  We show, assuming weak large cardinals, that in the context of games played
in a proper class of moves, clopen determinacy is strictly weaker than open
determinacy. The proof amounts to an analysis of a certain level of $L$ that
exists under large cardinal assumptions weaker than an inaccessible. Our
argument is sufficiently general to give a family of determinacy separation
results applying in any setting where the universal class is sufficiently
closed; e.g., in third, seventh, or $(\omega+2)$th order arithmetic. We also
prove bounds on the strength of Borel determinacy for proper class games. These
results answer questions of Gitman and Hamkins.
