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Message no. 1
From: davek@***.lonestar.org (David Kettler)
Subject: Probability Plots
Date: Sat, 16 Apr 2005 23:40:11 +0000
I had thought about doing something like this ever since the discussion of the new dice
rolling system in SR4 began. Basically these are plots of the probability of success as a
function of both the number of dice being rolled and for lack of a better term the
'difficulty factor' (TN in SR3, number of successes required in the speculative SR4 plot).
Originally I was going to do it analytically, but ultimately that proved to be difficult
to keep track of so I just took the lazy man approach and made the computer do all the
work. For each point on these graphs it 'rolls' 100,000 times and takes the percentage of
successes to get a pretty good estimate of the probability.

First, the SR3 plot:
http://davek.freeshell.org/sr3prob.jpg

Number of dice being rolled (from 3 to 12...less than 3 isn't really interesting) is on
the left, TN is on the right, and the probability of getting at least one success is on
the vertical axis. Nothing really earth shattering here. Note the clearly visible 5-6-7
artifact.

Now for the SR4 plot...well, I don't actually know what SR4 is going to use, so I plotted
what I personally view as the best suggestion: Varying successes required and
implementing rule of 6 behavior:
http://davek.freeshell.org/sr4prob.jpg

Again number of dice being rolled is on the left. On the right is a minimum number of
successes desired, and on the vertical axis is the probability of getting at least that
number of successes.

A couple things to note: First of all, unless you're rolling a *lot* of dice, there's
still a fairly high chance of failure even with only one desired success. Second of all,
the graph drops off much faster than the SR3 one. I plotted SR3 TNs up to 12 and SR4
desired number of successes up to only 6, and yet the SR4 plot still drops off noticably
faster. This could be a good or bad thing depending on how you look at it. Of course you
can't do a 1-1 replacement of SR3 rules because the failure rate would be so much higher,
but if you tweak the modifiers and reduce the number of modifiers (which would fit with
the whole 'make it simpler trend') then it could work. The last thing I'd like to note
about the SR4 graph is that it is overall much smoother than the SR3 graph, and the
probabilities tend to vary in a more sensible way. This is a good thing.

As for those who have voiced concerns that implementing the rule of 6 here would make even
an unskilled guy with a gun potentially deadly...well, so? I think it's pretty clear that
the probability of an unskilled guy with a gun taking out a skilled shadowrunner is
extremely low, but it is nonzero. I don't regard it being nonzero as a bad thing, though.
Guns are deadly. Even people who don't know how to use them occasionally get lucky.
It's good for runners to remember that and plan sensibly. Frankly I think it's a little
ridiculous how given the combat pools, augmented body scores, and armor of most runners in
SR3 they're basically immune to bullets fired by your average rent a cop. Maybe SR4 will
change that. And for those occasions of just shitty luck...well, isn't that what karma,
sorry, edge is for?

In conclusion I will remain cautiously optimistic about SR4.

BTW, if there are any other hypothetical probability curves (as I know there are plenty of
other theories out there) you'd like me to plot, let me know. It shouldn't be too hard to
implement them. As for the suggestion of just varying the number of dice...well, look at
the SR4 plot for a fixed desired number of successes and use your imagination. Personally
I think varying only one parameter is inferior to having a two parameter system, but I'm
not Fanpro.

Also if anyone would like to see my code or raw data, let me know.

--
Dave Kettler
davek@***.lonestar.org
http://davek.freeshell.org/
SDF Public Access UNIX System - http://sdf.lonestar.org
Message no. 2
From: jjvanp@*****.com (Jan Jaap van Poelgeest)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 02:33:59 -0700 (PDT)
--- David Kettler <davek@***.lonestar.org> wrote:

[snip]

> Now for the SR4 plot...well, I don't actually know
> what SR4 is going to use, so I plotted what I
> personally view as the best suggestion: Varying
> successes required and implementing rule of 6
> behavior:
> http://davek.freeshell.org/sr4prob.jpg

Might I ask how the ro6 behaviour was implemented for
the model?

[snip comparison of graph shapes]

I know noooothing about all this maths shtuff, but
probability&statistics isn't math, so I'm going to
have a go.

