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?
Here is a website for such things:
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)