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Dice and Probabilties

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Dice and Probabilties

Postby Gralamin » Sat Dec 04, 2010 1:12 am

I think this forum needs a good list, and a place to go to, to ask about dice probabilities, and dice systems in games.

The three most common types of rolling systems these days seem to be: Uniform, Bell Curve, and Dice Pools.

Uniform is something like d20. You roll a single die and add a modifier to get a result. The probabilities for this are simple, and it makes balance a bit easier the achieve.

Bell Curve is something like GURPS. You roll multiple small dice (such as 3d6) add a modifier, and get a result. The probabilities for this are more complex (requiring convolution to solve for, or abusing the fact bell curves are well studied), but balance is still mostly easy. The advantage here is you often get consistent rolls.

Dice Pools is something like WoD. You roll multiple dice, and count only those that meet some criteria. The probabilities are more variable here, and balance is harder, but it allows a greater degree of flexibility then the others.

That said, what is the most interesting dice system you've seen, and do you want the numbers run on anything?

My most interesting: Silhouette Core by Dreampod 9. It uses a dice pool system, but you only keep the value of the highest rolled die, + the number of other dice that rolled 6s. It's an interesting way to make it more advantageous to be versatile then specialized, a lot of the time.
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Re: Dice and Probabilties

Postby Proven Paradox » Sat Dec 04, 2010 2:28 am

I've played with all three distribution types in one game or another, and of those, I prefer uniform styles personally. DnD may have its problems, but by and large the d20 mechanic works really well.

I'm least experienced with bell curves, and my limited experience is a bad one. That was an attempt at running a DnD 3.5, but replacing d20s with 3d6. I wanted to build a character that specialized in defense, utilizing shut-downs like Stand Still to keep the hate. However, I specialized a bit too well, and soon my AC was so much higher than the 'appropriate' value that monsters they would need to roll a 17 or 18 to hit me. With a d20, that's still a 3/20 chance, and since I'd be eating most of the enemies' attacks, I could still look forward to taking a threatening number of hits. With 3d6, a 17 is [6, 6, 5], [6, 5, 6], [5, 6, 6], and an 18 is [6, 6, 6]. That's a 4/6^3 = 4/216 = 1/54 chance I get hit. Upon mentioning this to the DM, we immediately went back to a d20.

I've never played in a system with a bell curve being the intended RNG method straight from the beginning, but it seems to me that this would be a problem no matter what you do, unless you made 'specialization' in something relatively unimpressive. Someone more experienced have some input here?

Dice pools are a nice break from the norm for me, and I've gotten into a few WoD games simply because the numbers play out so differently. I like that such systems allow for partial hits, glancing blows, and such better than a uniform distribution. I'd appreciate it of someone with more time and energy would crunch the numbers a bit, but it's been my experience that dice pools produce the most extreme results, especially with re-rolling or doubling max dice in play. On the one hand I've seen a guy get 7 successes with a 5 dice pool, but on the other I've completely whiffed on a 15 dice attack. With a uniform distribution, there's a point at which you're just not going to miss anymore, barring fumble rules.
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Re: Dice and Probabilties

Postby Fax » Sat Dec 04, 2010 8:42 am

Just a note: smallroller is an excellent die probability tool.
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Re: Dice and Probabilties

Postby Siosilvar » Sat Dec 04, 2010 11:19 am

Fax wrote:Just a note: smallroller is an excellent die probability tool.

Side-side note: I use AnyDice. No downloads, though it takes a bit of figuring out how to program it.
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Re: Dice and Probabilties

Postby Gralamin » Sun Dec 05, 2010 10:42 pm

Siosilvar wrote:
Fax wrote:Just a note: smallroller is an excellent die probability tool.

Side-side note: I use AnyDice. No downloads, though it takes a bit of figuring out how to program it.


Nice program, I like it. Bit odd of a Syntax though.

This is the probabilities of Silhouette core.
This is standard d20 (This one is trivial).
This is various bell curves.
And This is a nWoD dice pool.
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Re: Dice and Probabilties

Postby Ina » Sat Dec 11, 2010 5:02 am

There's a variant on dice pools that seems to be getting more popular these days.

Roll X dice, keep the highest.
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