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I believe that mate with King, Bishop and Knight vs lone King can take up to 49 moves, which is the reason for the 50-move rule. IIRC, computer studies of more complex positions have shown mates requiring over 200 moves--which might or might not transgress the fifty move rule, as any capture or pawn move resets the clock. But in any case, the line has to be drawn somewhere and some wins (if arbitrary length games are allowed) will be draws under an x-move rule. I believe the 50-move limit should be increased for a larger board, but reduced for more powerful pieces (for the board size). The technical way would be to calculate the average crowded board mobitity of each piece (using Betza's method), then add up these values to get an approximation of the power on the board. Compare the ratio of this power to the number of squares to the ratio of the FIDE army (about 64, depending on the magic number) to 64 squares = about 1. The formula is movelimit = 50 times board size divided by total army mobility. For FIDE Chess this is 50 * 64 / 64 = 50. To examples for your duodecimal game: 1. Total army mobility = 90 50 * 144 / 90 = 80 2. Total army mobility = 200 50 * 144 / 200 = 36 You can probably guesstimate accurately enough without actually doing the calculations.
Sometimes changing the board size can actually change to outcome. In shogi on a board of 10x10 or smaller, king and gold vs. king is usually a win. On boards of 11x11 or larger, it is almost never a win. This phenomenon usually rears its head where most of the mating power available is in short-range pieces.
I am just designing a doucecimal chess variant (on a 12 times 12 board) and wonder how many moves I should reserve for the modified 50 moves rule. I think, there should be sufficient moves such that knight and bishop and king still can mate a bare king. The number of moves theoretically needed is surely known, has someone the numbers ready for different board sizes?
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