I have three sets of numbers, each one going from 1 to 21 (actually from -10 to 10, but it's still 21 numbers total per set). How do I determine how many possible combinations of three numbers there are?
Also, and this is just because I'm feeling a bit lazy at the moment, how do you determine a PCs chance to hit any given AC? For example, if a PC has a +3 to his attack, what formula would you use to determine his chance fo hitting, say, and AC14?
My husband and I used to know the formula for this, but we're drawing blanks at the moment:
I have three sets of numbers, each one going from 1 to 21 (actually from -10 to 10, but it's still 21 numbers total per set). How do I determine how many possible combinations of three numbers there are?
If we're keeping track of which one is first, which one is second, and which one is third, it would be 21^3 or 9261 possible combinations. If order is not tracked, it's 21*20*19 or 7980.
Also, and this is just because I'm feeling a bit lazy at the moment, how do you determine a PCs chance to hit any given AC? For example, if a PC has a +3 to his attack, what formula would you use to determine his chance fo hitting, say, and AC14?
[AC] - [Attack Bonus] * 5 = %chance.
so...
(14 - 3) * 5 = 55% chance to hit.
And thanks for the AC chance to hit formula!
Wow, thanks for the quick response! For the number ranges, I was reading the old 1e MotP and it gave a list of potential variables for alternate Prime Material Planes in physical, magical, and temporal variations from the PCs Prime Material Plane, which would be listed as 0, 0, 0 (the D&D world as we know it). Since we would be keeping track (as the first number in the set represents the physical properties, the second magical, and the third temporal), then I would use the 21^3 (9261)?
And thanks for the AC chance to hit formula!
If you can duplicate any number in any of the three variables, the chance of any given combination is 1 in (21)3 or 1 in 9261. The chance of getting 8,8,8 and -8,-8,-8 are all the same.
Now, if a value can only be present once in an array (-8 has been used, and cannot be present in the other two registers) then it becomes 12*20*19:1. If you have x number of repeatable integers, just use the number of registers as the exponent. The other should be obvious.
Sorry, felt that needed a tad bit of clarification. Apologies to all.
-Sarena
Wow, thanks for the quick response! For the number ranges, I was reading the old 1e MotP and it gave a list of potential variables for alternate Prime Material Planes in physical, magical, and temporal variations from the PCs Prime Material Plane, which would be listed as 0, 0, 0 (the D&D world as we know it). Since we would be keeping track (as the first number in the set represents the physical properties, the second magical, and the third temporal), then I would use the 21^3 (9261)?
To me it does sound as if the numbers used to measure the variations are independent of each other so you would, in this case, use the 21^3 formula which would give you the 9261 different possibilities.