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)
The prior probability of rolling a 1 is 1⁄6 = ~0.16. The prior odds of rolling a 1 are 1:5 = 1⁄5 = 0.2.
Some sources would call the 0.2 a “chance” to communicate that it’s an odds and not a probability, but Eliezer seems to not do that, he just uses “chance” as a synonym for probability:
If any face except 1 comes up, there’s a 10% chance of hearing a bell, but if the face 1 comes up, there’s a 20% chance of hearing the bell.
Don’t get confused, this 20% probability of hearing the bell is not the 0.2 from earlier.
Wouldn’t the prior odds in the bell example be 1:4 when the chance is 0.2? But written is 1:5.
The prior probability of rolling a 1 is 1⁄6 = ~0.16. The prior odds of rolling a 1 are 1:5 = 1⁄5 = 0.2.
Some sources would call the 0.2 a “chance” to communicate that it’s an odds and not a probability, but Eliezer seems to not do that, he just uses “chance” as a synonym for probability:
Don’t get confused, this 20% probability of hearing the bell is not the 0.2 from earlier.