Hello, and welcome to the blog. I'll be devoting this first post to explaining what I'll be doing for the next three months, besides playing Chutes and Ladders.
The question I am trying to answer is how can the game of Chutes and Ladders be modeled mathematically, and how does the structure of the game influence that model? For instance, how many moves on average should it take to complete a game of Chutes and Ladders, and how might changing the spinner size affect this average? What happens to this average if we add a ladder here or remove a chute there? You get the idea.
I'll be answering these questions using mathematical models, so I'm going to need some way to confirm that my results are valid. Since I would have to play the game thousands of times to get any statistically significant data, my plan is to instead create a simple command-line program that can run a million simulations of the game in a heartbeat and report the results. I suppose I won't be playing the game much after all!
While figuring out how to model the game is the primary goal of my project, it's equally important that I come up with a way to do it efficiently. Even with the convenience of a computer, there may be a lot of computation required. Thus, I'll be trying different approaches to answering my proposed questions and seeing which work most efficiently. At the end of my project, I'll write a short report documenting all of my findings.
More board game and math shenanigans to come.
