Fortnite Riddle

Last week, my daughter was working on probability problem sets. This prompted me to look at her math book and I was surprised to see that how short the chapter was on this topic l. Not much has changed from what I learnt and what she is learning at least in probability chapters.

Statistics and probability are the most relevant but least-taught maths in schools. They have so many real-world consequences about how people think about everyday risk.

For her to internalize these concepts, I unusually take lunch and dinner time as an outlet to throw interesting questions to them. Here’s one that I recently found on Twitter and shared with them.

My both kids love playing fortnight so painted the question with that color.

Here’s the riddle?

Ann, Brown, and Cathy each carry a paintball gun in Fortnite. They play “ordered Mexican stand-off” according to the rules below.

First, they draw lots to pick an “order”, i.e., who goes first, second, and third. All possibilities are equally likely.

Second, they take their places at the corners of a triangle. See image. Third, they start shooting taking turns in the order chosen, cycling back if necessary, until two of them are hit and only one “survivor” remains. This eventual survivor is the winner of the game.

At each turn, the shooting player has to choose one of the other surviving players to aim at. This is a strategic choice: each player chooses whom to aim at in order to maximize his chances of winning. (And each player knows this is how the other players will behave.)

All players know that Ann always hits whomever she aims at, Brown has an 80% chance of hitting his target, and Cathy only has a 50% chance of hitting her target.

Each turn of each player is independent of all the other turns and all the other players.

Assuming that nobody is hit by a shot not intended for them, who is most likely to win this game?

One of the best decisions that I have made in 2017 was not to eat in front of a TV. This has made dinner time a good family time. This has spurred many interesting games, conversations, questions and learning for me and my kids.

Now your turn to try the riddle? Who do you think will win? Give it a try? Tell me in the comments?

Here my son’s response to this.