The DRN, or Dominions Random Number, is the core randomization mechanic of Dominions. It is 2d6 exploding. That means two normal six-sided dice are rolled and summed, and any time a die comes up as a 6, the six is kept and the die is rolled again. However, for each successive roll, 1 is subtracted. That means if you roll a 6 that explodes and then rolls a 1, there is no net gain.
The randomizer in the DRN is not truly random, and distribution is not truly even, but the details of this are not clear.