I’ve always found the notion that “odds are easier” confusing. I’m not sure who they are easier for, but I find reasoning about betting odds confusing and unintuitive. I have a clear feel for what a probability of 0.25 is. I don’t have one for what 1:3 means. Maybe most people have greater experience with gambling?
I find if I try using probabilities in Bayes in my head then I make mistakes. If I start at 1⁄4 probability and get 1 bit of evidence to lower this further then I think “ok, Ill update to 1/8”. If I use odds I start at 1:3, update to 1:6 and get the correct posterior of 1⁄7.
So essentially I’m constantly going back and forth—like you I find probabilities easier to picture but find odds easier for updates.
If you roll a fair six sided die once, there is a probability of 1⁄3 of rolling a “1” or a “2″. While a probability (#) is followed by a description of what happens, this information is interlaced with the odds:
1:2 means there’s 1 set* where you get what you’re looking for (“1” or “2“) and 2 where you don’t (“3” or “4”, “5” or “6″). It can also be read as 1⁄3.
I tried to come up with a specific difference between odds and probability that would suggest where to use one or the other, aside from speed/comfort and multiplication versus addition**, and the only thing I came up with is that you used “0.25” as a probability where I’d have used “1/4″.
*This relies on the sets all having equal probability.
**Adding .333 repeating to .25 isn’t too hard, .58333 3s repeating. Multiplying those sounds like a mess. (I do not want to multiply anything by .58333 ever. (58 + 1⁄3)/100 doesn’t look a lot better. 7⁄12 seems reasonable.)
I’ve always found the notion that “odds are easier” confusing. I’m not sure who they are easier for, but I find reasoning about betting odds confusing and unintuitive. I have a clear feel for what a probability of 0.25 is. I don’t have one for what 1:3 means. Maybe most people have greater experience with gambling?
I find if I try using probabilities in Bayes in my head then I make mistakes. If I start at 1⁄4 probability and get 1 bit of evidence to lower this further then I think “ok, Ill update to 1/8”. If I use odds I start at 1:3, update to 1:6 and get the correct posterior of 1⁄7.
So essentially I’m constantly going back and forth—like you I find probabilities easier to picture but find odds easier for updates.
If you roll a fair six sided die once, there is a probability of 1⁄3 of rolling a “1” or a “2″. While a probability (#) is followed by a description of what happens, this information is interlaced with the odds:
1:2 means there’s 1 set* where you get what you’re looking for (“1” or “2“) and 2 where you don’t (“3” or “4”, “5” or “6″). It can also be read as 1⁄3.
I tried to come up with a specific difference between odds and probability that would suggest where to use one or the other, aside from speed/comfort and multiplication versus addition**, and the only thing I came up with is that you used “0.25” as a probability where I’d have used “1/4″.
*This relies on the sets all having equal probability.
**Adding .333 repeating to .25 isn’t too hard, .58333 3s repeating. Multiplying those sounds like a mess. (I do not want to multiply anything by .58333 ever. (58 + 1⁄3)/100 doesn’t look a lot better. 7⁄12 seems reasonable.)
Multiplying with odds: 1:2 x 1:3 = 1:6 = 1⁄7.
Adding: 1:2 + 1:3 = ? 3 worlds + 4 worlds = 7, so 2:5? Double checking: 1⁄3 + 1⁄4 = (4+3)/12 = 7⁄12
a:b + c:d = ac+bc:bd