Expected value and fair games

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Learn it Expected value = sum of (each value × its probability). It is the average result per try in the long run. A game is fair when the expected gain is 0.

Example: A game costs $\$2$. You win $\$10$ with probability $\frac{1}{8}$.

Expected winnings: $10 \times \frac{1}{8} = 1.25$.
Expected gain: $1.25 - 2 = -0.75$.
On average you lose $\$0.75$ per game: not fair.

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