[thethirdone]

Your analysis would pretty similarly apply to 5x5 Gardner's chess which has been weakly solved. Simple tree search can be quite effective as the branching factor is cut down a significant amount (2x in the starting position). Gardner's chess was completely solved without any tablebases.

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.

[Sesse__]

I'm not sure if you can call it “completely solved” if it's only weakly solved, but sure. It's a different goal (and my answer was a response to a “can't we just build a tablebase” comment).