A Mathematician Speaks: Rolling dice

[Vaxalon]

Correct me if I'm wrong, but doesn't WW have round-by-round combat, in the same manner as DnD?  It has been a long time since I've played, but I would recall if something more radical had been included.

[Valamir]

MJ, yes.  They are certainly not identical.  The d20 die pool has an interesting effect that you aren't sure exactly how many dice are going to be in the pool at the end (i.e. how long the combat is going to last), and the ability to signicantly change the nature of the conflict in the middle is also different.  But the effect of a bell distribution of expected results over time is the area I was drawing attention to.


Callan, I tend to think of the Take 10 rules as something of a patch.  Its a jerry rig solution to the issue that works and is simple.  The purpose is to allow the player to simply choose to get the expected value as opposed to actually coming up with a system that reliably produces the expected value.  It would be interesting to know whether the designers actually thought about this rule in terms of probability and distribution curves, or if it was just a more instinctive reaction to too much whiffing in the skill rolls.

[Vaxalon]

If you look at the designer's notes, the take 10 and take 20 rules were created in order to reduce handling time.

[jphannil]

My approach in Chaos & Order is to make the amount of fortune a 'game tool', a variable that can be changed in the game.

The basic idea is to always throw 2 dice, the plus die and the minus die, to this is added the trait value of character and then compared to difficulty rating. The thing is, the die to be used can be d2 or d20, or anything in between. The requirement is the fact that player needs to clarify why the particular die is used, gm can veto.

[Vaxalon]

I just put my game, Skein, up for you theorists to review, which has what I think is a fairly unique dice handling system in it.

Each competency has a rating, an even number between 4 and 10, that describes the "size" of the dice that are used for it.

The "chaos level" of the situation determines how many dice are rolled.  High chaos equals low number of dice.  Combat, for example, is usually a high chaos situation, where luck plays an important role.

Let's say you've got an ogre, very dangerous, whose "bashing things over the head" competency is 10, and a halfling, whose "stabbing things in the kneecap" competency is 6.  When they go head to head in a wild, riproaring fight, the ogre rolls 1d10 and the halfling rolls 1d6.  

On the other hand, when the halfling, with his competency of 10 in "get into places people want kept secret" tries to pick the competency-8 lock, he rolls 3d10 against the lock's 3d8.

[mindwanders]

Does it allow you to take rigerous planning on the part of the players into account (cyberpunk style casing of the joint before sneaking in and attacking the ogre while he's doing something else)?

[Itse]

For some reason, one of the bigger blind spots in experience seems to be exactly this:

- It's very unlikely that a player will roll X. This means that it's very unlikely that any player in the group will roll X.

Of course, this is all wrong. Some common things that occur due to this are:

- The characters are all sneaking past a sleeping guard, which is meant to be very easy. Just for fun's sake, the GM asks everyone to throw a d10, with "1" meaning their character will somehow stumble. Seems innocent enough, except that in a group with five characters there's actually a 41% chance of at least one character somehow stumbles. This is a common reason for the "the characters always screw up at crucial points" phenomenon.

 - There's something that's "extremely hard to spot"; it would need a roll of 20 on a d20.... Now if there's for example six characters who get to try this, the chance of them noticing this "extremely hard to spot" thingie would be 1 in 4 and then some. That's usually a lot more than what the GM had in mind.

The "power in numbers" thing get truly ridiculous in systems with large dice pools like WW:s Storyteller. But then again the Storyteller system sucks like no system I've used. Goes to prove that having good mechanics which fit the game theme is by no means necessary to sell a game.

[Vaxalon]

Does it allow you to take rigerous planning on the part of the players into account (cyberpunk style casing of the joint before sneaking in and attacking the ogre while he's doing something else)?

That depends on how the scene is set up.

Something as cold and calculated as a high-tech sniper ambush wouldn't be as high-chaos as a machete melee.

[Valamir]

Itse, good call.

Back in the day when I was GMing campaigns that made regular use of spotting checks I just had the character with the best skill make the roll.  If the most perceptive character misses it, its unlikely that the less perceptive character would notice it (assuming equal attention being paid).  This also provides some additional niche protection.  

Similiarly when sneaking I had the most clumsy character roll on the theory that if they succeeded, everyone less clumsy would have also.

