A Dice Run is similar to a poker run, in that you go to several stops. It can be run as simple list of stops or a clue gathering and figuring expedition.
The basic premise is similar to a Poker Run so I'll refer you to the article on Poker Runs for more general information, but the gist of it it is that at each stop there is a cup of 5 (flexible) dice. The rider rolls the dice and the person at the stop rights their total score on the riders score sheet and initials it.
At the final destination the score is totalled up and the riders with the highest and lowest scores win.