>From what I gather Graht has in fact managed to put it
quite well by saying that SR4 has "diminishing
returns" (but then, he's a playtester). SR4 appears
more "realistic" in that the higher levels of play
will involve the PC's being marginally more succesful
at very difficult tasks than total beginners. In other
words: in SR4 very difficult tasks remain very
difficult no matter how skilled one is, but the very
skilled do stand twice as much of a marginal chance to
succeed at the impossible.

In terms of the dice pool argument: throwing lots of
dice will result in more "guaranteed" successes than
very few dice. I.E.: when using very few dice, the
chance of getting no successes is bigger than the
chance of getting a success.
Thus when very few dice are involved, an additional
die increases the chances of getting that one single
success required to beat the more probable 0 successes
of the other pool more than when both pools involve a
lot of dice. If the target number were sufficiently
high (43, say) both pools would in fact stand very
little chance of achieving any successes at all,
rendering competition between them fairly purposeless
(that's my take on it, anyway).

On that note, what's the highest anyone's ever seen
rolled in-game? I think it must've been in the 20's
for me.

It appears required successes in SR4 map onto the TN's
of SR3 at a +2TN per success required (or maybe that's
just my shallow understanding of the matter). If this
is presumed to be the case, we find that chances of
getting a single success at tasks are lower in SR4
than SR3 across the board. On the other hand, a single
success in SR4 might be the equivalent of two (or even
more) successes in SR3 for resolving the in-game
effects (dependent on what skill is being tested),
which would probably even things out considerably.

[guns must be deadly]

I agree. Getting shot (at) should (always) be a
situation one wishes to avoid.

[nerfed NPC cops]

Well, if the cops notice a bunch of
far-too-heavily-armed&armoured people, they'll call in
the artillery. While crime is prevalent in Shadowrun,
if the cops get involved you should end up being toast
if you're not covering your tracks very well (though I
once tried to make this clear to a bunch of players
and just got shouted at, so since then I've been
running Shadowrun as the criminal's paradise it was
written as). Even if mere gangers have access to fully
automatic rifles, this doesn't mean they use them all
the time and all of life is so chaotic as to make
criminal proceedings impossible. Besides, modern-day
gangers potentially have access to that type of
weaponry and things go pretty well for the general
populace.
If a bunch of crazies is going to ram-raid a Lonestar
protected facility and are caught on camera touting
assault rifles and heavy body armour, then the cops
arriving won't be the local beat patrol. It'll be the
crack HRT team sneaking in the back door while any
exit routes are utterly sealed off by well-armoured
officers. I just can't imagine the 6th world to be
sufficiently callous that there will be "civilised"
regions (to be fair, in "The Barrens" and similar
regions almost anything goes) where those supposed to
be keeping law&order are purposefully ordered to face
threats far above their capability to deal with. If
the people handling the response consider a threat to
be above the average patrol's capability to handle,
they'll just send a yellowjacket or some drones out to
spy on the proceedings while trying to get a slot on
the HRT team's schedule (I do imagine these will be in
high demand).

> In conclusion I will remain cautiously optimistic
> about SR4.

I will probably like the new edition too.

cheers,

Jan Jaap



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Message no. 3
From: jjvanp@*****.com (Jan Jaap van Poelgeest)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 02:43:07 -0700 (PDT)
--- Jan Jaap van Poelgeest <jjvanp@*****.com> wrote:

> crack HRT team sneaking in the back door while any

> the HRT team's schedule (I do imagine these will be

I meant SWAT!

I think I in fact meant SWAT (though the Lonestar SB
probably has a unique name for something similar),
unless the runners botch the job and end up in a
hostage-taking situation (that movie... Swordfish let
someone get out of such a situation in a quite stylish
and hugely improbable manner, so I suppose it depends
on the plan).

cheers,

Jan Jaap



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Message no. 4
From: gurth@******.nl (Gurth)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 11:53:44 +0200
According to Jan Jaap van Poelgeest, on 17-04-2005 11:33 the word on the
street was...

> I know noooothing about all this maths shtuff, but
> probability&statistics isn't math

HAVO wiskunde A, so yes, you're right :)

> On that note, what's the highest anyone's ever seen
> rolled in-game? I think it must've been in the 20's
> for me.

