Goal markets are calculated at Over 0.5, Over 1.5, Over 2.5 and so on. But there are also the Asian markets for the goal line, where for example there is the Over 1.0 market (where if there are no goals in the match the bet gives a loss, if only one goal comes out the bet is returned like a Void and if there are two or more goals the bet returns profitably).
If I know the Odds of the market Over 0.5 Goals and the Over 1.5 Goals, can we calculate Odds of the market Over 1 Goals?
If possible, what would be the formula?
Best Answer
Assuming the odds are fair, the odds paid are the odds against the bettor. When a draw with money returned is a possibility these odds are given by $$\frac{Pr(Bettor LosesIfNotDrawn)}{Pr(Bettor Wins If Not Drawn)}:1=\frac{Pr(Bettor Loses)}{Pr(NotDrawn)}\times\frac{Pr(NotDrawn)}{Pr(Bettor Wins)}:1=\frac{Pr(Bettor Loses)}{Pr(Bettor Wins)}:1$$ Suppose the odds against a goal difference of more than $0.5$ are $a:1$ and the odds against a goal difference of more than $1.5$ are $b:1$, where $b>a$. Then the probability of a score of $0$ or less is $\frac{a}{a+1}$ and the probability of a score of $2$ or more is $\frac{1}{b+1}$.
As a check, the probability of a score of exactly $1$ is $$1-\frac{a}{a+1}-\frac{1}{b+1}>\frac{a}{a+1}+\frac{1}{a+1}=1-\frac{a+1}{a+1}=0$$ and so the probability that the score is exactly $1$ is positive, as it needs to be.
The the bettor wins with a goal difference of more than $1.0$ and loses with a goal difference of less than $1.0$, so the odds against him winning will be $$\frac{Pr(Bettor Loses)}{Pr(Bettor Wins)}:1=\frac{Pr(GD<1.0)}{Pr(GD>1.0)}:1=\frac{\frac{a}{a+1}}{\frac{1}{b+1}}:1=\frac{a(b+1)}{(a+1)}:1$$