Decimal odds 2.50, what probability is that?

Question

A bookmaker quotes decimal odds of 2.50 on an outcome (a \1 stake returns \2.50 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. Break-even requires p \cdot d = 1 \quad\Longrightarrow\quad p = \frac{1}{d}. Here p = 1/2.5 = 0.40, i.e. 40%. Fast mental step: 1/2.5 = 2/5 = 0.4, double top and bottom to clear the decimal. Takeaway. Implied probability is just the reciprocal of decimal odds. If your own estimate of the true probability is above 1/d, the bet has positive expected value; below it, negative. Every market-making interview question about "would you take this bet" starts with this one-step conversion.

Decimal odds 2.50, what probability is that?

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