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20120314, 12:48 PM (ISO 8601)
 Join Date
 Sep 2009
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Making graphs of die roll probabilities
So, I'm thinking of resuming work on an RPG system of my own. It will be a fairly generic fantasy game, with inspiration taken mostly from Basic D&D, Praedor, CODA and couple of CRPG roguelikes.
One thing I'd like to get right from the start would be solid system math. And for that, I need a bit help with counting probabilities.
To give a specific example, I'd like to have a probability distribution and graph for 2d12 roll. Like this.
Ideally, I'd like a crash course on how to do the maths so I can make these via Excell or by hand."It's the fate of all things under the sky,
to grow old and wither and die."

20120314, 12:56 PM (ISO 8601)
 Join Date
 Apr 2011
Re: Making graphs of die roll probabilities
IIRC the best normal distribution approximation of the d20 system is generated by 4d63 or 3d82
Beyond that, what sort of die sizes/pools are you looking at?

20120314, 01:04 PM (ISO 8601)
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 Sep 2009
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Re: Making graphs of die roll probabilities
But I'm not approximating d20 system, I'm making another one. I though of using 2d10 first, since that's easy enough to count in my head, but decided I like the slightly wider range of 2d12 more.
A curve created by throwing 3 or more dice is a bit too "high" for my tastes to use as a core mechanic, ie. middle numbers are too likely and numbers at the ends too rare."It's the fate of all things under the sky,
to grow old and wither and die."

20120314, 01:09 PM (ISO 8601)
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 Feb 2008
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 No, that other place
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20120314, 01:23 PM (ISO 8601)
 Join Date
 Nov 2009
 Location
 UK
Re: Making graphs of die roll probabilities
Someone has already coded it for you:
http://www.anydice.com/

20120314, 01:29 PM (ISO 8601)
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 Sep 2009
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Re: Making graphs of die roll probabilities
@LCP: Hah! Thanks! That's exactly what I need.
@Reaper_Monkey: Wouldn't know about that, never played GURPS and it's not on my list of inspirations."It's the fate of all things under the sky,
to grow old and wither and die."

20120314, 01:53 PM (ISO 8601)
 Join Date
 Dec 2008
Re: Making graphs of die roll probabilities
my favorite approach for getting sime kind of curve into the d20 system was using 3d20 take middle. if you roll 6, 14, 18 you'd take 14.
the curve is some kind of paraboloid.
the only stuff you would have to adjust would be the crit ranges for weapons...

20120314, 06:26 PM (ISO 8601)
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 Jun 2011
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Re: Making graphs of die roll probabilities
Projects: Homebrew, Gentlemen's Agreement, DMPCs, Forbidden Knowledge safety, and Top Ten Worst. Also, Quotes and RACSD are good.
Anyone knows blue is for sarcas'ing in · "Take 10 SAN damage from Dark Orchid" · Use of gray may indicate nitpicking · Green is sincerity

20120314, 06:32 PM (ISO 8601)
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 Feb 2012
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Re: Making graphs of die roll probabilities
*bookmarks*
My theory seems to be right! :D
Max damage from a Disintegrate is almost impossible.Last edited by Skyrunner; 20120314 at 06:32 PM.
Hngh?

20120314, 06:38 PM (ISO 8601)
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 Apr 2008
 Location
 USA
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Re: Making graphs of die roll probabilities
(1/6)^X, where X is the number of dice you roll, is fairly trivial. Multiply by 100 to get a percentage.
That's .0000000000000000760% chance to roll max damage on 22d6, by the way. Add another 14 zeroes in front to approximate 40d6.
So not only is it "almost impossible", it's "this is never going to happen in your lifetime". One in a hundred quadrillion for the first, one in 10 nonillion for the second (if my math is right).Last edited by Siosilvar; 20120314 at 06:40 PM.
ze/zir  she/her
Omnia Vincit Amor

20120314, 06:43 PM (ISO 8601)
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 Feb 2012
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Re: Making graphs of die roll probabilities
Whoops, wrong theory.
I meant 'randint(20,400)' and sum(1>40)(rad(1,6)) were different ^^^;Hngh?

