Definition
Expected Value (EV) is the average amount a player can expect to win or lose on a specific bet if it were repeated an infinite number of times. It is the mathematical “fair value” of a wager, combining the probability of winning and losing with the amounts gained or lost.
In context
In a simple $10 coin toss where “Heads” pays you $11 and “Tails” costs you $10, the Expected Value is +$0.50. This means that while you will either win $11 or lose $10 on any single flip, you will average a 50-cent profit per flip over the long run. In a casino, most bets have a negative Expected Value (-EV).
Why it matters
EV is the language of professional gamblers and casino operators. A “+EV” bet is an investment that will eventually make money, while a “-EV” bet is a guaranteed long-term loss. Understanding EV allows a player to look past the “flash” of a big jackpot and see the underlying reality of whether a bet is worth making.
Related terms
In detail
Expected Value (EV) is arguably the most important concept in all of gambling, finance, and decision-making. It is the “No-Spin” reality of any risk. While the term sounds academic, it’s actually a very practical tool for identifying the difference between a “good bet” and a “bad bet.”
The Anatomy of EV
To calculate the EV of a bet, you follow a simple two-step logic:
- Multiply the probability of winning by the amount you win.
- Multiply the probability of losing by the amount you lose.
- Add them together.
EV = (Win Probability × Win Amount) - (Loss Probability × Loss Amount)
If the result is positive (+EV), the bet is in your favor. If it is negative (-EV), the bet is in the house’s favor.
Example: Roulette
Let’s look at a $10 bet on a single number in American Roulette (38 numbers total).
- Probability of Winning: 1 in 38.
- Win Amount: $350 (the payout is 35 to 1).
- Probability of Losing: 37 in 38.
- Loss Amount: $10.
Calculation: (1/38 * 350) - (37/38 * 10) = 9.21 - 9.74 = -$0.53
This means that for every $10 you bet on a single number, you are “giving” the casino 53 cents. That is the -EV reality. The casino doesn’t need to “win” every spin; they just need to offer -EV bets and wait for the volume to do the work.
EV vs. Reality (Short-Term vs. Long-Term)
The biggest mistake people make with EV is thinking it describes what will happen now. It doesn’t. If you have a +EV bet, you can still lose ten times in a row. This is called “negative variance.” Conversely, you can make a -EV bet (like a lottery ticket) and win millions. This is “positive variance.”
EV is the weighted average. If you could play the same bet 10 million times, your actual results would perfectly match the EV. This is why professional poker players or sports bettors focus entirely on “making +EV decisions.” They don’t care if they lose a single hand or a single game, as long as the decision was mathematically correct. Over time, the +EV will manifest as profit.
The “House Edge” Connection
The House Edge is simply the negative Expected Value of a game expressed as a percentage.
- If a game has a 5% house edge, its EV is -0.05 for every dollar wagered.
- If a player finds a way to get a +1% edge (through card counting or edge sorting), their EV becomes +$0.01 per dollar wagered.
Finding +EV in the Casino
For the average player, +EV opportunities are rare but they do exist:
- Progressive Jackpots: Sometimes a slot machine or Caribbean Stud Poker jackpot grows so large that the “Win Amount” in our formula becomes huge. At a certain point (the “breakeven point”), the EV flips from negative to positive.
- Casino Promos: If a casino offers “Double Points” or “Loss Rebates,” the added value can sometimes turn a slightly -EV game into a +EV situation.
- Poker: In poker, you aren’t playing the house; you are playing other people. If you are more skilled than your opponents, your EV is positive.
- Sports Betting: If you can predict a game’s outcome more accurately than the market, you can find +EV “lines.”
The “No-Spin” Reality
In the real world of the casino floor, 99.9% of what you see is -EV. The lights, the free drinks, the beautiful decor—all of it is paid for by the gap between the player’s wager and the true mathematical EV. The “Truth” of ChipsAndTruths is that unless you are a professional advantage player, you are paying for the experience of variance. You are buying the chance to defy EV in the short term. As long as you know the “cost” (the -EV), you can gamble responsibly.