My intention is to add a twist to the dice game called "10,000 dice" by using three colored pairs of casino dice. My thought is that more fun probability-scoring could be incorporated. My problem is that I am not a mathematician.
What is the probability of simultaneously rolling three sets of colored 6-sided fair dice (a red pair, a green pair, and a blue pair) and the red pair rolling the lowest pair-set, the green pair rolling a middle-numbered pair-set, and the blue pair rolling the highest numbered pair set?
For example, the red pair rolls a pair of twos; the green pair rolls a pair of fours; and the blue pair rolls a pair of sixes?
I'm thinking that if you were to roll such a combination you should earn quite a bonus. I'm also interested in hearing your thoughts about what the bonus should be if you are familiar with the game and its scoring.