Only in the 20s? ISTR 41 being rolled once, or maybe even higher than
that (44 or 46 or so).

> [guns must be deadly]
>
> I agree. Getting shot (at) should (always) be a
> situation one wishes to avoid.

And face it, many guns are not deadly enough in SR2/3 -- work out the
situation of someone with average skill and Body trying to kill himself
with a light pistol, for example. Others, of course, are a bit too much
(like sniper rifles or assault cannons).

> Well, if the cops notice a bunch of
> far-too-heavily-armed&armoured people, they'll call in
> the artillery. While crime is prevalent in Shadowrun,
> if the cops get involved you should end up being toast

IMHO, that's what every player should believe, even if it's not at all
true :)

> if you're not covering your tracks very well

I tried to point that out to my players, and they took it a bit the
wrong way, in that I guess they decided that the best thing to do would
be to leave no tracks at all -- and the best way to leave no tracks is
to not do anything unless you have to.

> Even if mere gangers have access to fully
> automatic rifles, this doesn't mean they use them all
> the time

Well... You could have a very deadly arms race developing. Let's assume
a situation in which all gangs have only basic weapons (light pistols,
knives, clubs, etc.). One gang then buys itself some shotguns, giving it
a lot more firepower than its enemies. Those enemies now buy shotguns
and SMGs to make sure they won't be wiped out, and the first gang then
buys assault rifles in response. The enemies now invest in LMGs, forcing
the first gang to dig up a MMG, missile launcher or something similar.

At some point in this race, a gang will, say, run out of money to buy
weapons with. So they have only two options: let their wealthier enemies
buy better weapons that may eventually be used to kill them, or attack
those enemies while the now-poor gang still has a firepower advantage.

Not to mention that once everyone has such weapons, nobody will want to
be the first to give them up in order to return to the more peaceful
times old. Just look at a few RL examples to see this in action, like
the armed groups in Northern Ireland with their weapons caches, or the
USA and Russia with their nuclear weapons.

--
Gurth@******.nl - Stone Age: http://www.xs4all.nl/~gurth/index.html
Kemen (keemde, h gekeemd): het spelen van computerspelletjes
-> Possibly NAGEE Editor & ShadowRN GridSec * Triangle Virtuoso <-
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Incubated into the First Church of the Sqooshy Ball, 21-05-1998
Message no. 5
From: jjvanp@*****.com (Jan Jaap van Poelgeest)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 06:37:11 -0700 (PDT)
--- Gurth <gurth@******.nl> wrote:
> According to Jan Jaap van Poelgeest, on 17-04-2005
> 11:33 the word on the
> street was...

[gangs with nukes]

I don't think things would necessarily happen that
way: in the 6th world gangs are just small game and
there are plenty of environmental factors other than
just gangs that keep them from getting too powerful.
Maintaining the status quo is a serious concern for
the next step up in the streets (criminal
organisations & security firms). Open gang warfare
will often be bad for business and these organisations
have their own affiliated toughs to make sure it
doesn't happen (too often).

If a gang is running behind in an arms race, all kinds
of things could happen. For example, after catching
one of the gang members at trying to buy highly
illegal weaponry (with the PCs help), a Lonestar
official might indirectly pass on the recently
"acquired" security keycodes of a local Weapons World
(with the PCs help), seeing as how the gang's turf is
patrolled by Knight-Errant security and Lonestar would
like to see them very busy (more potential for a few
runs for the PCs). To add just a little bit of depth,
this is in fact part of a gambit by "insert yet bigger
player x," who/which is trying to (subtly) alter
events to bring about "advantageous situation y" for
"reason z". The clue to this depth is hidden in
"corporate memo q" on the Lonestar official's
Pocketsec, so the PCs will have to be thorough if they
want to be actively aware of the bonus plotline, or
the GM will just have to hand it to them. The point
for the PCs would be that "bigger player x" might have
taken notice of their meddling (especially if it was
the PCs tracking him/her/it down) and therefore wants
to entrust them with (one or more) tasks to be carried
out, thereby making the PCs the decisive facter
whether or not "advantageous situation y" occurs.
Result: PCs actions make it into the Intelligencer, a
new contact with potentially goodsome and more
interesting runs has been made and new toys can be
purchased.

