Deep Analysis on Match Scene from This is the End

Complicated math incoming.

I was watching This is the End with my friends the other day, and among the various goofs and gaffs, we witnessed the match scene.

Just to provide a little context of the scene I will be talking about, in case any traces of the scene was removed from all corners of the internet, a couple people are stuck in a house due to an apocalypse. They need water, but it’s in a basement that can only be accessed from the outside. To decide who goes, Seth Rogen lights a match and hides it with a bunch of other matches, and whoever pulls the burnt match has to risk his life to get some water.

As the scene was unfolding, I assumed that they would all pick a match at the same time and then reveal who picked the burnt match. Then, when Craig Robinson volunteers to go first, I had a little internal monologue. Is he dumb? Why would you volunteer to go first? Wouldn’t it be better to let others go first so they incur risk before you do? But after discussing with my friends for a bit, we concluded that he was a genius because going early is better than going last because you have a larger population of matches and thus a smaller chance of drawing the burnt match. As the movie progressed, my mind stayed behind. Maybe it doesn’t matter who goes first. Or maybe there is some optimal turn to go based on the number of matches. Anyway, let’s figure this out with basic math.

In this scenario, if Craig were to go first, he has a 1 in 7 chance of picking the burnt match. Now, say he decides to wait to be the third person to draw a match, if it gets to that. The probability of his drawing a match is 6/7 * 5/6 * 1/5. This even extends to the event of drawing a match as the second to last person: 6/7 * 5/6 * 4/5 * 3/4 * 2/3 * 1/2. The numerators and denominators nicely cancel out with neighboring terms, so that no matter which turn Craig waits until, the probability is 1/7. Just to be thorough, let’s take into account every possible outcome in the event that Craig decides to wait to be the third person. The probability that he draws the burnt match is 1/7, the probability that he doesn’t is 6/7 * 5/6 * 4/5 = 4/7, and the probability that someone before him draws the burnt match is 2/7, as each person before him also has a 1/7 chance of drawing the match. All of the probabilities nicely sum to 7/7.

In conclusion, yes, this is all very simple math. I wouldn’t be surprised if this is common knowledge in a field like game theory or combinatorics. This also explains why Craig was so quick to go first. He quickly crunched the numbers and realized it didn’t matter.