However, this past while I have become interested in the properties of chess as a game, and in the idea of the programming side of it. For example, there are a few things I'd be interested in looking into:
- Analysis of games ending in mate-in-n after x plies from the starting position- there is some info on it here I've seen looking at mate-in-5 games up to 5 plies in, and mate-in-1 games up to 10 plies in, but I'd be interested to see if we could find how many mate-in-6, mate-in-7 and so on games there are among the first plies in chess. Related to this is obviously the question of finding perft(16), etc, how far that can be realistically pushed, and having the games up to a given perft(n) mapped and available, in a searchable format (if this isn't already the case?), so that they can be analysed like tablebases can be analysed
- Analysis of the existing 7-man tablebase to find out what percentage of legal positions are checkmate positions, what percentage are mate-in-1, mate-in-2, etc, or draw-in-1, draw-in-2, etc, and to compare those stats across 7-man positions, 6-man positions etc.
- Analysis of random positions in chess (8-man or greater positions) to find what percentage of legal positions in chess are checkmate positions, what percentage of legal positions are mate-in-1, what percentage are mate-in-2, or draw-in-1 or draw-in-2, etc. Even the question of how you generate a random position, while ensuring there isn't any skew in your sample, is a difficult one - I've seen some of John Tromp's work on this and it's clearly complicated.
- Overall - mapping chess. Figuring out what percentage of legal chess positions are 'solved'/known, as checkmate, mate-in-1, mate-in-2, draw-in-1, draw-in-2 etc, figuring out what percentage of legal chess positions aren't solved, and mapping all of this. A further example - many chess positions exist (8-man or greater) where one side has a significant material advantage (with the other side having insufficient material to checkmate) and likely have a short mate-in-x sequence available, though likewise many of these positions will be stalemate positions instead - one could categorise these positions and produce estimates for how many are mate-in-x for the winning side and how many are stalemates/draws, thereby further mapping out how many chess positions are 'solved', and reducing the number that aren't.