I recon the above could keep a group of at least 4
busy for 2 to 3 month's worth of gaming sessions. All
this because of a gang running behind in an arms race
(given that the rest was made up after I assumed
that). It'd be a terribly boring campaign though,
because all this stuff's already been decided upon :).

cheers,

Jan Jaap



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Message no. 6
From: davek@***.lonestar.org (David Kettler)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 17:57:15 +0000
On Sun, Apr 17, 2005 at 02:33:59AM -0700, Jan Jaap van Poelgeest wrote:
> --- David Kettler <davek@***.lonestar.org> wrote:
>
> Might I ask how the ro6 behaviour was implemented for
> the model?
>

I used the behavior suggested by me and others to avoid the
don't-have-enough-dice-to-succeed pitfall. Basically when you roll a 6 it not only counts
as a successs but also gives you the chance to roll again. This let's any number of dice
being rolled achieve any number of desired successes, but with rapidly diminishing
probability.

--
Dave Kettler
davek@***.lonestar.org
http://davek.freeshell.org/
SDF Public Access UNIX System - http://sdf.lonestar.org
Message no. 7
From: maxnoel_fr@*****.fr (Max Noel)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 19:08:57 +0100
On Apr 17, 2005, at 18:57, David Kettler wrote:

> On Sun, Apr 17, 2005 at 02:33:59AM -0700, Jan Jaap van Poelgeest wrote:
>> --- David Kettler <davek@***.lonestar.org> wrote:
>>
>> Might I ask how the ro6 behaviour was implemented for
>> the model?
>>
>
> I used the behavior suggested by me and others to avoid the
> don't-have-enough-dice-to-succeed pitfall. Basically when you roll a
> 6 it not only counts as a successs but also gives you the chance to
> roll again. This let's any number of dice being rolled achieve any
> number of desired successes, but with rapidly diminishing probability.

That's also the mechanic used by the new World of Darkness. And one
that makes perfect sense to me.

-- Wild_Cat
maxnoel_fr at yahoo dot fr -- ICQ #85274019
"Look at you hacker... A pathetic creature of meat and bone, panting
and sweating as you run through my corridors... How can you challenge a
perfect, immortal machine?"
Message no. 8
From: jjvanp@*****.com (Jan Jaap van Poelgeest)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 11:26:04 -0700 (PDT)
--- Max Noel <maxnoel_fr@*****.fr> wrote:
>
> On Apr 17, 2005, at 18:57, David Kettler wrote:
>
> > On Sun, Apr 17, 2005 at 02:33:59AM -0700, Jan Jaap
> van Poelgeest wrote:
> >> --- David Kettler <davek@***.lonestar.org> wrote:
> >>

[snip sensible ro6]

I agree, now let's hope it'll be in there. The curve's
pretty, does it look similar without the ro6?

cheers,

Jan Jaap



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Message no. 9
From: mattgbond@********.com (Matthew Bond)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 20:23:51 +0100
Jan Jaap van Poelgeest wrote:
> From what I gather Graht has in fact managed to put it
> quite well by saying that SR4 has "diminishing
> returns" (but then, he's a playtester).

No, he didn't. It may or may not be that in SR4 that is the case, but
Graht said nothing on the matter.

He wasn't commenting on SR4 at the time, but explaining to somone who
didn't understand what a previous poster had meant by calling focussing
on a single skill under the SR3 system as being 'anti-munchkin' by
requiring expending more and more karma on getting less and less
incremental gain as being 'diminishing return'

Just because someone is an SR4 playtester by no meams implies that every
comment they make involes revealing the mystical secrets of forbidden
knowledge that is SR4...

Matt



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Message no. 10
From: maxnoel_fr@*****.fr (Max Noel)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 21:07:01 +0100
On Apr 17, 2005, at 20:23, Matthew Bond wrote:

> Just because someone is an SR4 playtester by no meams implies that
> every
> comment they make involes revealing the mystical secrets of forbidden
> knowledge that is SR4...

