If you've ever wondered whether a casino bet is "worth it" from a mathematical perspective, you're asking about expected value. Expected Value, or EV, is one of the most important concepts in gambling—it tells you exactly what you can expect to win or lose on average every time you place a bet. Most players make decisions based on feelings, hunches, or recent results. But the math tells a different story. Understanding EV gives you a clear, objective way to compare bets, evaluate casino games, and set realistic expectations about what gambling actually costs. The truth is straightforward: nearly every casino bet has a negative expected value, meaning you'll lose money on average over time. But some bets are much worse than others, and knowing the difference helps you make smarter choices. This guide explains what expected value means, how to calculate it, and why it's the foundation of making informed gambling decisions.
Understanding Expected Value
Expected value is the average amount you can expect to win or lose per bet if you made that same bet thousands of times. It's calculated by weighing every possible outcome by its probability. A bet with positive EV means you'll make money on average over time. A bet with negative EV means you'll lose money on average. A bet with zero EV means you'll break even in the long run. In casino gambling, almost every bet has a negative EV. The casino's business model depends on this mathematical advantage—they don't need to cheat or manipulate outcomes when the math guarantees profit over enough volume. Understanding whether a bet has an EV of -$0.05 or -$0.25 might seem minor, but over hundreds or thousands of bets, that difference becomes significant.
How to Calculate Expected Value
The formula for expected value is simple:
EV = (Probability of Winning × Amount Won) - (Probability of Losing × Amount Lost)Let's start with a simple example: a fair coin flip where you win $10 on heads and lose $10 on tails. - Probability of winning: 50% (0.5) - Probability of losing: 50% (0.5) - EV = (0.5 × $10) - (0.5 × $10) = $5 - $5 = $0 This is a zero EV bet—you'll break even over time. Now let's look at a real casino example: betting $10 on a single number in American roulette. - Probability of winning: 1/38 (2.63%) - Probability of losing: 37/38 (97.37%) - Payout if you win: $350 (35 to 1 on your $10 bet) - Amount lost if you lose: $10
EV = (1/38 × $350) - (37/38 × $10)EV = $9.21 - $9.74EV = -$0.53This means every time you bet $10 on a single number in roulette, you can expect to lose $0.53 on average. Make this bet 100 times, and you'll lose about $53 on average, though individual sessions will vary.
Expected Value in Casino Games
The reason casinos make money is because they design every game to have a negative expected value for players. The house edge and negative EV are two sides of the same coin. Different games and different bets within those games have different EV levels. Some are terrible; some are just bad.
Negative EV Examples
Slot machines typically have EV between -$0.02 and -$0.15 per dollar wagered, depending on the specific game and its RTP. A 95% RTP slot has an EV of -$0.05 per dollar bet. In roulette, all bets on an American wheel have an EV of approximately -$0.053 per dollar wagered (5.26% house edge). European roulette is slightly better at -$0.027 per dollar (2.7% house edge). Side bets in blackjack are particularly bad. Insurance, for example, has an EV around -$0.07 per dollar wagered when playing with a standard six-deck shoe.
The Lowest Negative EV Games
Some casino games offer much better expected value than others. Blackjack with proper basic strategy has an EV around -$0.005 to -$0.01 per dollar wagered, depending on the specific rules. This makes it one of the best bets in the casino, though you still lose money over time. Baccarat's banker bet has an EV of approximately -$0.0106 per dollar wagered. The player bet is close at -$0.0124 per dollar. Craps offers several bets with low negative EV. The pass line has an EV around -$0.014 per dollar, and the don't pass is slightly better at -$0.0136. These games won't make you money in the long run, but they'll cost you less per hour of play than games with higher house edges.
Expected Value vs Actual Results
Understanding EV doesn't mean you can predict what will happen in any individual session. Variance—the natural fluctuation around the expected value—means short-term results will differ from long-term expectations. You might bet $100 on a single number in roulette (EV: -$5.26) and win $3,500. Or you might lose ten times in a row. Neither outcome changes the EV of the bet. The law of large numbers tells us that actual results converge toward the expected value as the number of trials increases. After 10 bets, your results might be wildly different from EV. After 10,000 bets, you'll be much closer. This is why casinos always win over time—they have the volume. Individual players experience variance, but across thousands of players and millions of bets, the casino's results match the mathematical expectation almost perfectly.
Positive EV Opportunities (Rare)
While most casino bets are negative EV, there are rare exceptions where you might find positive expected value. Some casino bonuses create positive EV situations if the wagering requirements are low enough and the terms are favorable. For example, a $100 bonus with 10x wagering at a 99% RTP game might have a small positive EV after accounting for expected losses during playthrough. Promotional offers like free spins with no wagering requirements or cashback programs can sometimes offer positive EV for players who understand the terms. Advantage play techniques in games like blackjack (card counting) or poker (playing against weaker opponents) can shift EV from negative to positive, though casinos actively prevent or ban these practices. These situations are exceptions, not the rule. Most players will never encounter true positive EV opportunities in standard casino games.
Why Understanding EV Matters
Expected value gives you the mathematical foundation for every gambling decision. First, it helps you set realistic expectations. If you know a game has an EV of -$5 per $100 wagered, you can estimate your expected losses over a session and decide if that entertainment cost is acceptable. Second, it lets you compare bets objectively. Would you rather play a slot with -$0.05 EV per dollar or blackjack with -$0.01 EV per dollar? The choice becomes clear when you see the numbers. Third, it helps you evaluate bonus offers. A bonus that looks generous might have terrible EV once you calculate the expected losses during wagering requirements. Finally, understanding EV protects you from magical thinking. No betting system, lucky charm, or "feeling" changes the mathematical expected value of a bet.
Common Mistakes About EV
Many players misunderstand how expected value works.
"I'm due for a win": Past results don't change future EV. If you've lost ten roulette spins in a row, the next spin still has the same negative EV. This is called the gambler's fallacy.
"This bet feels luckier": Feelings don't change mathematics. A bet you "feel good about" has the same EV as an identical bet you feel neutral about.
"My system changes the EV": Betting systems like Martingale or Fibonacci change how variance affects your session but cannot change the underlying expected value of the bets you're making.
"Short-term wins mean positive EV": Winning money over a weekend doesn't mean your bets had positive EV. Variance can produce winning sessions even with negative EV bets. Understanding these misconceptions helps you avoid the mental traps that lead to larger losses.