A Simplified Variant of Chess for which a Short Program Computes a Non-trivial Upper Bound for the Number of Reachable Positions Obtained from 65141475298198504104226577310812726424- 036 Naturally Defined Initial Configurations of Pieces

We simplify the rules of chess. We assume that the initial configuration of pieces is not fixed and satisfies some general conditions. Let I denote the set of all these configurations. By our assumptions, for every C
I, after 0 or more moves, the configuration obtained from C and the information who has a move determine the set of all ways of continuing the game i.e. the reachable position. For C
I, let R(C) denote the set of all reachable positions obtained from C. A short program shows that card (I) = 65141475298198504104226577310812726424036 and card < 42959232120882551923988994948073848799479217319544.