Playtesters are forbidden to reveal those things, anyway. Breaking a
FanPro NDA on this list would be quite a stupid thing to do, given who
reads it.

In any case, SR4 still has diminishing returns, they're just not as
diminishing as in SR3. The average number of hits is now a linear
function of the number of dice rolled (avg. number of hits = dice
rolled / 3), but if the progression system is anything like SR3 (and
it'll probably be), it's still horribly expensive to focus on a single
skill/attribute.

-- Wild_Cat
maxnoel_fr at yahoo dot fr -- ICQ #85274019
"Look at you hacker... A pathetic creature of meat and bone, panting
and sweating as you run through my corridors... How can you challenge a
perfect, immortal machine?"
Message no. 11
From: davek@***.lonestar.org (David Kettler)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 23:10:59 +0000
On Sun, Apr 17, 2005 at 11:26:04AM -0700, Jan Jaap van Poelgeest wrote:
>
> [snip sensible ro6]
>
> I agree, now let's hope it'll be in there. The curve's
> pretty, does it look similar without the ro6?
>
> cheers,
>
> Jan Jaap
>

Well, without the ro6 it's impossible to get more successes than dice being rolled so you
would see it suddenly drop to zero. Various ways around that have been suggested here, so
we'll have to wait and see what Fanpro does.

--
Dave Kettler
davek@***.lonestar.org
http://davek.freeshell.org/
SDF Public Access UNIX System - http://sdf.lonestar.org
Message no. 12
From: jjvanp@*****.com (Jan Jaap van Poelgeest)
Subject: Probability Plots
Date: Sun, 17 Apr 2005 16:16:37 -0700 (PDT)
--- Matthew Bond <mattgbond@********.com> wrote:
> Jan Jaap van Poelgeest wrote:
> > From what I gather Graht has in fact managed to
> put it
> > quite well by saying that SR4 has "diminishing
> > returns" (but then, he's a playtester).
>
> No, he didn't. It may or may not be that in SR4 that
> is the case, but
> Graht said nothing on the matter.

I suppose he did not claim that "SR4 has diminishing
returns". I will have to rescind my statement to that
effect, then. I merely thought it made for an
interesting sentence. Unfortunately I had to involve
someone's nickname, thus stepping into the sandpit of
authorship.

> He wasn't commenting on SR4 at the time, but
> explaining to somone who
> didn't understand what a previous poster had meant
> by calling focussing
> on a single skill under the SR3 system as being
> 'anti-munchkin' by
> requiring expending more and more karma on getting
> less and less
> incremental gain as being 'diminishing return'

I guess my muddled mind must've confused a few things
somewhere. Maybe it was the fact that the notion of
dice pools competing against each other has been a
part of SR3 and will be present in SR4. Oh dear, I
might just have revealed a secret. Good thing I didn't
sign no NDA anywhere.

> Just because someone is an SR4 playtester by no
> meams implies that every
> comment they make involes revealing the mystical
> secrets of forbidden
> knowledge that is SR4...

Oh but it does. I can tell from what you are saying
that you have a conception of what region of knowledge
said mystical secrets of forbidden knowledge might
reside in. Even if you are not a playtester,
sufficient meditation on this issue should reveal
these secrets to you. They are logically implicit
within the sacred essence of reality...

*inane sniggling laughter*

If I did want to (pretend to) know what SR4 is going
to be like, I would not be as blatant about pursuing
this matter as you seem to suggest I am. I'm having
far more fun wildly speculating and driving others mad
;), thank you very much.

cheers,

Jan Jaap



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Message no. 13
From: gurth@******.nl (Gurth)
Subject: Probability Plots
Date: Mon, 18 Apr 2005 11:23:38 +0200
According to Jan Jaap van Poelgeest, on 17-04-2005 15:37 the word on the
street was...

> I don't think things would necessarily happen that
> way

I never sai anything about it being so, just that it's a possibility :)

> in the 6th world gangs are just small game and
> there are plenty of environmental factors other than
> just gangs that keep them from getting too powerful.
> Maintaining the status quo is a serious concern for
> the next step up in the streets (criminal
> organisations & security firms). Open gang warfare
> will often be bad for business and these organisations
> have their own affiliated toughs to make sure it
> doesn't happen (too often).

