I'm creating a custom game with a very unique dice mechanic and need to make sure it is neither too powerful nor too weak. roll a d4. If 1-3, do not reroll the die. If 4, reroll the die AND add another d4. With my primitive math skills I know there is a 75% chance that starting with 1d4 will not yield an "split". However, I'd like to derive the formula to: calculate the average splitting" chances of rolling multiple "splitting" d4 calculate the chances of going from a single d4 to:5d4's,10d4's, 20d4's calculate the average total of the pool repeat using other die "bases", like d6, d8, and d10. In other words, will it increase the average total of the pool to go from d4 to d6's if you start with 1,2,3,4,5 dice? I'm using excel and can easily create formulas for dice with multiple crits and multiple fails and rerolls, but splitting dice is proving difficult with my current set up. Thank you for your time Samurai Jack ******************************************************************************************* I found a site called anydice.com and I found the solution to my problem.