Decimal odds 1.25, what probability is that?

Question

A bookmaker quotes decimal odds of 1.25 on a heavy favorite (a \1 stake returns \1.25 total if it wins). Solve in your head. What win probability makes this bet break even? Aim: under 5 seconds.

Accepted Answer

With decimal odds d, a \1 stake returns d on a win and 0 on a loss, so break-even requires p \cdot d = 1 \quad\Longrightarrow\quad p = \frac{1}{d}. Here p = 1/1.25. The fast mental move is to clear the decimal: 1/1.25 = 4/5 = 0.80, i.e. 80%. A quick way to see 1/1.25 = 4/5: multiply top and bottom by 4, turning 1.25 into 5 and 1 into 4. Short odds imply a high probability, exactly what you expect for a strong favorite. Takeaway. Implied probability is the reciprocal of decimal odds. Odds near 1 mean the market is nearly certain; 1.25 prices an 80% chance. If your own estimate exceeds 1/d, the…

Decimal odds 1.25, what probability is that?

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