True, but I can see criminal organizations wanting "their" gangs to be
properly armed -- again, it's an escalation thing. If the Mafia allows
their gangs to have assault rifles when everyone else has SMGs, then the
Yakuza will allow theirs to get assault rifles as well, to prevent them
being wiped out by the Mafia's gangs _should_ something happen.

--
Gurth@******.nl - Stone Age: http://www.xs4all.nl/~gurth/index.html
Kemen (keemde, h gekeemd): het spelen van computerspelletjes
-> Possibly NAGEE Editor & ShadowRN GridSec * Triangle Virtuoso <-
-> The Plastic Warriors Site: http://plastic.dumpshock.com <-

GC3.12: GAT/! d- s:- !a>? C++(---) UL+ P(+) L++ E W--(++) N o? K w(--)
O V? PS+ PE@ Y PGP- t- 5++ X(+) R+++$ tv+(++) b++@ DI- D+ G+ e h! !r y?
Incubated into the First Church of the Sqooshy Ball, 21-05-1998
Message no. 14
From: aautran@****.fr (Achille Autran)
Subject: Probability Plots
Date: Tue, 19 Apr 2005 00:51:52 +0200
> From: David Kettler <davek@***.lonestar.org>
> BTW, if there are any other hypothetical probability curves (as I
> know there are plenty of other theories out there) you'd like me to
> plot, let me know. It shouldn't be too hard to implement them. As
> for the suggestion of just varying the number of dice...well, look at
> the SR4 plot for a fixed desired number of successes and use your
> imagination. Personally I think varying only one parameter is
> inferior to having a two parameter system, but I'm not Fanpro.


(Attention, maths ahead.)

It would be interesting to see the complete density of the law of a
roll, plotting the frequency of each number of hit P(TH) ((Target Hit
?), for various dice numbers. That way everyone would have a clear view
of the variance of each roll, and how narrow a single roll is around its
mean and its median, instead of its cumulative density function. And
maybe the same stats without the open-roll, since it pulls up the
chances of success quite a bit against high THs.

By plotting as well P(TN) and its cumulative density function for a set
number of dices with the SR3 roll, we could evaluate numerically which
change of variable could best fit SR3 rolls to SR4 rolls, and thus have
a rough guideline for translating TN and modifiers to TH and modifiers
(maybe both to the number of dices and TH). I don't know if it's very
clear... I don't have much time, but if need be I can take a hack at
that with Matlab.

BTW, did you use a symbolic formula (easy without the ro6, it's a
binomial law, a bit more tricky with the ro6) or just computed averages
over a large number of rolls ?

Molloy

PS : if this is a double post, I'm sorry. It's been a while since I
posted on ShadowRN, and I got a bounce back. Wrong address I guess, but
I'm not sure and I can't check since the archive is offline. (Note to
admins : is that normal and is there no archive of the ML accessible
from the web ?)
Message no. 15
From: davek@***.lonestar.org (David Kettler)
Subject: Probability Plots
Date: Tue, 19 Apr 2005 05:18:20 +0000
On Tue, Apr 19, 2005 at 12:51:52AM +0200, Achille Autran wrote:
>
> (Attention, maths ahead.)
>
> It would be interesting to see the complete density of the law of a
> roll, plotting the frequency of each number of hit P(TH) ((Target Hit
> ?), for various dice numbers. That way everyone would have a clear view
> of the variance of each roll, and how narrow a single roll is around its
> mean and its median, instead of its cumulative density function. And
> maybe the same stats without the open-roll, since it pulls up the
> chances of success quite a bit against high THs.
>
> By plotting as well P(TN) and its cumulative density function for a set
> number of dices with the SR3 roll, we could evaluate numerically which
> change of variable could best fit SR3 rolls to SR4 rolls, and thus have
> a rough guideline for translating TN and modifiers to TH and modifiers
> (maybe both to the number of dices and TH). I don't know if it's very
> clear... I don't have much time, but if need be I can take a hack at
> that with Matlab.
>

I think I get what you're saying. You just want plots of the probability of every result
for different numbers of dice being rolled rather than the probabilities of exceeding a
certain number of successes? At least for the SR4 stuff making my code do that should be
trivial.

