If you can get used to applying Bayes Theorem in your head as a second nature, it helps greatly as a quick dummy check with reality. Obviously this doesn't mean

If you can get used to applying Bayes Theorem in your head as a second nature, it helps greatly as a quick dummy check with reality. Obviously this doesn't mean calculating hundreds of probabilities in your head at once, but it can be very useful as a litmus test for all manner of things. Knowing roughly what the value will come out to be if your priors are ~10, ~100, or ~1000x apart is very helpful when trying to discern if you're just being led down a wrong path. Generally speaking doing Monte-Carlo simulations in your head would be nothing more than a stress test on your brain, but the simple multiplications and divisions used in reasoning under uncertainty can take you quite far, and with very little effort. You can even double check your work in the future if you really felt you did a bad job, and you'll be able to point out exactly where the error was (to yourselves or others) because it's more formalized than "I had a gut feeling."