>>11923099Then how about you tell me where the mistake is?
I found a typo but it still gives me a strange answer.
Let x1 be the probability of picking the number 1.
Let x2 be the probability of picking the number 2.
Let x3 be the probability of picking the number 3.
Let x4 be the probability of picking the number 4.
Let x5 be the probability of picking the number 5.
P(Winning) = x5 * P(Winning | You pick 5) + x4 * P(Winning | You pick 4) + ... + x1 * P(Winning | You pick 1)
P(Winning | You pick 5) = (x1+x2+x3+x4)^4
P(Winning | You pick 4) = (x1+x2+x3)^4+6*x5^2*(x1+x2+x3)^2+4*x5^3*(x1+x2+x3)+x5^4
P(Winning | You pick 3) = (x1+x2)^4+6*x5^2*(x1+x2)^2+4*x5^3*(x1+x2)+x5^4+6*x4^2*(x1+x2)^2+4*x4^3*(x1+x2)+x4^4+6*x4^2*x5^2
P(Winning | You pick 2) = x1^4+6*x1^2*x3^2+6*x1^2*x4^2+6*x1^2*x5^2+4*x1*x3^3+4*x1*x4^3+4*x1*x5^3+x3^4+6*x3^2*x4^2+6*x3^2*x5^2+x4^4+6*x4^2*x5^2+x5^4
P(Winning | You pick 1) = x5^4+x4^4+x3^4+x2^4+6*(x2^2*x3^2+x2^2*x4^2+x2^2*x5^2+x3^2*x4^2+x3^2*x5^2+x4^2*x5^2)
So if I tell the tool to maximize
x5*(x1+x2+x3+x4)^4+x4*((x1+x2+x3)^4+6*x5^2*(x1+x2+x3)^2+4*x5^3*(x1+x2+x3)+x5^4)+x3*((x1+x2)^4+6*x5^2*(x1+x2)^2+4*x5^3*(x1+x2)+x5^4+6*x4^2*(x1+x2)^2+4*x4^3*(x1+x2)+x4^4+6*x4^2*x5^2)+x2*(x1^4+6*x1^2*x3^2+6*x1^2*x4^2+6*x1^2*x5^2+4*x1*x3^3+4*x1*x4^3+4*x1*x5^3+x3^4+6*x3^2*x4^2+6*x3^2*x5^2+x4^4+6*x4^2*x5^2+x5^4)+x1*(x5^4+x4^4+x3^4+x2^4+6*(x2^2*x3^2+x2^2*x4^2+x2^2*x5^2+x3^2*x4^2+x3^2*x5^2+x4^2*x5^2))
under the constraints
x1+x2+x3+x4+x5 = 1
x1 >= 0
x2 >= 0
x3 >= 0
x4 >= 0
x5 >= 0
It now tells me that x1 = x2 = x3 = x4 = x5 = 1/5.
