The vig in a 1.95 / 1.95 market

Question

A two-outcome market (essentially a coin flip) is quoted at decimal odds $1.95$ on each side. Solve in your head.

What do the implied probabilities sum to, and what margin is the bookmaker running? Aim: under 20 seconds.

Accepted Answer

Each side's implied probability is 1/1.95. Write 1.95 = 	frac{39}{20}, so \frac{1}{1.95} = \frac{20}{39} \approx 0.5128. (Quick check: 	frac{20}{39} is just under 	frac{20}{40} = 0.5, nudged up because the denominator is 39 not 40.) Sum over both sides: \frac{2}{1.95} = \frac{40}{39} \approx 1.0256. Implied probabilities total about 102.56\%, an overround of 2.56 points. A fair coin-flip market prices both sides at 2.00; tightening to 1.95 shaves the margin to roughly half of what a 1.90 market (\approx 5.26\%) charges. Takeaway. Sum the reciprocals of the quoted decimal odds; the excess o…

The vig in a 1.95 / 1.95 market

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