# Odds vs Probability

• Feb 7th 2010, 02:41 PM
GoodRobot
Odds vs Probability
A newspaper article preceeding the 1994 World Cup semifinal match between Italy and Bulgaria stated that "Itality is favored 10-11 to beat Bulgaria, which is rated at 10-3 to reach the final". Suppose this means that the odds that Italy wins are 11/10 and the odds that Bulgaria wins are 3/10. Find the probability that each team wins, and comment.

Okay, so I know the transformation from Odds to Probability is given by:

Probability = Odds / 1 + Odds

and the transformation from Probabilities to Odds is given by:

Odds = Probability / 1 - Probability

Plugging in, I get:

Probability Italy wins: 0.23

Probability Bulgaria wins: 0.52

Comment: So, from the question, it sounds like Bulgaria is less likely to win given the odds. However, if we calculate the probabilities, its clear that Bulgaria actually has a better shot at winning.

Is this how you would approach the question? I found it a bit easy, I'm afraid I've missed something or interpreted it in a different way.

Cheers
• Feb 7th 2010, 04:18 PM
Hi GoodRobot,

you've miscalculated...

Italy at bookmaker odds of $\displaystyle \frac{10}{11}$ is $\displaystyle Odds_{win}=\frac{11}{10}\ \Rightarrow\ P_{win}=\frac{\frac{11}{10}}{\frac{11}{10}+\frac{1 0}{10}}=\frac{11}{11+10}=\frac{11}{21}$

Converting back...

$\displaystyle Odds_{win}=\frac{P}{1-P}=\frac{\frac{11}{21}}{\frac{21}{21}-\frac{11}{21}}$

Similarly for Bulgaria
• Feb 8th 2010, 05:15 AM
GoodRobot
Ahh, I missed that.

Thank you :)(Smirk)