The vig hidden in a 1.90 / 1.90 market

Question

A two-outcome market (essentially a coin flip) is quoted at decimal odds $1.90$ 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 1/1.90 = 10/19. Fast conversion: 	frac{10}{19} \approx 0.5263, because 	frac{1}{19} = 	frac{1}{20} 	imes 	frac{1}{1 - 1/20} \approx 0.05 	imes 1.0526 \approx 0.05263. Sum over both sides: \frac{2}{1.9} = \frac{20}{19} \approx 1.0526. Implied probabilities total \approx 105.26\%, an overround of 5.26 points. A fair coin-flip market would price both sides at 2.00; at 1.90 you're paid 90 cents on a fair-value dollar of winnings. Takeaway. Sum the reciprocals of all quoted decimal odds; the excess over 100\% is the market's margin. And the series trick \fr…

The vig hidden in a 1.90 / 1.90 market

Your answer

More Mental Math questions