# Castles

For the first time ever, I have joined a Fantasy Football League. There are 12 of us in the league and we all roll jiu jitsu which should add an interesting dynamic. This weekend, we drafted and set the lineup.

Also this weekend, a very interesting game was suggested by FiveThirtyEight’s “The Riddler” called Castles. It mixes elements of Battleship and Rock, Paper, Scissors. You have 100 soldiers you can deploy to fight for 10 different castles. Castles 1, 2, 3, …, 9, and 10 are all worth as many points. That is, Castle 1 is worth 1 point, Castle 2 is worth 2 points, and so on. There is a total of 55 points to be obtained if you do the math.

Once both sides deploy their soldiers the war begins. If you have more soldiers than your opponent at any given castle, you obtain those points. If you have the same number of soldiers at the castle, you split the points. So, if each of you had 9 soldiers at castle 5, you both would receive 2.5 points. Whoever collects the most points wins the ‘war’.

There is no optimal answer. If you know the distribution of someone else’s soldiers, there are many, many distributions of soldiers that would beat that one.

What makes this game fun, is that you can go to war with thousands of other players, have wars with all of them, and see who comes out on top. This seems to be a pure and much more nerdy form of Fantasy Football, and it can carry on indefinitely. You don’t have to be restricted to 17 weeks.

Want to play a round? I have a distribution of soldiers that is pretty solid. As long as you believe me to be honest, submit a distribution of soldiers and I’ll let you know how the war turned out. I’ll give you a hint. It can beat each of these:

• 10, 10, 10, 10, 10, 10, 10, 10 ,10, 10
• 2, 4, 5, 7, 9, 11, 13, 15, 16, 18
• 3, 5, 8, 10, 13, 1, 26, 30, 2, 2
• 0, 1, 2, 16, 21, 3, 2, 1, 32, 22
• 0, 0, 12, 1, 1, 23, 3, 3, 33, 24
• To give you one further hint, there exists a distribution that loses to all of the above that beats mine. Good luck!