The entropy bound for optimally compressed chess endgame tablebases

Let $H_x$ be the entropy of a position for an optimal search heuristic in chess, and let $L$ be an optimally compressed endgame tablebase capable of returning the perfect result for any legal and reachable position.

Entropy–tablebase bound. The relation

$$H_x \leq L \leq H_x + 1$$

holds. This connects the entropy of chess positions under optimal search with the space required to encode perfect endgame decisions; the source provides no evidence that the bound has been proved or disproved.