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A poll taken in Massachusetts in October 2012 showed Obama leading Romney by 60% to 40% in the U.S. presidential race. Let's assume that these numbers represent probabilities. I wished to make a bet with my friend on who would win Massachusetts, and we agreed to base our bet on that poll. I predicted a victory for Obama and would win a profit of \$10 if I were right. Assuming we wished this to be a fair game, how much should I have agreed to pay my friend if he was right and Massachusetts went to Romney?

Feb 25, 2018

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Here is a website for such things:

https://www.oddsshark.com/tools/odds-calculator

You have to bet \$15 to win the \$10 at 60%

a bet of \$15 to win at 40% should win \$22.50    (according to the calculator)

Perhaps   ?    60% bet  ==    15 x 40/60 = \$10 win

40% bet  ==    15 x 60/40 = 22.50 win   ??

....or another way to look at it...

Total payout on \$15 bet

bet on 60%   :    100/60  x \$15  = \$25 payout (\$10 winnings)

bet on 40%   :    100/40  x   15  =   37.20  (22.50 winnings)

Feb 26, 2018
edited by ElectricPavlov  Feb 26, 2018
edited by ElectricPavlov  Feb 26, 2018