Expected Value: The Only Number That Matters
Every gambling decision, every bet, every casino game can be reduced to a single number: expected value. Understanding this concept is the difference between gambling as entertainment and gambling as slow financial suicide.
The Formula
Expected value (EV) tells you how much you can expect to win or lose on average per bet. The formula is simple:
A positive EV means you'll profit in the long run. A negative EV means you'll lose. Every casino game has negative EV for the player—that's how casinos stay in business.
A Concrete Example
You bet $10 on red. There are 18 red slots, 18 black slots, and 2 green slots (0 and 00). Total: 38 slots.
Probability of winning: 18/38 = 47.37%
If you win, you get $10 profit.
If you lose, you lose $10.
EV = (0.4737 × $10) − (0.5263 × $10) = $4.74 − $5.26 = −$0.53
On average, you lose 53 cents per $10 bet. This is the house edge.
Why This Matters
The house edge on American roulette is 5.26%. That sounds small. But it compounds over time. If you bet $10 a hundred times, you've wagered $1,000 and can expect to lose about $53. Bet a thousand times and you're down $530.
Casinos don't need to cheat. The math guarantees they win over time. Every spin, every hand, every roll moves money from players to the house, on average.
Finding Better Games
Not all games are equally bad. Blackjack with perfect basic strategy has a house edge around 0.5%. Video poker with optimal play can get below 0.5% on certain machines. Craps pass line bet is 1.41%.
Compare this to slot machines, which typically have house edges of 5-15%, or keno, which can exceed 25%. The games that are easiest to play are usually the worst mathematically.
The Variance Trap
Even with negative EV, you can win in the short term. Variance—the natural fluctuation around expected outcomes—means anything can happen over a few sessions. Someone wins the jackpot. Someone hits a hot streak. These outcomes are real but misleading.
Casinos love variance because it creates stories. Winners tell their friends; losers stay quiet. The visible winners obscure the invisible army of losers that funds the casino's profits.
Over a long enough timeline, expected value always wins. Always. If you're playing a negative EV game, you will lose money. The only question is how long it takes.
The Real Calculation
Gambling can be entertainment. Paying for entertainment is fine. But be honest about what you're paying.
If you play $10 blackjack for four hours at 60 hands per hour with a 0.5% house edge, you're wagering $2,400 and your expected loss is $12. That's $3 per hour for entertainment. Reasonable.
If you play $1 slot pulls at 600 spins per hour with a 10% house edge, you're wagering $600 per hour with an expected loss of $60. That's expensive entertainment.
Know the EV of what you're playing. Budget for your expected loss. And never, ever convince yourself that you've found a way to beat the math. The math always wins.