What are the odds that the face showing is 1? Well, the prior odds are 1:5 (corresponding to the real number 1⁄5 = 0.20)
I’m years late to this party, and probably missing something obvious. But I’m confused by Yudkowsky’s math here. Wouldn’t it be more correct to say that the prior odds of rolling a 1 are 1:5, which corresponds to a probability of 1⁄6or0.1666...? If odds of 1:5 correspond to a probability of 1/5 = 0.20, that makes me think there are 5 sides to this six-sided die, each side having equal probability.
Put differently: when I think of how to convert odds back into a probability number, the formula my brain settles on is not P = o / (1 + o) as stated above, but rather P = L / (L + R), if the odds are expressed as L:R. Am I missing something important about common probability practice / jargon here?
The real number 0.20 isn’t a probability, it’s just the same odds but written in a different way to make it possible to multiply (specifically you want some odds product * such that A:B * C:D = AC:BD). You are right about how you would convert the odds into a probability at the end.
I’m years late to this party, and probably missing something obvious. But I’m confused by Yudkowsky’s math here. Wouldn’t it be more correct to say that the prior odds of rolling a
1are1:5, which corresponds to a probability of1⁄6or0.1666...? If odds of1:5correspond to a probability of1/5=0.20, that makes me think there are 5 sides to this six-sided die, each side having equal probability.Put differently: when I think of how to convert odds back into a probability number, the formula my brain settles on is not
P = o / (1 + o)as stated above, but ratherP = L / (L + R), if the odds are expressed asL:R. Am I missing something important about common probability practice / jargon here?The real number 0.20 isn’t a probability, it’s just the same odds but written in a different way to make it possible to multiply (specifically you want some odds product
*such thatA:B * C:D = AC:BD). You are right about how you would convert the odds into a probability at the end.