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.