I design games, systems, whatever. I run games. I like to know what the fuck I'm doing. I want to run a NWoD game, but I've run into a problem.

I don't know how to calculate odds on a dice pool. Very frustrating. Here's what I'm looking at:

In the rules, any result of an 8-10 on a 10-sided die is a success. That's a 3/10 or 30% chance of success for a single die. I estimate (perhaps wrongly) that it takes 4 dice to have something approximating a sure success on a single die. You only need one success to be successful unless rolling against something.

If you have a specialization in what you're rolling, 10's give a bonus roll.
1's only botch if you're going for a 'chance roll' - a roll where you're rolling when you have no dice left or no relevant dice.

How do I figure out the odds of X successes on Y dice given 30% odds on a single dice? What if you factor specializations in?

I want to know because I like knowning what I'm doing. In D&D, I feel confident in the creatures I design because I understand how the d20 works with the skills and other modifiers. But I'm not good at math, so I can't figure these. I know it's probably not too crucial, but I like covering all my bases, and this is irritating me.

(I held off posting this because it's all NWoDy, and I guess people are biased against it. I didn't want 'why don't you use a different system' arguments, but I figured, what the hell, I'm trying to run a game here. At least it's not bitching about something, right?)

Is the matter compounded by 1 = failure (botch?) cancelling a success? I'm not too up on nWoD.

- Q

Botches (and specialisations?) aside, the percentage chance of getting X successes on Y dice appears to be:

(3 * X) * (100/(Y * 10)) = %

I think that's right.

What I find interesting about this is that where X = Y, it always stays at 30%. That's obvious, really, but I've never thought about dice pool probability before.

- Q

1's arn't botches anymore, I gather. Which is nice, considering I think botches really weight the system towards 'failure' more then I'd like.

But I really appreciate that formula. I'll mess around with it and test what I find later.

Ooh, this just occurred to me. It can be simplified to:

(3 * X) * (10/Y) = %

I blame the beer.



- Q

Awesome.

Quote from: QuireBotches (and specialisations?) aside, the percentage chance of getting X successes on Y dice appears to be:

(3 * X) * (100/(Y * 10)) = %

I think that's right.

That's totally not right.  First of all, you've got your X and Y reversed.  i.e. More dice should increase the chance of getting X successes, not decrease it.  

The above suggests that on two dice, there is a 60% chance of getting 1 success.  Actually, there is a 9% chance of two successes, a 42% chance of one success, and a 49% chance of zero successes.  

I'd recommend using some software if you can.  I have a page of Dice Mechanics Links.  For most dice questions, it's better to use a computer to run through all the probabilities rather than just trusting your math.  I haven't used Troll or such, but some people have used them well.  For ten dice or less, it's pretty quick to run through all possibilities.  

I can generate a table pretty quickly -- just suggest the format.  (I have a similar page for Trinity dice mechanics, say.)

Ooh. Me and my crappy maths! Sorry to have led you in the wrong direction, Thanatos!

- Q

IIRC, it's not just specialized skills that 10s repeat on - the specialty just gives you an extra die.  Your friend Joe actually has the answer to your prayers lying around on his server.

-=EDIT=-
And here's some non-graphical probability tables that are probably more useful in the long run.

Ugh. Math is hard.