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Applause to Agback! Here's the # of ways of rolling an outcome 3 through 18 for the 3d6, 4d6 drop lowest, and 5d6 drop two lowest methods. These numbers can be generated by a lot of tedious counting or by using a complicated counting formula. oc____3d6_____4d6_____5d6...

Yup, that is an Exact way of rolling odds of 1-in-prime number. The approximation I was thinking of wouldn't involve rerolling. Instead play with dice probabilities such that their product = the probability of, say, 1 in 47, or 0.0213. One crazy fix would be: roll d20, accept 1 then roll d6...

This is a very good question: How to simulate the odds of an outcome by rolling dice. If one-in-ten, throw a d10. If one-in-500, throw a few dice, such that the s/r for every die multiplied together = 500. Here, r = # acceptable die results and s = # of sides. So in this example...

Let me restate the method I like to use. Granted, it's not an official method, but I think it offers the best of point buy and random generation. Besides, rolling multiple characters and selecting the best one isn't an official method either. The method is based on the assumption--no...

This is not a general solution (equation), since I did a lot of counting for only the 4d6 drop lowest and 5d6 drop 2 lowest methods, but here at least are these results. To check with. # ways: oc___3d6____4d6____5d6 18____1_____21_____276 17____3_____54_____610 16____6_____94_____935...

Good work LL42! At a glance this looks right, but to honor your formulae I'm gonna work out a couple examples when time permits. I'm 44 reg.

I'm guilty of propagating the "recursive" code label--sorry! Can anyone add to LL42's explicit equation for the #ways a single outcome can be achieved for two kinds of dice, each rolled a parameterized # of times? I haven't dived into it yet.

That's like cheating. It's not the wheel that's interesting, it's how it was invented. For some of us, anyway.

That's beautiful LazarusLong42! Hell, I've had problems with my symbology. It's also nice not to have those clunky IF statements.

Maybe I should have sold my site more. On it are two spreadsheets which take into account improved critical, power attack, and damage reduction. Simply parameterize the fighter and weapon or weapons he wields, including weapon-specific feats, etc., and choose DR for the opponent. Then against...

And/or visit my site: http://www.geocities.com/frisbeet/DandDandFightin.html I believe 3e has TWF right, except I'd like to see TWF and ambidexterity merged to a single feat. Damage/round wise it's very comparable to expertly wielding a two-handed weapon, if you take all the feats needed to...

True enough Storminator. Was in a hurry, and I was starting to confuse myself posting that reply. So it's corrected now, but let the record show that originally the 2nd term in my example was quite wrong. I'd like to see how this checks out with lots of dice handled by some of the recursive...

Sure thing. I made an error in the orignal formula (since corrected), which might have thrown you off: ...IF[oc<(i*n+s)... should read ...IF[oc<(i*s+n)... Here's the logic behind the formula # ways = COMB(oc-1,n-1) + SUM(i=1,n-1) {(-1)^i * IF[oc<(i*s+n),0,COMB(n,i)*COMB(oc-i*s-1,n-1)]}...

An example, because I don't want this thread to die today. If # ways = COMB(oc-1,n-1) + SUM(i=1,n-1) {(-1)^i * IF[oc<(i*s+n),0,COMB(n,i)*COMB(oc-i*s-1,n-1)]} Then for 4d6, # ways of getting a 17 = = COMB(16,3) - COMB(4,1)*COMB(10,3) + COMB(4,2)*COMB(4,3) - 0 = 16!/(13!*3!) -...

Well, I'm not good at math terminology. So I'll create my own, replete with IF statements. I'm not sure but what this replicates Kugar's work, except that it works for all outcomes(for identical dice). Again, oc = outcome n = number of identical dice s = sides of die Also, COMB(a,b) =...

In the spirit of Drawmack's posts, particularily the discrete mathematics ref., help me with this: oc = outcome n = number of identical dice s = number of sides on die Then sometimes, #ways= (oc-1)!/[(oc-n)!(n-1)!] - n*(oc-s-1)!/[(oc-n-s)!(n-1)!] So for 3d12, the # of ways of getting a 19...

bahh! All you CS people like programs. I don't even know how to get my PC to do that crap, and I don't wanna know (actually that last part's not true). Give me tables, like the logarithm tables of old. I mean, there is an explicit answer to these probabilities--it's not like the three-body...

Another unconventional method (mentioned by me on this board before): For a 1-in-216 character, assign an 18 to a single attribute of your choice. Roll 3d6 for the other 5 attributes. I paid too much money for my stuff to play an average character--I already have that in spades in reality.

This is a great question! I've wondered too about an analytical formula for determining the probability of achieving one outcome from throwing some set of dice. I couldn't figure it out. The issue to which I wanted to apply this idea was D&D weapon damage calculations. Determining the...

Also posted on the WotC boards--not an apology, but an admission. Wanted to advertise a tool I've pimped here before, because I think I've got it to be pretty useful, if a little slow to download. Check out: http://www.geocities.com/frisbeet/DandDandFightin.html What it'll do is allow you to...