Moneyline Wagering

With the orange jackass (aka widdle Donnie) first declaring the coronova virus a hoax, then telling people to go ahead and go to work if you are sick, and only today tweeting that the people at the CDC are amazed at how much he knows about covid-19, it is time to have some fun.

Tonight (March 7) at 6PM in Cameron Indoor Stadium the Blue Devils with a conference record of 14-5 will take on the UNC Tarheels  who are 6-13 and will end up in lst place if they lose. If you go online to look at the odds for tonight’s Duke-UNC you find the curious looking

Duke -350

UNC 280

What this means is that you have to bet $350 on Duke to win $100, while if you bet $100 on UNC you win $280

Let p be the probability Duke wins.

For the bet on Duke to be fair we need 100p – 350(1-p) = 0 or p = 7/9 = 0.7777

For the bet on UNC to be fair we need -100p + (1-p)280= 0 or p = 0.7368

If 0.7368 < p < 0.7777 both bets are unfavorable.

This suggests that the a priori probability Duke wins is about 3/4.

Another way of looking at this situation is through the money. If a fraction x of people bet on Duke then

When Duke wins the average winnings are 100x – 100(1-x)

When UNC wins the average winnings are -350 x + 280 (1-x)

Setting these equal gives 200 x + 630 x = 100 + 280 or x = 38/83 = 0.4578

If this fraction of people bet on Duke then the average payoff from either wager is -500/83 = -$6.02 and the people who are offering the wager don’t care who wins.

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