Expected value is the weighted average of every possible outcome when each outcome is multiplied by its probability. It is used in statistics, insurance, finance and game mathematics. EV answers what the arithmetic average would approach across many comparable observations under stable assumptions. It does not identify the most common result, the next result or the result any individual is entitled to receive.
A simple two-outcome example
Imagine an abstract experiment that pays $8 with a 20% chance and costs $3 with an 80% chance. Multiply each outcome by its probability: 0.20 × $8 gives $1.60, while 0.80 × minus $3 gives minus $2.40. The expected result is therefore minus 80 cents per trial. Neither a loss of 80 cents nor a partial outcome needs to be possible in one trial; that is why an average can differ from every actual result.
Expected gross return versus net result
For gambling, readers should distinguish prize money returned from net profit after stakes. A game described as returning an average of 95 cents per dollar staked has a theoretical net result of minus five cents for each dollar of turnover. That statement is about the underlying mathematics. The separately maintained pokies article applies the same arithmetic directly to reel-game RTP and total stakes.
What EV leaves out
Two processes can have the same expected value and very different distributions. One might usually produce a small loss with a rare large win; another might cluster near its average. Variance, the size of a person's exposure and the possibility of extreme outcomes are additional questions. EV alone does not say whether an activity is affordable, safe or suitable.
Assumptions matter
The probabilities must describe the correct event, and the listed returns must include all material outcomes and costs. If fees, rules or programme settings change, the computed EV changes. A number copied from a different market or game edition may be irrelevant to the case being discussed.
Use expected value as one tool for interpreting a model, not as a strategy for reversing a negative mathematical advantage. The related guide on short-term results explains why a person's real observations can remain far from the expected average.