SR3 is more complex...you have to worry about number of dice, TN, *and* number of
successes. That's why the plots I did were for getting only one success...I'd run out of
dimensions to plot in otherwise.

> BTW, did you use a symbolic formula (easy without the ro6, it's a
> binomial law, a bit more tricky with the ro6) or just computed averages
> over a large number of rolls ?
>

It's based on the average of 100,000 rolls. I wanted to do it analytically, but it gets
rather complex for arbitrary numbers of dice with re-rolling, and ultimately I decided
that my time was more valuable than my computer's time. Making the computer crunch away
for large numbers is easy. Plus doing it this way makes adopting different algorithms
easy, while doing a different algorithm analytically can potentially mean starting almost
from scratch.

--
Dave Kettler
davek@***.lonestar.org
http://davek.freeshell.org/
SDF Public Access UNIX System - http://sdf.lonestar.org
Message no. 16
From: scott@**********.com (Scott Harrison)
Subject: Probability Plots
Date: Tue, 19 Apr 2005 11:31:41 +0200
On Apr 19, 2005, at 07:18, David Kettler wrote:

> On Tue, Apr 19, 2005 at 12:51:52AM +0200, Achille Autran wrote:
>>
>> (Attention, maths ahead.)
>>
>> It would be interesting to see the complete density of the law of a
>> roll, plotting the frequency of each number of hit P(TH) ((Target Hit
>> ?), for various dice numbers. That way everyone would have a clear
>> view
>> of the variance of each roll, and how narrow a single roll is around
>> its
>> mean and its median, instead of its cumulative density function. And
>> maybe the same stats without the open-roll, since it pulls up the
>> chances of success quite a bit against high THs.
>>
>> By plotting as well P(TN) and its cumulative density function for a
>> set
>> number of dices with the SR3 roll, we could evaluate numerically which
>> change of variable could best fit SR3 rolls to SR4 rolls, and thus
>> have
>> a rough guideline for translating TN and modifiers to TH and modifiers
>> (maybe both to the number of dices and TH). I don't know if it's very
>> clear... I don't have much time, but if need be I can take a hack at
>> that with Matlab.
>>
>
> I think I get what you're saying. You just want plots of the
> probability of every result for different numbers of dice being rolled
> rather than the probabilities of exceeding a certain number of
> successes? At least for the SR4 stuff making my code do that should
> be trivial.
>
> SR3 is more complex...you have to worry about number of dice, TN,
> *and* number of successes. That's why the plots I did were for
> getting only one success...I'd run out of dimensions to plot in
> otherwise.
>
>> BTW, did you use a symbolic formula (easy without the ro6, it's a
>> binomial law, a bit more tricky with the ro6) or just computed
>> averages
>> over a large number of rolls ?
>>
>
> It's based on the average of 100,000 rolls. I wanted to do it
> analytically, but it gets rather complex for arbitrary numbers of dice
> with re-rolling, and ultimately I decided that my time was more
> valuable than my computer's time. Making the computer crunch away for
> large numbers is easy. Plus doing it this way makes adopting
> different algorithms easy, while doing a different algorithm
> analytically can potentially mean starting almost from scratch.
>
When I saw this thread earlier I started wondering about the
probabilities involved. I did all my work in SR3 with actual maths and
did not rely on the data from rolls. I wanted to do the same for SR4.
That is why I posted my question about converting rolls from SR3 to SR4
because if there is a chance we will know about it I can create the
needed comparison. However, if no one has actually thought about it or
cannot release that information then we are going to have a difficult
time since all we can do is assume what type of roll is made in SR4,
take guesses about different variants (like a 6 allowing a reroll to
see if another 6 comes up, etc.), and then make a comparison of the
MANY types of rolls from SR3 that can approximate the same percentage.
Just look at one of my TN PDF files and you can see there are many
rolls with approximately the same percentage.

--
·𐑕𐑒𐑪𐑑
·𐑣𐑺𐑦𐑕𐑩𐑯 Scott
Harrison PGP Key ID: 0x0f0b5b86

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