October 2, 2015
A recent article in the Wall Street Journal discusses the “hot hand” paradox. Basketball players especially believe in the hot hand, when making a shot you can suddenly have a hot hand and make several more shots in a row. The Wall Street Journal proposes this experiment:
Toss a coin four times. Write down the percentage of heads on the flips coming immediately after heads. Repeat that process one million times. On average, what is that percentage?
The article claims that the correct percentage is 40%, not the 50% that you would expect from an unbiased coin, and that this is proof that the hot hand exists, even from such a random source as coin flips. If you’re interested, you can read the academic article that the Wall Street Journal account is based on, or see discussion of it at Hacker News.
Your task is to write a program to confirm the 40% figure. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.