For the general case, For simplicity,we can write z[-1,N]=0 and z[M,-1]=z[M,-2]=z[M,-3]=-1And for M>=0 and N>=0, z[M,N]=1+1/3*Max(z[M-1,N],1+z[M,N-1])+1/3*Max(z[M-1,N],1+z[M,N-2])+1/3*Max(z[M-1,N],1+z[M,N-3]).1 corresponds to dice=4,5,6, second term to dice=3, third dice=2 and last dice=1.We can see:* for dice= 3, 1+z[M,N-1] is always > z[M-1,N] so use a bullet if you roll 3.* for dice= 1, 1+z[M,N-3] is always < z[M-1,N] so use a heart if you roll 1.* for dice=2, it depends. It's better to use an heart if the number of heart is >= number of bullet-x(number of bullet), x starts from 0 and increases slowly (x(5)=1 and x(10)=2).z[3,3]=8.18.Need probabilities to meet a token, a zombie or both to solve the general case (with the rules of 5 hearts)
Last edited by Vanubis1
on September 16th, 2015, 10:00 pm, edited 1 time in total.