Contemplating the truth that the variety of choices for the most important seize is 9, the most important variety of strikes ought to come from positions with no captures out there, the place there are as many kings as attainable.
I simply self performed from the preliminary place a recreation the place white has managed to create 7 kings, leaving it 7 * 4 = 28 authorized strikes on this place W:B28,K32:WK6,K7,K8,K14,K15,K16,K22.
If there exists a sequence of strikes the place white creates 8 kings and locations the eighth king on sq. 23 earlier than the 40-moves rule kicks in, then white would have 8 * 4 = 32 authorized strikes.
Going even additional, if white creates 9 or 10 kings and locations them in the identical trend, apart from ninth and tenth kings someplace on the sting, then white would have 8 * 4 + 1 * 2 = 34 or 8 * 4 + 2 * 2 = 36 authorized strikes.
If I can show that white or black can by no means create greater than 7, 8 or 9 kings from the preliminary place (as a result of the opposite facet is pressured to seize), then I’d have a solution.
36 strikes appears an inexpensive higher sure, since that will imply that the opposite facet has solely captured 2 items, which appears to be like unattainable. Even capturing solely 3 items appears unattainable.
My very own reply does not fulfill me a lot, so I am nonetheless in search of details.
