So, he finds that intuitive guesstimates of probabilities are not very effective.  No joke.<p>While probability is a really nice and useful theoretical construct, often in practice getting an accurate numerical estimate is from challenging to not doable.<p>Broadly there are three approaches:<p>(1) For something like coin flipping, just call it 1&#x2F;2 and move on!<p>(2) There are stacks of theorems that can help, sometimes a lot.  E.g., there is the renewal theorem that says that lots of stochastic arrival processes converge to Poisson processes, and there  often in practice a good estimate of the arrival rate is easy and, then, a lot more probabilities just drop right out of various expressions for Poisson processes.  Can also make use of the central limit theorem, the law of large numbers, the martingale inequality, a Markov assumption, etc.  Here one of the best little tricks is to use intuition to justify independence (generally much more effective than using intuition in estimation of Bayes <i>priors</i>) and, then, exploit that assumption.<p>(3) Start with a Bayes <i>prior</i> or whatever the heck but have an iterative scheme where can have several or many iterations and for that scheme have some solid theorems that the scheme converges.  Then, iterate your way there.