We have seen craps and how it is played based on the sum of two dice. And here is how the totals distribute. The question is: is there another way of throwing two dice (with another set of numbers on it) and playing the game of craps using the same rules.
Before finding the answer, let’s check how to represent a die. You can describe a die with this polynomial.
f(x) = x6 + x5 + x4 + x3 + x2 + x1
Rolling a pair of dice is nothing but multiplying this function with itself.
f(x) x f(x)= (x6 + x5 + x4 + x3 + x2 + x1) (x6 + x5 + x4 + x3 + x2 + x1)
x12 + 2x11 + 3x10 + 4x9 + 5x8 + 6x7 + 5x6 + 4x5 + 3x4 + 2x3 + x2
Check the table again; you will see from the coefficients and the exponents of the resulting polynomial that there is one way to roll a 12, two ways for 11 etc.
