| We can do a rough estimate. There are (_very_) roughly half as many squares in 6x6 as there are in 8x8. This means that for every piece you add, you can expect (again very roughly) a 50% bonus to your branching factor. Now look at the best tablebases currently available (Syzygy): Up to 5 pieces: 1GB
Up to 6 pieces: 151GB
Up to 7 pieces: 17277GB So, let's assume the factor of 140 per extra piece; of course this doesn't hold perfectly, but still: Up to 8 pieces: 2418TB
Up to 9 pieces: 338PB
Up to 10 pieces: 47320PB Now divide that last number by our 2^10 bonus. That leaves 46PB for 10-piece tablebases. We were asked for 24-piece. This is unlikely to go down well. Of course, there will be some small additional bonus for the fact that fewer positions are possible (easier to be in check), double-pawn-push doesn't apply, no en passant or castling to worry about, and fewer piece types. Still, it honestly doesn't look that good. :-) |
It is only an argument against building a complete tablebase. Additionally because the extra space is reduced the high piece count version is likely the be much smaller than this would predict because pieces cannot overlap.
Just looking at the piece positions without regard to the types shows a better than 2x relationship for tablebase size.
(64 choose 7) / (64 choose 8) ~ 10% whereas (36 choose 7) / (36 choose 8) ~ 25%
Additionally, because the tablebase would need to go past 18, the possible piece positions would actually shrink. To be clear, the tablebase would not shrink because of the piece types.