How do you convert a percent into X-to-1

[BlawBlaw]

The subject says it all. How do you convert a percent into X-to-1? Such as 10% is 9-to-1. How would you figure out lets say 0.04%?

[AaronBrown]

You have to be careful of the difference between odds and probability.

A percentage is always a probability, so 0.04% = 0.0004 is 1 chance in 1/0.0004 = 2,500. That's also a probability statement, just expressed as a ratio. It's the chance of the event occuring.

Odds are the ratio of the probability of the event happening versus not happening. In this case, there's 1 way for it to happen and 2,499 ways for it not to happen. This is 1:2,499 or 1 to 2,499. If you're betting on this event, you pay $1 if it doesn't happen and your opponent should pay $2,499 if it does to make it a fair bet.

So the formula is 1 to (1/p - 1), where p is the probability expressed as a decimal. If it's expresses as a percent, use 100/p instead.

[BruceZ]

[ QUOTE ]
The subject says it all. How do you convert a percent into X-to-1? Such as 10% is 9-to-1. How would you figure out lets say 0.04%?

[/ QUOTE ]

10% means 10 wins to 90 losses or 90-to-10 against = 9-to-1 against. 0.04% means 0.04 wins to 99.96 losses or 99.96-to-0.04 = 9996-to-4 = 2499-to-1.

Also, take 1/probability - 1 to get odds-to-1. So 10% -> 1/0.1 -1 = 9-to-1.