That is the title of this little paper by economist Steve Landsburg. In his blog post with the same title, Professor Landsburg introduces the coin-flipper’s dilemma with this story:

When I was in high school, my English teacher must have had a free period at the time when my math class met, because every day he would march into the math class and empty his pockets on the table, whereupon my math teacher did the same. Then whoever had put down the most money scooped up everything on the table. I am ashamed to admit that it took me until this summer to think about computing the equilibrium strategy is in that game …

If you were the English teacher (or in the alternative, if you were the math teacher), how would you play this game?

Let’s start with some small questions, shall we?