This is one of the great reasons to do your math with odds rather than probabilities. (Well, this plus the fact that Bayes’ Theorem is especially elegant when formulated in the form of odds ratios.)
There is no reason, save the historical one, that the default mode of thinking is in probabilities (as opposed to odds.) The math works just the same, but for probabilities that are even slightly extreme (even a fair amount less extreme than what is being talked about here), our intuitions about them break down. On the other hand, our intuitions when doing calculations with odds seem to break down a lot less.
When money is on the line, people have more of incentive to avoid errors. That’s why, traditionally, gamblers use odds and not probabilities. (e.g. the chance of a horse winning a horse race might be written as “two to nine odds” (or 2:9), and not “eighteen percent chance” (or 0.18). And this example isn’t even nearly as extreme as the cases ChrisHallquist talked about, yet still putting it in odds form makes it quite a bit easier to deal with.)
I’m not sure of the value of odds as opposed to probabilities for extreme values. Million-to-one odds is virtually the same thing as a 1⁄1,000,000 probability. Logodds, on the other hand, seem like they might have some potential for helping people think clearly about the issues.
I’d also note that probabilities are more useful for doing expected value calculations.
This is one of the great reasons to do your math with odds rather than probabilities. (Well, this plus the fact that Bayes’ Theorem is especially elegant when formulated in the form of odds ratios.)
There is no reason, save the historical one, that the default mode of thinking is in probabilities (as opposed to odds.) The math works just the same, but for probabilities that are even slightly extreme (even a fair amount less extreme than what is being talked about here), our intuitions about them break down. On the other hand, our intuitions when doing calculations with odds seem to break down a lot less.
When money is on the line, people have more of incentive to avoid errors. That’s why, traditionally, gamblers use odds and not probabilities. (e.g. the chance of a horse winning a horse race might be written as “two to nine odds” (or 2:9), and not “eighteen percent chance” (or 0.18). And this example isn’t even nearly as extreme as the cases ChrisHallquist talked about, yet still putting it in odds form makes it quite a bit easier to deal with.)
I’m not sure of the value of odds as opposed to probabilities for extreme values. Million-to-one odds is virtually the same thing as a 1⁄1,000,000 probability. Log odds, on the other hand, seem like they might have some potential for helping people think clearly about the issues.
I’d also note that probabilities are more useful for doing expected value calculations.
Anyone know whether gambling being expressed as odds is cross-cultural?