Game Theory For Your Lame Ass Friends

Game theory can be a fun and interesting topic. Here's a game you can play with a group of friends to see how well you can predict them, they can predict you, you can predict them predicting you, they can predict you predicting them predicting you...and so on. It's called half the average.

Each player takes a slip of paper and writes down a number between one and one hundred. All the numbers then get totaled up and averaged. The objective of the game is to guess the number closest to half the average of the group. At first this may seem simple but the more you and your friends try to predict and understand each other, the more complex the game becomes. As each player tries to undercut the other the average continuously shrinks. The key is to predict how many steps each player has thought through and be sure to remain one step ahead of the group.

My favorite memory of this game is playing back on Trinity campus at UVM (T-town represent!). We had played a few rounds and the competition was heating up as everyone began to anticipate each other more accurately. A mutual friend from down the hall came into my room who I believe was somewhat "impaired". I explained the rules, he watched one game, smiled and said "I know I'm guna win". I didn't think anything of it, we all entered our numbers and I started adding them up. The guesses were pretty typical. I was feeling confident since I'd won the last two or three rounds. As I added them up I exclaimed "Who the hell wrote 70?". 70 is obviously a ridiculous guess because the highest possible half average is 50 and that could only happen if everyone wrote 100. My friend simply explained "I figured if I guessed high it would pull the half average up and I would win". This completely illogical guess caused me to lose the game but I had to laugh considering it was my inability to predict his lack of reasoning that caused me to lose.

At this point I know what you are thinking "Did Mark just tell a whole story about math games?"...Big Time

Or as Anna Speidel put it "Math games...ew"