Spring 2014 MTCA Workshop #3

Post date: Mar 28, 2014 10:22:11 PM

Mathematics of Candy Land

Presented by

Dr. Dave Rusin

The University of Texas at Austin

Thursday, March 27

NOA 1.116

If you have ever played Candy Land, it is likely that after a few minutes of play, you have asked yourself, "How long will this game

last?" Dr. Rusin led us in an analysis of this question, beginning with the problem of really defining what we mean when we ask

that question. We discussed the game Hi-Ho Cherry-O, which has the same characteristics as Candy Land, but with fewer

possible "game states". We talked about ways in which to efficiently compute the probability of being at a particular game state

after a given number of plays. This led to a discussion of matrices and matrix multiplication. In the end, we were able to

determine the average number of plays in a game, the most likely number of turns before the game ends, and the median number

of turns in a game, assuming that there was one person playing alone. We then discussed ways to generalize to cover the

situation when there were two players alternating turns.