# Probability and Game Theory in The Hunger Games

Wired Magazine takes a look at the statistics and theories behind The Reaping and the Careers’ strategy in **The Hunger Games**. This involves numbers that can make some people’s heads hurt, but I’m sure there are those of you who find this type of thing fascinating, and it’s worth a read!

First they look at the probability that someone will be chosen at The Reaping, by age:

Suppose the parents in a given district gave birth to only 10 children, five boys and five girls, and that all of these kids were born at the same time. This would mean that they would all turn 12 at the same time and that all their names would go into the lottery at the same time. Since the boys’ and girls’ drawings are done separately, each boy and each girl would have a 1-in-5 or 20 percent chance of being chosen for the game. Now in any given year, one girl and one boy will be chosen for the game and either because of victory or death, their names won’t appear the next year. Thus, in the next year all the kids that are eligible for the drawing would be 13 years old and all of their names would appear in the drawing two times. There would now be 8 boys’ names in the pool for boys (2*4 = 8 names), 8 girls’ names in the pool for girls, and each boy and girl would have a 2-in-8 or 25 percent chance of being chosen for the game. That is, the number of times that each person’s name appears in the lottery will have increased and the chance of being chosen will have as well. It shouldn’t be too difficult to see that each boy and girl will have a 3-in-9 or 33 percent chance of being chosen when they are 14, a 4-in-8 or 50 percent chance when they are 15, and at age 16 each would have a 5-in-5 or 100 percent chance of being chosen for the game. The figure below shows how the chance of being chosen increases with age:

He goes on to even more detail before moving on to how game theory – specifically the prisoner’s dilemma – applies to The Hunger Games.

In both the movie and the book we see a coalition of some of the players develop where they attack other players as a group. As I considered this, and being aware of game theory, I wondered how such an alliance could be stable, given the powerful incentive all members of the coalition have to kill each other in order to better position themselves to win the game. In fact, I wondered how members of the coalition would even get any sleep, especially given that they slept near each other. This may seem like a strange question but the PD game can show that it isn’t so strange.

Consider the following table:

Don’t Sleep _{all}Sleep _{all}Don’t Sleep _{1}Tired, Tired Kill, Killed Sleep _{1}Killed, Kill Rested, Rested Here subscript “1″ refers to any member of the coalition and subscript “all” refers to all other members of the coalition. Let’s consider matters from any given member’s perspective (the subscript 1 player). What if the other players don’t sleep? If you don’t either, then you will be tired and, perhaps, more vulnerable to better-rested contestants. But if you sleep while others are awake, any one of them can kill you in your sleep. Presumably, it’s better to be tired than dead so you are under tremendous pressure to stay awake.

If all participants choose not to sleep and make this choice evening after evening, then all of them will end up being tired and more vulnerable to better-rested contestants. So why do members of Cato’s coalition in

HGget any sleep at all?

Check out the full article here if this type of thing interests you!

But shouldn’t children be born each year? So, theoretically, the year that the 8 remaining kids turn 13, there should be other kids who turn 12 and are entered once each (if tessarae are inapplicable for this math problem). Therefore, the 16-year-old should not have a 5-in-5 chance, especially if 10 kids are born every single year. Does that make sense?