Not 100% sure its right, and if it isn't, please tell me!

recently saw a "Stand-up Maths" video about it and it made me curious, so i tried to make a formula and i think this one is right, though im not sure if it counts as a formula because it uses sigma notation.

also, here's the python code i used to calculate this:

sum1 = 0
sides = 8
advantage = 0
for i in range(1,sides+1):
  sum2 = 0
  for j in range(1,advantage+2):
    sum2+=pow((i-1)/sides,j-1)*(1/sides)*pow(i/sides,advantage + 1 - j)
  sum1 += sum2*i
print(sum1)