Split betting outcome example

[Guest MacPhee]

I've just looked at a leading Bookmaker's website, which gives betting odds on the outcome of the US presidential election.

 

The odds quoted are:

 

OBAMA - 2/5

ROMNEY - 15/8

 

These odds seem asymmetrical. I mean if Obama is 2/5, shouldn't Romney be 5/2 - not a mere 15/8?

 

Could this asymmetry be exploited, by placing a big bet on one candidate, plus a smaller side bet on the other - and making a profit whichever one wins?

 

I've tried to calculate how much would have to be bet on each candidate. But can't quite figure the maths out, can anyone help please?

[CraigD]

OBAMA - 2/5

ROMNEY - 15/8

...

Could this asymmetry be exploited, by placing a big bet on one candidate, plus a smaller side bet on the other - and making a profit whichever one wins?

In a wanton demonstration of how computers can make even folk with degrees in it eschew algebra, this little bit of MUMPS code

s P=2+5/5,Q=15+8/8 f A=0:.01:1 w $j(A,8,2),$j(A*P,8,2),$j(1-A*Q,8,2),!

shows there's no way to make a profit regardless of who wins, by showing

A bet of 0.65 for OBAMA and 0.35 for ROMNEY pays 0.91 or 1.01

A bet of 0.72 for OBAMA and 0.28 for ROMNEY pays 1.01 or 0.81

 

Splitting your 1.00 with 0.66 to 0.71 to OBAMA assures you lose money no matter who wins, but no split can assure you make money no matter who wins.