When I received Kahneman’s Thinking: Fast and Slow, I opened to a random page, and found a big error:

The idea that large historical events are determined by luck is profoundly shocking, although it is demonstrably true.  It is hard to think of the history of the twentieth century, including its large social movements, without bringing in the role of Hitler, Stalin, and Mao Zedong.  But there was a moment in time, just before an egg was fertilized, when there was a fifty-fifty chance that the embryo that became Hitler could have been a female.  Compounding the three events, there was a probability of one-eighth of a twentieth century without any of the three great villains and it is impossible to argue that history would have been roughly the same in their absence.

Kahneman drastically understates the power of (bad) luck.  Yes, just prior to fertilization, there was a 50/50 chance that Hitler would have been a girl.  But it’s also true that just prior to fertilization, there was roughly a 149,999,999 in 300,000,000 chance that a different “male” sperm would have hit the egg.  (There are roughly 300,000,000 sperm per incident, roughly half of them “male”). 

Yes, such a baby would still have been named Adolf Hitler.  But in all likelihood the world never would have heard of him.  A quarter of his DNA would have been different.*  The chance he would have attained Hitler’s political prominence would have been near-zero.  If we compound the births of Hitler, Stalin, and Mao, the probability of a twentieth century without any of the three isn’t 12.5%; it’s (1-1/299,999,999)^3=99.99999901%!

Under hereditary monarchy, Kahneman’s calculation might be defensible.  Maybe any male sibling of an infamous king would have been comparably villainous in his stead.  But Hitler, Stalin, and Mao all had humble origins.  They traveled from obscurity to power on hazardous paths.  The chance that a substitute sibling would have made the same journey – and been at all the right places at the right time – is vanishingly small.

Of course, this just confirms Kahneman’s deeper point: Human beings underestimate luck – even the great Kahneman himself.
* The egg’s DNA would have been the same, but two sperm from the same man have only half their DNA in common, so the shared DNA would be 50%+.5*50%=75%.