20120314, 07:24 PM (ISO 8601)
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 Apr 2008
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 USA
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Re: Making graphs of die roll probabilities
Last edited by Siosilvar; 20120314 at 07:25 PM.

20120314, 07:51 PM (ISO 8601)
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 May 2007
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 Tail of the Bellcurve
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Re: Making graphs of die roll probabilities
The central limit theorem is rather inexorable that way  the sum of anything that's remotely well behaved goes to a normal distribution at infinity. If you really want things not to cluster, you're going to need to start with a skewed distribution. Adding up too many of them will become mostly normal again, but if you stick to a few, it'll be nonnormal.
Without crunching the numbers, I'd imagine you could get some fun results with, say a d6 labeled 1, 1, 2, 3, 4, 5.Bloodred were his spurs i' the golden noon; winered was his velvet coat,
When they shot him down on the highway,
Down like a dog on the highway,And he lay in his blood on the highway, with the bunch of lace at his throat.
Alfred Noyes, The Highwayman, 1906.

20120315, 01:33 AM (ISO 8601)
 Join Date
 Aug 2010
Re: Making graphs of die roll probabilities
The central limit theorem is the key to dice based systems. Even when you are rolling a single die, like with an attack roll, that single die roll is not the determining factor in everything. You have many attack rolls, many damage rolls, and so while the moment to moment fluctuations are unpredictable and provide interest to the game, the overall trends follow probabilistic norms.
Which is why things start to break down when you start determining things based on a single roll, for instance a save or die effect. The probabilities cannot average out, and instead you have a random fluctuation kill your BBEG, things end up unsatisfying. Or a player rolls poorly, and is killed, more because of the fall of the die than his own decisions and tactical choices. For a similar reason, a character dealing enough damage to kill something with one blow is not a desirable mechanic, unless that one thing is one of many minions, so the progress in whittling down their numbers is its own amortization.
What, I don't spend hours contemplating game theory, what you are talking about?

20120315, 04:27 AM (ISO 8601)
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 Feb 2006
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 Seattle, USA
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Re: Making graphs of die roll probabilities
Game theory is a very important field of study for anyone who wants to make good RPG's(or games in general), and I've seen quite a few games do good or bad based solely on their dice mechanics.
D&D shows it's wargaming roots strongly with it's dice system. It's all about statistics and bonuses, there are very few ways to actually influence the random part of the equation, and their is no curve to the probability at all, the game system relying on the sheer number of times you'll be rolling that d20 to average things out.
Shadowrun, on the other hand, goes in the other direction. You only roll d6's, and a 5 or a 6 on a die is a hit. As your character becomes more skilled you roll more and more dice. This makes the numbers fairly interesting. While anyone who's taken middle school math can tell you you'll average .33 successes per die, the curve the numbers make is very interesting, as you add more dice not only do you increase your chances at getting more successes, but you also dramatically reduce the likelihood you'll get a bad roll. It creates a bigger disparity between those who are skilled and those who are not."Sometimes, we’re heroes. Sometimes, we shoot other people right in the face for money."
Shadowrun 4e, Runner's Companion

20120315, 05:22 AM (ISO 8601)
 Join Date
 Aug 2010
Re: Making graphs of die roll probabilities
Indeed, the spread of 20 in your capability is always odd. If you take 10 above your skill as your point of competence(aka what you get when you take 10), and you have 1 skill point increase per level(there are other factors, but they are sporadic), then you range from failing to do something someone ten levels below you can do competently do pulling off something somebody 10 levels above you should be doing. In essence, you have a 20 level spread in how well you will do. In a game with 20 levels. This is simply an absurd range. It kinda works when you have fixed DC to make, but when you have a sliding scale(such as with jump checks), all of that variance comes into play. And jump checks really illustrate the absurdity of that spread; a bad roll, and you can fail to jump over a small 5ft gap, or roll well and you can go sailing 20 ft. Imagine watching jumping along. They hop forward a few feat, then are launched a couple dozen feat, then 7 feat, and just randomly fluctuate. All skills work like that, its just normally less graphic and hidden behind a single pass/fail DC. There is not even a normalizing aspect from multiple dice, which wouldn't necessarily cut down on the range, would at least make it more consistent.