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Compression at shallower nodes is more interesting than compression at deeper nodes, since deeper compression probably saves us less room and usually represents words with strange suffixes.

It would be statistically interesting to find shallow nodes that compress, especially if they have any subnodes that don't compress. I'm thinking something like "pne" might be a good candidate (pneumonia, etc), with "ne" compressing down but then having many uncompressed nodes.

A board (well, DiceSet, really) should be able to be ranked / unranked to represent it as a BigInteger.

Note that we do not take isomorphisms into account with this, as that would be far too complicated; thus, boards will be represented many times.

For a given board, implement an algorithm that counts the number of words on the board, preferably keeping them separated by number of letters.

This will be useful to tell players how many more words they have not found.