Savage Worlds probability calculation

Over at A Critical Kobold Review of Savage Worlds the Kobold asks, "So, while it's harder to succeed on a lower die, your chances of getting an ace and thus rerolling and getting a higher number are better. So, is it better to roll a d4 and get more Aces, or a d6 which gives some higher numbers, but fewer Aces?"

Assuming I understand the mechanic, the answer is: it's always better to roll a higher die. One could probably develop a mathematical proof of this, but one is lazy, so an Excel spreadsheet will have to do. Actually, I'll send the spreadsheet if anyone wants it, and just give the method here.

To calculate the chance of rolling at least X in a Savage Worlds dieroll using a die with a number of sides D:

1) Divide the target number X by the number of sides D and express the result as a quotient (Q) and a remainder (R). E.g., if you're rolling a d6 and your target is 10, you get 10/6, which has a quotient of 1 with remainder 4.

2) If the remainder is 0, then the probability is (1/D)^Q. In other words you need to roll the max Q times in a row to hit the target.

3) If the remainder is nonzero, then the probability is [(1/D)^Q]*(D+1-R)/D. In other words, you need to roll the max Q times in a row, then you have to roll at least the remainder to hit the target.

So I made a spreadsheet that looks at all the probabilities for d4, d6, d8, d10, d12, and d20 up to a target value of 40, and it turns out that having a bigger die always helps you. The only tricky thing about writing the formula is handling the two separate cases of a zero and nonzero remainder. While you could use a boolean formula for this, the easiest way I could think of was to write the formula as in (3) but to use the MIN function to make sure the second factor was always at most 1.

BTW, while Excel has a Quotient function, the remainder is known as the MOD (modulo) function.