Fair coin bet, win $10 or lose $5

Question

You take a bet on one fair coin. Heads wins you 10. Tails loses you 5. On average, how much do you win per flip?

Accepted Answer

Expected value is the average outcome over many repeats: each result times its probability, summed. The coin is fair, so heads and tails each carry weight one half. - Heads (probability one half): win 10. - Tails (probability one half): lose 5, that is negative five dollars. Combine: EV = 	frac{1}{2}(10) + 	frac{1}{2}(-5) = 5 - 2.5 = 2.5. The win contributes an average of 5 and the loss pulls back 2.50, so the net average is a 2.50 gain per flip. Notice the win is twice the size of the loss, which is exactly why the average lands halfway between them at a positive number. Takeaway. Average …

Fair coin bet, win $10 or lose $5

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