I agree that using odds rather than probabilities is better for mental calculation, and I started applying Bayes’ rule much more often upon realizing this. You can also use odds to express the Bayes factor, and thus avoid having both probabilities and odds in the same calculation. Rob Wiblin recently gave a good illustration:
Doing Bayesian updates in your head isn’t as hard as you might think!
Imagine you think X has 4:7 odds of being true. (That’s a probability of 4/(4+7) = 36%.)
Then imagine you see something which you think you’re twice as likely to observe if X is true, as if it isn’t. Those are odds of 2:1.
To get updated odds of X being true, just multiply the first number by the first number and the second number by the second number, like so:
I agree that using odds rather than probabilities is better for mental calculation, and I started applying Bayes’ rule much more often upon realizing this. You can also use odds to express the Bayes factor, and thus avoid having both probabilities and odds in the same calculation. Rob Wiblin recently gave a good illustration:
This is also discussed at greater length in the 80k podcast episode with Spencer Greenberg.