How a scientist thinks.

The following is from Carl Sagan's book Demon-Haunted World:

[When] the Italian physicist Enrico Fermi, newly arrived on American shores, enlisted in the Manhattan nuclear weapons Project, and [was] brought face-to-face in the midst of World War II with U.S. flag officers: 

So-and-so is a great general, he was told.

What is the definition of a great general?  Fermi characteristically asked.

I guess it's a general who's won many consecutive battles.

How many?

After some back and forth, they settled on five.

What fraction of American generals are great?

After some more back and forth, they settled on a few percent.

But imagine, Fermi rejoined, that there is no such thing as a great general, that all armies are equally matched, and that winning a battle is purely a matter of chance.    Then the chance of winning one battle is one out of two or 1/2; two battles 1/4, three 1/8, four 1/16, and five consecutive battles 1/32 - which is about 3 percent.  You would expect a few percent of American generals to win five consecutive battles - purely by chance.  Now, has any of them won ten consecutive battles?