In the Shadowrun RPG (at least, the edition I remember) one of the core mechanics of the game was that you rolled a number of dice equal to your skill against a difficulty number. Rolling a 6 meant you could re-roll that die and add the result to the total.
So, for example, say I have a skill of 3 and that I have to roll against a 10:
Die 1 = 4 -> no luck Die 2 = 6. I re-roll a 2 for a total of (6+2=) 8 -> still no luck Die 3 = 6. I re-roll for another 6. I re-roll again and get a 3. Total = 6+6+3 = 15 -> Yay!
How can I calculate the probability of me succeeding, knowing only the number of dice I have and the target number?