Your view is 20%, what are the fair odds?

Question

You believe an outcome has a true probability of $20\%$ . A counterparty asks you to quote fair decimal odds on it (a $1 stake returns your quoted number on a win). Solve in your head.

What decimal odds are fair for a 20% chance? Aim: under 5 seconds.

Accepted Answer

Break-even ties probability and decimal odds by p \cdot d = 1, so inverting the usual direction, d = \frac{1}{p} = \frac{1}{0.20} = 5.0. Fair decimal odds are 5.0: a \1 stake returns \5 total, which at a 20% win chance earns 0.20 	imes 5 = \1 on average, exactly break-even. Fast mental step: 1/0.2 = 10/2 = 5. A one-in-five shot pays five-for-one at fair value. Takeaway. Fair decimal odds are the reciprocal of your probability, d = 1/p. To make money you would quote tighter than fair (below 5.0) when laying the bet, so the built-in margin favors you rather than the taker.

Your view is 20%, what are the fair odds?

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