[Christopher Weeks]

Here are 3 major types of probability curves...flat curves...bell curves...[and] modified bell curves when rolling multiple, differently sized dice

Note too, that you can achieve non-normal curves by using multiplication (and division, which is the same thing).  1d20/1d4 has a range of zero to twenty (if you're rounding for integers) but the mean result is five (or just under five and a half).  The distribution of 80 possible rolls looks like:

Code Select Expand


00 2
01 10
02 10
03 10
04 10
05 9
06 6
07 4
08 3
09 3
10 3
11 1
12 1
13 1
14 1
15 1
16 1
17 1
18 1
19 1
20 1


Chris

[simon_hibbs]

- It's very unlikely that a player will roll X. This means that it's very unlikely that any player in the group will roll X.

Of course, this is all wrong. ...

RuneQuest famously 'suffered' from this, especialy with regard to fumbles. Supposedly in a mass battle using the RQ rules, several dozen people would decapitate themselves.

Of course that wasn't realy a problem, because nobody would run a battle with thousands of soliers using the RQ combat rules. Still, the basic fact remained that during the life of a campaign, there was a very high chance that incredibly unlucky things would happen at some point in the game to someone.

I remember one guy at uni running a Rolemaster game with a table for the magic items you started the game with (home grown). Apparently there was a 1/1000 chance of getting an uber-powerful supersword that would make you champion of the universe. Riight...... I never found out what the point of that was, but I think it was just a lure to attract munchkins to play the game.


Simon Hibbs

[Mike Holmes]

The problem with that, Ralph, is that then what's the use of having that perception score for my character, if yours is one higher? For when we're not together?

Hero Quest handles this well. The "lead" player uses his total score, and the other players augment, meaning that they add one tenth of their ability. This keeps the niche protection, and allows the other scores to be useful. And when they split up, like I suggest above, then each individual score can be counted on.

The fact that this is encoded as the normal method in the rules is a godsend.

Mindwanders, this is precisely the dangerous thing that one should not say about these curves. First, yes, the "expected value" is 150. Meaning that if you make the 100d2 roll many times, you should expect to get 150 per roll or so. And it is the most common result as well. And, yes, the tails get extremely small. But the fact of the matter is that the standard deviation on this is not so small as you might think. First off, the chance to get 150 itself is actually very small, less than 8% (as opposed to about 1% for a flat curve covering the same range).

But more importantly, though most of the rolls will range from 145 to 155, every third one will be outside that range. Given that the results of this roll are 100-200, that's a ten percent range for just the common results. Whenyou use the oft quoted 95% of results, you get around from 140 to 160. Yes, that means that, during play you're likely to see scores ranging from 140 to 160 every night. Moreover, there's a chance that you might see from 136 to 164 in a night. And you'll likely see something a little outside that range once every campaign. Yeah, you'll probably never see anything lower than 130, or higher than 170 (only one in 25,000 rolls or so), but the result is hardly what I'd call "karmic."

Mike

[Vaxalon]

Hero Quest handles this well. The "lead" player uses his total score, and the other players augment, meaning that they add one tenth of their ability. This keeps the niche protection, and allows the other scores to be useful. And when they split up, like I suggest above, then each individual score can be counted on.

You can do this in D20, as well.  It doesn't say it explicitly applies to perception rolls, but it ought to.

[Vaxalon]

...you'll probably never see anything lower than 130, or higher than 170 (only one in 25,000 rolls or so), but the result is hardly what I'd call "karmic."

Here's some basic assumptions:

1> People roll dice about 20 times a night, individually.
2> There are about 5 people around a table.
3> 100 sessions is about right for a long campaign; two years weekly or four years bi-weekly.

This means that the dice get rolled about 10,000 times in a baseline campaign.

If something only happens one die-roll in a million, then that means you'd have to poll 100 campaigns before you'd expect to find one where it happened once in the entire history of the game.

I'd say that this is a sufficient level to say that fortune has been entirely removed from the question, and it has become effectively karmic.

[ErrathofKosh]

I'd like to point out the obvious:

   The more sides on a die, the more random the outcome.  Thus, using a D12 is more random than 2d6, which is more random than 3D4, but not only because there are more dice.  A d4 can only produce 4 results, a d6 can produce 6, etc.  

Also, the more that is added to a roll, the less random it becomes, in terms of overall variation.  Thus, rolling a d4 generates a result between 1 and 4.  Rolling d4+100 generates results of 101 to 104.

So, in summary the dice rolling convention used by D20 is more random than that used by GURPS for instance.  Rolemaster is the one of the most random (it's two dice count as one) and D6 has a sliding scale.  Not that these are particularily good examples, but this is what is most important about dice mechanics: that they are inline with your design intent.

Just wanted to make sure that the obvious remained so.

Cheers
Jonathan