This made me laughIf a little money were to change hands,is it possible for you to produce a different ranking, which you can and must justify mathematically?

If you look at the sum of the rows in M, M^{2}, M^{3}, M^{4}; when put in order of highest to lowest they always have the same order so unless the constants are negative which would make no sense.

I only checked up to M^{4}, I didn't prove that in the general case their sums always have the same order but there is certainly a trend.