If a bookmaker quotes pay off odds of $99$ to $1$ against a particular horse winning a race, does that suggest that the chance that the horse will win is $\frac{1}{100}$, less than $\frac{1}{100}$ or more than $\frac{1}{100}$?
I tried doing this on my own but saying "Oh it's subjective so it depends on whether or not we trust the bookmaker's intuition" and then I realized I was messing up the definitions between chance and odds. Can someone please help me this?
Thank you so much in advance.
On
odds against = unfavorable occurrences : favorable occurrences,
whereas probability = favorable occurrences / total occurrences,
thus odds against of $\;99:1 = \dfrac1{99+1} = \dfrac1{100}$
On
Bookmakers adjust the odds so as to make a profit regardless of who wins. Typically less than 90% of the money bet is paid back. If 30% has been bet on one horse, they may offer 3 to 1 on it. If the proportion of money bet on it increases before the race, they will lower its odds. The odds reflect what other bettors have been thinking, up to that point in time.
99 to 1 odds just means money is staked more in favor of other horses. This does not necessarily reflect the actual probability of a horse winning a race.
If you assumed the odds were a literal interpretation of the actual statistical outcome then 99 to 1 would mean 1/100 probability.
1/100 = 1/100
You can find more info here about it in the link below.
Odds