Let E be some endgame in chess. Let 'B' be a 'bottleneck' set of positions where (say) White has a win. Let 'DB' be the set of positions that are currently wins for White but would be draws if all the positions in 'B' were defined as draws [in a Chess Variant called Chess(B)]. DB is a set of 'dependant positions' - 'dependant' because their wins depend on some position(s) in B being theoretical wins. Of course, B =< DB for all B, and so the 'Bottleneck Factor' |DB|/|B| >= 1. Now for the computational challenges: 1) Given an endgame 'E', what set of positions 'B' maximises the Bottleneck Factor |DB|/|B|? 2) what endgame 'E' has the greatest Bottleneck Factor? ... and the algorithmic challenge: 1) what ideas might help improve the efficiency of an algorithm to address computational challenge 1 above? Guy