This rabbit hole leads to Triple Town data analysis

Well, how did I get here?

1. Commenting on a previous post, a friend suggested a new game to try.  
2. The Wikipedia page for Gone Home notes it uses the Unity Engine.
3. The Unity Engine page lists Triple Town as a client app.
4. The Triple Town page notes some research done on the distribution of tiles
5. This Triple Town Tribune post by Andrew Brown mentions that the data was collected by David de Kloet.
6. The data was originally shared in the comments of this post, which I found by searching on "David de Kloet triple town" in G+. (NOTE: I also asked Andrew if he had a copy of the data, which he was kind enough to share)

Now, the distributions are a good start, but my first question is: does the probability of getting a particular tile on your next tile depend upon the tile you've just been given?  For example, if you've just been given a bear, are you more or less likely than the overall estimated probability of 0.15 to get another bear with your next tile?

A quick way to start examining this is to look at a crosstabulation of the tile you've just been given by the next tile.  In this table, the rows show the current tile, and the columns show the next tile.  Looking at the first row, what this means is that of the 1043 total times that a Bear appeared, it was followed by another Bear 157 times, by a Bush 157 times by Grass 637 times, and so on.  

The raw counts are useful, but it can be hard to compare rows to see if they're different.  So now let's look at the row proportions.  Again, the rows show the current tile, and the columns show the next tile.  Looking at the first row, what this means is that of all the times that a Bear appeared, it was followed by another Bear 15.1% of the time, by a Bush 15.1% of the time, by Grass 61.1% of the time, and so on.  Bears appear pretty consistently around the overall average of 15.1% of the time, though they seem to appear less often after a Hut (11.4%) and more often after a Tree (18.4%).  However, Huts and Trees don't appear very often, so these differences could be due to chance.
 

So let's look at the chi-square test.  SPSS Statistics produces both Pearson and Likelihood Ratio chis-square tests.  Since the significance values of the tests are each under 0.05, this suggests that there is, in fact, a relationship between what tile you have now and the next tile you'll get, but I'm a little worried about the large number of cells with low expected cell counts.  That can throw the results of the test off.

So another set of tests to look at are pairwise comparisons of the column proportions.  (NOTE: I really want to compare the row proportions, but that's not an option, so I've reorganized the table so that the current tile is in the columns and the next tile is in the rows)  At any rate, the tests suggests that when your current tile is a Tree, the distribution of your next tile is different from when you current tile is a Bear, Bush, or Grass.  

Looking back at the table of proportions, what's not clear from the test is whether the detected statistically significant differences come from the relatively higher rate of Bears and lower rate of Bushes when the current tile is a Tree, or whether it comes from the relatively higher rate of Huts and lower rates of Bots and Trees.  The latter sets of relative differences arises from very rare events, and I wouldn't trust results based on that.  We could re-run the test while ignoring those columns, but for now I'm pretty comfortable saying that there is no practically significant relationship between the current tile and the probability distribution of the next tile.

These tables were produced using this SPSS Statistics syntax on this text file.