However, other smaller chess versions (e.g. 5x5 w/ 20 pieces) are at least weakly solved and given the piece/pawn/move restrictions of this 6x6 variant, I wouldn't be surprised if a weak solution here is possible as well.
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. :-)
Given that 5x5 is (weakly) solved, even though your rough estimates would put its 20-piece 5x5 starting position outside the realm of possibility, I don't think you're discounting accurately how much a reduced board/piece/ruleset can affect those exploding permutations for 6x6 as well.
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.
For a more sophisticated estimation of the number of legal positions, taking into account _true_ legality (a legal position must be reachable by a sequence of legal moves from the starting position, however dumb), see https://github.com/tromp/ChessPositionRanking. You can probably filter their sample by number of pieces to gain pretty accurate estimations for number of 29-piece positions if you wish.
Improved counting shows the maximum to occur at 28 pieces [1] (also see the issue I filed on your github repo).
[1] https://www.chess.com/forum/view/general/on-the-number-of-ch...
> Upper bound estimate of possible legal chess position (counts en passant, castling, sides to move, allows underpromotions): 8.7E+45.
But how exactly is this number determined? Is this a sampling based estimate?
My 8726713169886222032347729969256422370854716254 is an exact upperbound on the number of so-called urpositions, and is not sampling based.
In any case it will be easier to continue this discussion at https://github.com/lechmazur/ChessCounter/issues/1