third
The third order loss function, (1/6)Emax(X-x,0)*max(X-x-1,0)*max(X-x-2,0).
The geometric gains one factor of b = (1-p)/p per order against the same q^x, so where G1 is b*q^x and G2 is b*b*q^x, this is b*b*b*q^x. That form is correct at negative whole numbers too, unlike the lower orders' separate branches: at x = -1 it gives b^3/q, which is b^3 + b^2, the accumulation running one step the other way.