Probabilities?

[Agent 333]

Ah, sorry for mistranslating you Uysses.

[Akerbos]

The machine ran for a day? Did he brute-force it? O.o I feel that a mathematician should be able to do better. Maybe I'll try to come up with some closed formula as I perceive some potential issues in the distribution on Outcomes. Showing only success rates hides a lot of interesting data.

[MOOSE]

I'm the "statistician" in question. I'm actually a physicist with a math minor who now makes his living as a software developer. The guys at CG had me run probability checks against two different dice rolling systems, one of which was eventually used. I decided to brute force it because a) I was a bit rusty with my probabilities (it's been 16 years since I took that class, and I've mostly used it for statistical and quantum mechanics problems since then), b) I was comparing each die set for multiple interpretations of the rules they'd given me, and c) they weren't paying me to do it; they just wanted the results. The program I wrote gave very detailed output for each of the two systems so that I could check any result if I so desired to make sure it was sorted correctly for each rule interpretation. I was originally asked to provide probabilities for dice pools between 2 and 20 in size. The smaller dice pools were trivial, but as the pool size grew, so did the time needed for that run. It was originally running with some graphic output so I could see progress, but that was slowing it down too much. With that, running a pool of 9 wound up taking most of a day. When I dropped the bells and whistles I was able to get up to 14 dice before the times needed for brute force got to that point.

[Uysses]

Thanks for the work on the game and thanks for describing your methods. I appreciate the work you put in to making the game a success. Especially as you did it for free!

I can see why you went for doing it by running iterations if you went out that far. And at 20 dice I can see why that killed your laptop. A recursive function that deep is a lot of cycles.

[Akerbos]

I decided to brute force it because a) I was a bit rusty with my probabilities (it's been 16 years since I took that class, and I've mostly used it for statistical and quantum mechanics problems since then), b) I was comparing each die set for multiple interpretations of the rules they'd given me, and c) they weren't paying me to do it; they just wanted the results. [...] With that, running a pool of 9 wound up taking most of a day. When I dropped the bells and whistles I was able to get up to 14 dice before the times needed for brute force got to that point.

Fair enough; I guess tenacy beats science sometimes (time to market, sanity preservation, ...). No offense intended, in any case; I hope that is assumed.

(By the way, runtimes of about a day are sweet. We work with biologists who have had calculations run for four weeks.)

[MOOSE]

Thanks for the work on the game and thanks for describing your methods. I appreciate the work you put in to making the game a success. Especially as you did it for free!

You're welcome. I'm not saying I was doing it for free. My name appears on a credits page for the first time in about 8 years and they sent me a complimentary copy of the book, but there was no monetary compensation, which is why I said they weren't paying me for it.

Fair enough; I guess tenacy beats science sometimes (time to market, sanity preservation, ...). No offense intended, in any case; I hope that is assumed.

None taken. You were obviously led astray by Alex's earlier misstatement that I have a Master's in math. My MS is in Physics. The difference isn't always clear to everyone, but there are plenty of jokes about how to tell the difference between us. My favorite involves a room with a bucket of sand on a table and fire in a wastepaper basket. Seeing the situation, a physicist will grab the bucket, carry it to the basket, and pour the sand over it, extinguishing the flames. A mathematician will grab the bucket and put it in the corner of the room nearest the door, thus reducing it to a problem that he has already solved.

[Glacialis]

As a former astrophysics student who ran out of college money, all I can say is that math is a necessary evil en route to discovering the secrets of the universe. An awesome evil, but an evil nonetheless.

[Morgenstern]

You can get a formula that represents each number of times a specific combination is found.
So if you take, say. (A+B+C+D+E+F)^2 and expand it (which you can do on Wolfram Alpha per the link above) you get something like:
a^2 + 2 a b + 2 a c+2 a d+2 a e+2 a f+b^2+2 b c+2 b d+2 b e+2 b f+c^2+2 c d+2 c e+2 c f+d^2+2 d e+2 d f+e^2+2 e f+f^2

Each term is a combination of dice, but using letters for each face (A=1, B=2, etc). So [2 a b] means a 1 and a 2. The coefficient represents the number of times each combination occurs. So [2 a b] means there are two ways to roll a 1 and a 2 on two dice i.e. 1,2 or 2,1.. Everything to ^2 is a pair.

Oooh baby. *Yoink*