LATER EDIT:

If you have {000777} then 7 beats everything and zero beats nothing so the probability of a win is 18/36

I want to show that if you change a 7 to other numbers that add up to 7 the number of wins goes down.

General theorem. A number n beats everything lower so the number of wins associated with n is (n-1)

If you change n to a lower number m:

There are two new numbers generated by this: n-m and m

The win total from n-m is (n-m-1) and from m is (m-1) so the new total is (n-m-1) + (m-1) = n - 2 so the change has caused the total wins to go down (n-1 drops to n - 2)

This happens whenever you substitute a lower pair of numbers. So reducing a 7 will lower the win total. So {000777} is best.

example {002577} The win total is now 1 + 4 + 6 + 6 = 17.

Bob

]]>The reason I said there is no point is because 8 and 7 give you the same chance of winning so does 9 and so on.

Sides can also be 0]]>

I see no point of using numbers above 7

I'm wondering if you meant above 6 here? If your modified die is {7,7,7,7,7,7} then you win every time. If {6,6,6,6,6,6} then the probability is 30/36.

Am I following your post correctly?

Bob

]]>The sides of a typical 6 sided die add up to 21. So with a 6 sided die whose sides add up to 21, what is the highest probability you can get to win in a die rolling contest against a normal die. Ex 0,0,3,6,6,6 has a 17/36 chance of winning. You can not put negative numbers, and I see no point of using numbers above 7.]]>