I just discovered something that I thought was very interesting. The concept/mechanic is EXPLODING DICE. It can work a number of ways. You roll a number of dice and if you roll the target number you roll it again. You can either count the first roll or not.

Example of counting the first roll: You roll 3d6 and on any rolls of 6 you count the roll and then roll those 6s again. This can result in amazingly powerful results. So, you roll a 1, 3, and a 6 for a total of 10. You then re-roll the six and get another 6 for a total of 16. You then re-roll again and get a 4 for a total of 20.

Example of not counting the first roll: You roll 3d6 and on any rolls of 1 or 6 you do not count those die rolls and then roll those dice again. This will remove the outlier effects of extremely low rolls and extremely high rolls. I think it would make the game rather boring, but if you want to remove “strange” outcomes this would be the way to do it. On the other hand you could do something really crazy and remove any rolls of 3 or 4 without counting and then re-roll those dice. This would do the exact opposite creating either extremely high rolls or disastrously low rolls.

Using different types of dice will have an even more profound effect. D4 dice will have a much higher probability of hitting the high number and thus causing a potentially cascading effect of EXPLODING DICE if you use enough D4s. If you roll 5 D4s you should get 1 to 2 4s, but if you get 3 or 4 4s then the re-rolls could continue for some time.