casinos

Variance. Over a hundred spins, anything can happen, and that short-term noise is exactly what you’re buying: the possibility of walking away up. There’s nothing wrong with paying for entertainment. The mistake is believing a streak, a system, or a “due” number changes the underlying arithmetic. It never does — each spin resolves to the same −5.3%.

What you can actually control

You can’t make a casino bet positive-EV, but you can choose how much edge you give away:

• Game selection. House edge ranges from under 0.5% (blackjack with correct play) to over 15% (keno, some side bets). See our ranking of which games give you the best shot.
• Bet selection within a game. In craps, the pass line gives up 1.41% while the “any 7” bet gives up 16.7% — same table, twelve times the price.
• Speed. EV loss compounds per bet. Half the hands per hour is half the expected cost.
• Bankroll rules. Decide your loss limit before you play. EV tells you the average; variance guarantees the worst sessions will be much worse.

The takeaway

Expected value strips gambling of mythology. Every bet has a precise long-run price; the casino publishes it implicitly in the rules. Know the price, decide if the entertainment is worth it, and never pay more edge than you have to.