It is impossible to fully implement Bayes’ Theorem in all but the simplest circumstances, so we must settle for approximations.
The key in most things is not to be exact but to avoid mistakes that can lead to large errors.
Putting too much mental effort towards knowing the math behind a situation can be as damaging as putting forward too little effort as it has high opportunity cost and detracts from other aspects of your game or even your life.
If you keep examining the trees, you may never see forest.
Jennifer Harmon has famously admitted that she knows little poker math, but she is successful because she focuses on other aspects while knowing enough of the principles to avoid making costly mathematical mistakes.
The most important mathematics to know are the odds of a given hand beating another given hand, or of a given hand improving.
There are easy rules of thumb for approximating both in Hold ‘Em.