Say there is a dice with six faces, each face has a positive real number different from others. There is a chessman on the origin of the number axis. After the dice rolls, the chessman moves forward the distance as the dice rolls out. And the dice rolls again, the chessman moves on. For every point on the number axis, there is a chance that chessman walks on it. If a point, if exists, owns a highest chance over others on the axis, we call it the Best Point of the dice. If a dice, if exists, whose Best Point's chance is over other dice, then the corresponding six-number array is the Best Array, and its Best Point is called as the Best Best Point. The question is to get the Best Array.

Supposing the six numbers are $0<x0<x1<x2<x3<x4<x5$, for any real number n, there exists:

$f(n) = (\sum_{i=1}^6 f(n-x_i))/6$ $(n>0)$

$f(n) = 1$ $(n=0)$

$f(n) = 0$ $(n<0)$

According to the formula above, there are some easy conclusions I have got, based on the exist of the Best Array:

[1]: For any dice, the smallest best point should be in its six-number array;

[2]: The best best point should be $x_6$

[3]: For the best array, $x_6 = x_i + x_j (\exists i,j, 1<=i, j<=5)$

[4]: The numbers of the Best Array are in the same field, which means there exists an integer version of the Best Array

[5]: Multiple the numbers of the Best Array by some number produces a new Best Array, which means there exists the most simplified integer version.

Using greedy algorithm or some program, I pretty sure the most simplified integer best array should be [1, 2, 3, 4, 5, 8]. However, I have no clue about proving it.