I don't want to knock the article, since this kind of exploration is fun and well written blogs are always a joy to read.<p>But knowing some statistics, the entire of Snakes and Ladders is an absorbing markov chain [1] and can be very quickly analyzed as such without having to resort to sampling.<p>Random sampling is easy but take a step back and the entire state space is an integer in [1,100]. (Actually there are fewer than 100 states because the bottom of a ladder or top of a snake isn't a state).<p>The state transitions are very easy to model, they're just 1/6 to each of the 6 next states (sometimes fewer, in which case they just add).<p>Having constructed our markov chain, we can instantly and accurately get back our time-to-victory from each square.<p>[1] <a href="http://en.wikipedia.org/wiki/Absorbing_Markov_chain" rel="nofollow">http://en.wikipedia.org/wiki/Absorbing_Markov_chain</a>
Great read. I have one suggestion:<p>Get better games.<p>My 5 year old LOVES King of Tokyo playing with me as a family. <a href="https://boardgamegeek.com/boardgame/70323/king-tokyo" rel="nofollow">https://boardgamegeek.com/boardgame/70323/king-tokyo</a><p>Also Animal Upon Animal is a fun game with my kid. It is a stacking game with animals and kids love it. <a href="https://boardgamegeek.com/boardgame/17329/animal-upon-animal" rel="nofollow">https://boardgamegeek.com/boardgame/17329/animal-upon-animal</a><p>There are so many good games for kids and almost no one knows about them.
As a note for the quantative analysis aspect of the code, I <i>strongly</i> recommend looking into dplyr, especially since you have very many subset and column-wise operations: <a href="http://cran.rstudio.com/web/packages/dplyr/vignettes/introduction.html" rel="nofollow">http://cran.rstudio.com/web/packages/dplyr/vignettes/introdu...</a><p>I almost quit R due to the tedious verbosity of the default syntax, but dplyr made it simple and fast.
Previously, related posts:<p><a href="https://news.ycombinator.com/item?id=3386970" rel="nofollow">https://news.ycombinator.com/item?id=3386970</a><p><a href="https://news.ycombinator.com/item?id=6323427" rel="nofollow">https://news.ycombinator.com/item?id=6323427</a><p>The first of these is more sophisticated than the current post, because it calculates the distributions analytically using the fact that the move sequence is Markov and the transition matrix is known. So, exact probabilities can be found.
That is just the analysis I think about doing every time I play Chutes and Ladders with my daughter. I think "I should just simulate this game, it would be much more fun."
Thanks for this awesome analysis. I've been wanting to do a simulation of how much of Settlers of Catan is luck vs skill. Has anyone seen an analysis like this completed?
The same topic on: <a href="http://datagenetics.com/blog/november12011/" rel="nofollow">http://datagenetics.com/blog/november12011/</a> with more in depth explanations.