Assume you have a standard dice with labels 1, 2, 3, 4, 5, 6 on each respectively. Pretend you are playing a simple game where you roll the two dice and add their values together. Is it possible to relabel the dice using positive integers in such a way that if you play the same dice game you would have an equal probability of rolling the same sums?
Note: What I mean by relabeling is not simply rotating all of the numbers on the dice where by each dice still contains the same six numbers but rather actually making new dice that has a different set of six integers than the original. (e.g. one dice could be 1, 2, 3, 4, 5, 9 and the other could be 1,1,1,1,1,1 ... would this pair produce the same sum probabilities as the original?--in short, no )