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by guenther
Mon Aug 11, 2008 10:04 pm UTC
Forum: Mathematics
Topic: Something I've been wondering since 7th grade
Replies: 22
Views: 3472

Re: Something I've been wondering since 7th grade

I've wondered about this topic as well, but perhaps from the other end. I've always assumed that addition was the most basic, and multiplication and exponentiation were built on that. But why are addition and multiplication commutative while exponentiation is not?
by guenther
Mon Jul 21, 2008 5:52 am UTC
Forum: Mathematics
Topic: Randomly determining ranking (initiative from D&D)
Replies: 16
Views: 3054

Re: Randomly determining ranking (initiative from D&D)

That worked! Sorry it took me so long to reply. I was busy, and I wanted to make sure I could verify it all with code. It took me a bit to figure out how to program the two-variable polynomial multiplication, but then I figured out that 2D convolution works. If you're curious, I posted over on the W...
by guenther
Tue Jul 15, 2008 11:17 pm UTC
Forum: Mathematics
Topic: Randomly determining ranking (initiative from D&D)
Replies: 16
Views: 3054

Re: Randomly determining ranking (initiative from D&D)

It took me a while, but I figured out that this technique is wrong (but seemingly a good approximation). I can show this by boiling down the problem to something much simpler. Suppose instead of d20s we use coins, where Heads = 1 and Tails = 0. We have three players, A, B, and C. Rank them in numeri...
by guenther
Tue Jul 15, 2008 12:50 am UTC
Forum: Mathematics
Topic: Randomly determining ranking (initiative from D&D)
Replies: 16
Views: 3054

Re: Randomly determining ranking (initiative from D&D)

Hey Yakk, that's pretty cool stuff! That's what I was looking for. :) I liked your method of mapping it to a polynomial; I'd never seen that before. Is this a common technique for these types of problems? Now that I've seen the answer, it makes perfect sense to do it this way, but I had to map it to...
by guenther
Fri Jul 11, 2008 5:29 am UTC
Forum: Mathematics
Topic: Randomly determining ranking (initiative from D&D)
Replies: 16
Views: 3054

Re: Randomly determining ranking (initiative from D&D)

You're both probably correct. It's just that finding the exact solution gives me warm fuzzies. :)

I'll try the monte carlo thing. I don't know R programming, but I can probably figure out how to convert it to something I do know.

Thanks for the help!
by guenther
Thu Jul 10, 2008 6:39 pm UTC
Forum: Mathematics
Topic: Randomly determining ranking (initiative from D&D)
Replies: 16
Views: 3054

Re: Randomly determining ranking (initiative from D&D)

Doesn't work unless their bonus is fixed and known. If you have no idea what the distribution of bonuses is, you *still* can't do anything. Do you know this? In D&D, I doubt you would, as combat is usually between you/your party (who's bonuses you know) and monsters (who's bonuses you don't). T...
by guenther
Thu Jul 10, 2008 6:14 pm UTC
Forum: Mathematics
Topic: Randomly determining ranking (initiative from D&D)
Replies: 16
Views: 3054

Re: Randomly determining ranking (initiative from D&D)

Assumine everyone elses bonuses are known and N isnt too high, this is just algebra. If we let A be my final score (bonus+dice roll) then there are 20 values that A can take, each with a 0.05 probability. For each value of A, you can calculate the probability that its the highest/2nd highest/etc in...
by guenther
Thu Jul 10, 2008 6:14 pm UTC
Forum: Mathematics
Topic: Randomly determining ranking (initiative from D&D)
Replies: 16
Views: 3054

Re: Randomly determining ranking (initiative from D&D)

As noted, this is the issue. If everyone has an arbitrary random function, then you have absolutely no clue what the distributions are, and thus have no way to perform any statistics at all. If you'd be so kind as to fix that to a particular function, then we can proceed. That's what the simple ver...
by guenther
Thu Jul 10, 2008 4:50 am UTC
Forum: Mathematics
Topic: Randomly determining ranking (initiative from D&D)
Replies: 16
Views: 3054

Randomly determining ranking (initiative from D&D)

I'm trying to work out some D&D statistics for initiative. That better make sense to most people reading this board. :) Here's the simple version of the problem. You have N people; each person has a bonus (arbitrary integer) that's fixed throughout the whole game. Each person rolls a d20 (random...

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