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In textbooks you find diagrams about key squares and similar concepts. For example, white can promote a pawn if white's king can control three particular squares infront of the pawn. I would like to analyze tablebase evaluations of multiple positions to arrive at similar but more complicated conclusions, for example going through all possible positions of King and Queen vs King and Rooks pawn on the seventh rank and show all positions of the white king that win (this is also known already, but you get the idea).

Which software could be used to query a tablebase in such a way? I would be very glad for any suggestions, thanks a lot!

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You can use Lichess. https://lichess.org/api#tag/Tablebase Here is an example where I used Lichess table base for my chess engine : https://github.com/PaulJeFi/ramses-chess/blob/main/tablebase_online.py

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