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<blockquote data-quote="mamba" data-source="post: 9107862" data-attributes="member: 7034611">yes, the chance obviously gets lower, but unless the goal is to just roll the highest number, that does not matter.Exploding dice means that you roll again when you do roll the maximum number, and that is what evens things out.Simply put, the chance of rolling the highest number on an n-sided die is 1/n, the average roll is (n + 1) / 2. So your second roll on average is (n + 1) / (2 * n) or an increase of roughly 0.5 over your first roll. Repeat for additional maximum rolls.This is close to the series (1/2)^x, the sum of that is 1. So no matter what sided dice you use, having it explode increases the average roll by essentially 1. A d4 then has an average of 3.5, a d6 of 4.5 and so on. The increase is essentially constant, the smaller die does not increase the average result more (by much, there is a little bit of rounding here)</blockquote>

[QUOTE="mamba, post: 9107862, member: 7034611"] yes, the chance obviously gets lower, but unless the goal is to just roll the highest number, that does not matter. Exploding dice means that you roll again when you do roll the maximum number, and that is what evens things out. Simply put, the chance of rolling the highest number on an n-sided die is 1/n, the average roll is (n + 1) / 2. So your second roll on average is (n + 1) / (2 * n) or an increase of roughly 0.5 over your first roll. Repeat for additional maximum rolls. This is close to the series (1/2)^x, the sum of that is 1. So no matter what sided dice you use, having it explode increases the average roll by essentially 1. A d4 then has an average of 3.5, a d6 of 4.5 and so on. The increase is essentially constant, the smaller die does not increase the average result more (by much, there is a little bit of rounding here) [/QUOTE]

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