Re: [DL] Dice Rollin'

["Michael Sprague" <mds@rochester.rr.com>]

Yep, I think that's exactly what I did ... and why I pointed out that my
numbers were a little off, because they didn't take into account the chance
of Going Bust.  Heh!  Been a while since I had to force my brain to think
this way.

~ Mike

----- Original Message -----
From: "Johnny Burlin" <Johnny.Burlin@home.se>
To: <deadlands@gamerz.net>
Sent: Saturday, March 15, 2003 10:01 PM
Subject: Re: [DL] Dice Rollin'


> > No problem what-so-ever.  If my math was incorrect, I want to know ...
one
> > of the reasons I posted it.  Obviously, I didn't then do a proof.  :-)
My
> > numbers might be off when going above the max for a die as well ... I
based
> > it on the chance of getting an Ace, and may not have taken into account
the
> > chance of getting more than one Ace.  If so, that would mean that the
> > percentage chances are all slightly higher ... but not by much.
>
> I assume that you use:
> pd = chance of dice succeeding
> p = chance of roll succeeding
> n = number of dice
> p = 1 - (1 - pd)^n
> Or, in words, the chance of not all dice failing
> That takes care of everything. If not all dice fail,
> then at least one succeed, possibly more but that
> doesn't matter (in DL/HoE, it matters in other
> games, that uses successes, like Vampire or Shadowrun).
> Your numbers are correct as far
> as I can tell (no, I didn't check them all... ;-),
> with the exception of bustin', but as you clearly
> stated that you didn't handle that.
>
> The above formula is appealing since it is simple
> and takes care of everything except a bustin'.
> You need to do the combinatorial approach to
> solve that one, at least that is the only solution
> that I have found. The problem is that you need
> to compute the number of results that are busts
> but beat the TN.
>
> Let's do the 3D10 vs 7 case.
>
> There are 28 bust results.
> A "succeeding bust" result is:
> 1-1-(7-10)       4 combinations
> And there are 3 dice that can end up at 7+,
> 4 * 3 = 12
> The chance of getting a succeding bust is 1.2%
> Now, the chance of rolling 7+ on a single D10
> is 40%, on 3D10 it is 78.4% (1 - 0.6^3) but
> you also need to avoid the bust chance so the
> final probability ofs success is:
> 0.784 * (1 - 0.012) = 0.774592 ~= 77.46%
>
> > I understand this, but I only see 28 combinations.  What am I missing?
>
> Absolutely nothing, I somehow managed to get 3 * 9 to 29...
> No matter how much math you have studied, you can always
> screw up the basics... ;-(
> Yes, it should be 28, and the bust chance is 2.8%.
>
> /Johnny
>
>
>
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