I worked out the probability of scoring at least x successes on n dice for a given test - were people looking for that a bit ago?


I don't know how to make equations look pretty in bbcode, here.. so it might be hard to read.

A few notes:
(1) n! = n*(n-1)*(n-2)*...*3*2*1
(2) Sum((i=1 to n), A_i) = A_1 + A_2 + A_3 + ... + A_n

Then the probability P(x) of rolling exactly x successes on n dice is:

P(x) = (1/3)^x * n! / (x! * (n-x)!)

And the probability of rolling at least x successes on n dice is:

Sum((i=x to n), P(i) )

Can anyone make that look a bit nicer? Or does that work...?

Feel free to double check my math, too. I'm certainly not immune to error..
Edit: Ignore these calculations. Not accurate. Damn.

Wait ... crap. That 2nd part doesn't look right.

Try using

You asked for something to make your math look pretty. Ain't my job to be supplying the math.

just on a side note, there are already some old threads with this information in them. i remember the threads existing, but my search-fu has failed me as far as finding them....

so if you can track down those threads, you can save yourself the bother of making anything look pretty =D

Well, the most obvious error is that you have a variable k as the lower index of summation which is never actually defined or provided.

(Yeah, it's trivial to figure out what it should be, but it's still wrong)

~J

k is a better choice (m might be even better), since x traditionally implies a real number where you want an integer or natural number.

Though I guess k is usually considered a real as well, and an unspecified constant at that. If you're in the mood for nitpicking, go with m.

~J

Oh, don't be so lazy. Add in probabilities if you throw in edge at first.

If you think it's complicated now, wait til the rule of six rears it's ugly head

I worked it out by hand for DP 2 and DP 3, treating it as "need 3 on 1d3".
DP 2: 44% 0 hits, 44% 1 hit, 11% 2 hits (totals 99% due to rounding)
DP 3: 30% 0 hits, 44% 1 hit, 22% 2 hits, 4% 3 hits

So if you only need one hit - eg firing a gun or throwing a rock at a static person-size target - then you have better-than-coinflip odds even at low DP.

Adding chance of crit-glitch is more math that I'm up to off the cuff.

Here are the probabilities for dice counts up to 20. I'll post the exploding results when I get rid of a minor accuracy bug.

I used a simple recursive calculation.

Basically, if you have know the roll probabilities for 1 die:

I put together some nice tables in PDF format regarding these types of probabilities. However since I've moved from cable to DSL I lost my webspace (Curse you DSL). So until I get myself an alternative I don't have them hosted. But if you'd like them PM me your email and I'll send them to you.

Edit: Here's my original thread. The links are broken until I can get these rehosted somewhere. In the mean time, like I said, PM me and I can EMail them to you.

http://forums.dumpshock.com/index.php?showtopic=16917

Actually, lets first throw out the E portion and then do a by hand demo of 2 dice:

http://en.wikipedia.org/wiki/Binomial_distribution

For at least n successes, evaluate the cdf at n-1, and subtract from 1, yes?

For exactly n successes, evaluate the pdf.

http://mathworld.wolfram.com/MultinomialDi...stribution.html gets you past the glitch hurdle, but, computationally, to generate the entire table, it's as expensive as the brute force calculation (since you do in fact need the entire probability map to answer the glitch question), and isn't of much help when it comes to exploding dice.

Actually, I've just realized I may have a bug in my glitch calculations when dealing with exploding dice. Given 3 dice, exploding, would any of these results be considered a glitch:
1, 1, 6:6:4 (2 hits, 2 original 1s, 3 original dice, 5 total dice)
1, 6:1, 6:1 (2 hits, 1 original 1, 3 total 1s, 3 original dice, 5 total dice)
1, 6:4, 6:1 (2 hits, 1 original 1, 2 total 1s, 3 original dice, 5 total dice)

Oh, yeah. The (1-1/3)^i part being the assurance that none of the other n-i dice are successes. For some reason I was specifically ignoring binomial expansion when I first posted. No idea what my justification was, at the time...

Exploding dice should be able to be incorporated by sticking a geometric sum in the summand somewhere.