Academy Contents
Expected Value in Gambling
Learn how expected value (EV) determines the long-term outcome of gambling decisions and why negative EV is unavoidable in casino games.
Key Formula
EV = Σ (Probability of Outcome × Value of Outcome)What is Expected Value?
Expected Value (EV) is the mathematical average outcome of a bet if it were repeated infinitely many times. It represents what you would expect to win or lose per bet on average. In casino games, EV is almost always negative for players, which is how casinos make money.
Key Points
- EV combines probability and payout into a single number
- Positive EV favors the player; negative EV favors the house
- Short-term results vary widely around the EV
- Long-term results converge toward the EV
Calculating Expected Value
To calculate EV, multiply each possible outcome by its probability, then sum all these values. For a simple coin flip game where you win $1 on heads and lose $1 on tails, the EV is zero—a fair game.
Key Points
- List all possible outcomes
- Determine probability of each
- Multiply outcome value by probability
- Sum all weighted outcomes
Expected Value and Time
The Law of Large Numbers states that as the number of trials increases, the actual results will converge toward the expected value. This means short-term luck eventually gives way to mathematical certainty.
Key Points
- Short term: Variance dominates (luck)
- Medium term: Results begin converging
- Long term: EV dominates (mathematical reality)
- More bets = closer to expected loss
Using EV for Decisions
While you cannot overcome negative EV in casino games, understanding it helps you choose games with lower edges and set realistic expectations about your gambling entertainment budget.
Key Points
- Choose games with lowest EV loss
- Understand expected hourly loss rates
- Budget based on EV, not best-case scenarios
- Accept EV as entertainment cost
Try It Yourself
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Continue Learning
The mathematical foundation of casino games. Learn how the house edge works, why it exists, and how to identify the best and worst bets.
Understanding how variance affects short-term results. Learn why even games with the same house edge can have very different risk profiles.
Understanding the probability of losing your entire bankroll before achieving your goal. Critical for bankroll management.
18+ Only. Gambling involves risk. Please gamble responsibly. Learn more →