# Mains: The World Series of coin flipping

From SABR member Rob Mains at Baseball Prospectus on November 29, 2016:

Let’s have our own World Series, you and I. A World Series of coin flipping. First to four wins. Your call, heads or tails. Ready? Let’s go.

There are four ways you can win. First, you can win four flips in a row. Since the odds of winning any one flip are 50/50, your chance of a sweep are ½ x ½ x ½ x ½, or ½4, which equals .0625. You have a 6.25 percent chance of winning four straight flips.

There are a few ways you can beat me 4-1. I can win the first flip, you the next four. Or you can win one, I win one, then you win three. Or you win two, I win one, and you win another two. Or you take three, I win my one flip, and then you finish me off. The odds of each of those sequences, since there are five coin flips total, is ½5. But there are four ways for you to win, so 4 x ½5 = .125. You have a 12.5 percent chance of winning our World Series 4-1.

I’ll spare you the narrative, but you have a 15.625 percent chance of beating me 4-2. And our series will go to seven games, with you victorious, 15.625 percent of the time as well.