Retooled dice mechanic (probability issue)
 

There's a question at the end of this exposition.

So my friends and I started up GURPS and have played for a few months. We are a crunchy group but also a minimalist group, and GURPS' rolling gets a little too complicated at times. To that end, I am attempting to compound multiple rolls into single rolls by adapting a strategy from O.R.E. : a dice pool that generates separate probability curves - that is, I could technically pull three separate outputs (or more if I wanted to get complicated) from a single roll of multiple dice: the number of matching dice (preferring the highest number on matches), the total score of the roll, and a single score on a dedicated die and/or the number shown on the matched set. O.R.E. does not bother with the second output - the total shown on the whole roll, but this is because it uses a variable dice pool.

I was thinking I would go from 3d6 to 6d6, so I could use a very similar probability curve to the one that GURPS already uses and it would not be difficult to adapt the system. By making it a static number of dice, I could pull the total in addition to the outputs that O.R.E. uses.

The most immediate feature of this would be the ability to pull to-hit and hit location from one single roll, rather than two. Granted, this is only using two of my three proposed outputs, but I was also going to use this system to run a horror game with nested outputs of unknown quantity (let's say, any IQ roll would be done 6d6 and the player would only know what the total roll would mean, but not the width or height, and I would use it to determine, for instance, a hidden measure of sanity effects or corruption or something similar).

That all was both background and discussion fuel. I don't know how partial the GURPS forum is to maintaining the purity of its mechanics, but I feel the community is flexible enough for my needs and I thought this would make for an interesting thought process.

My question is this: I don't know much about probability. I know that 3d6 is a bell curve whereas 1d20 is linear. I know, too, that the Height of the roll (the number shown on the matching set) would therefore be linear as far as I know (since there is equal chance of 1-6 being the result)(although perhaps the chance of a given match set beating another match set would factor into the probability interestingly). What I do not know is how to find a probability calculation for finding different match sets from a roll of XdY - save that the distribution of matches in 3d6 would not yield many positive results for my purposes, which is why I'm doubling the number of dice. That is, I don't know what the chances of, in a roll of 6d6, for there to be a matching set of two, a matching set of three, four, five, six. My question is, can anyone teach me in very lay terms, or better yet just direct me to a probability calculator for my purposes? I can find calculators for any number of any type of dice -- but these lay out tables for given sums, not for given match sets. I am not sure how to relate the two.

Re: Retooled dice mechanic (probability issue)
 

I guess I don't know anything about statistics because I can't see how you're hoping to mix to hit and random hit location into one roll just by using 6d6 rather than 3d6.

Re: Retooled dice mechanic (probability issue)
 

Sarcose, what do you mean by matching sets?

If your talking about rolling 6d6 and letting that be your Attack and Location all at once then we have to look at it at least 2 ways.

Lets say you have 3 red dice and 3 blue dice and you roll all of them as 6d6 then treat the red as Attack and the Blue as Location.

Lets say you have 3 white dice and roll them once for Attack and again for location.

These are the same.

Lets say the red are the Attack dice. Rolling the three attack dice and the 3 location dice (blue) at the same time means that you simply disregard the location result (the blue dice) on a miss.

Is that what you meant?

Nymdok

Re: Retooled dice mechanic (probability issue)
 

Sorry, I must not have been clear.

What I was referring to was when multiple dice showed the same face value, the number of dice that match in this manner constitutes an output from a probability curve (edit: and this probability curve is unrelated to the one that outputs the sum total of the dice rolled; therefore, a single roll can generate the effective results of two). In the ORE system this is called "Width" and is done with a dice pool of 10d10. With 10d6, the chances of coming up with matches is higher, but this makes converting GURPS more difficult, so I was going to try and find out the probability curve for matches in a 6d6 pool.

Re: Retooled dice mechanic (probability issue)
 

After searching, I couldn't find a probability calculation for matching sets.

After experimentation and much consideration, I've decided to scrap my 6d6 plan. ORE is better suited a variable dice pool, which creates an exploding probability distribution against which the game would be balanced. Taking out the dice pool mechanic simply introduces a probability curve that starts at around a 40% chance to get a matched set then drops off steeply.

I had thought about therefore acquiring two outputs ; one sum of all dice with matches, and one sum of all dice. I decided this was ineloquent.

So Nymdok, after reading your post I understood what was the issue here. Multiple curves could be attained any number of ways, and for curves derived from different functions of the dice it would be more appropriate to use a dice pool system. Otherwise I would just be complicating the retrieval. I could use 6d6 with two colors of dice, and achieve three curves, one heavily weighted toward the middle (the sum of all dice) and the other two weighted as standard GURPS - but this would in effect be three simple rolls in one.

What I wanted was probability curves nested within one roll that could not be excised from said roll. I have therefore dropped 6d6 and gone with this:

3d6 standard GURPS rolls, with two dice of one color and one die of another. This results in: a roll of 3-18, weighted moderately heavily toward the middle; a roll of 2-12, weighted slightly toward the middle; and 1-6, with a linear progression. Two curves, one linear result. Three rolls achieved with no additional dice and no fudged up exceptional mechanics.


It's not what I started with, but I like it, and I'll go with it. Thoughts?

(
If you are curious, I am planning on running a sins and virtues themed horror game. The combat roll will use the two curved probability outputs to determine both to-hit and hit location, and I haven't really thought of a use for the solo die (it would be interesting to use it as a modifier die to the 3-18 sum); but the true use of this is to nest hidden uses for the additional probabilities in the players' rolls. Each time they roll a check, they only know the effect of the total, but not the effect of the other two outputs. Therefore, 1 in 3 of every noncombat roll has a known use while the rest of them will be something I use behind the scenes. The intent of nesting these rolls is to both make it feel as though actions have hidden consequences, and to get the players to make multiple rolls without telling them what they are for, but without it interrupting the flow of the game.

Further, any time I need to determine multiple things in a series of rolls I can nest rolls together to reduce the amount of time spent rolling.
)

(I will further point out that I feel a sadistic glee at the potential for paranoia induction as the players learn that the dice mean many things I am not telling them, in addition to what they can readily determine. If I wanted to get really sadistic, I could make every die a different color and choose, by my own system, which dice to use to extract which outputs.)

Re: Retooled dice mechanic (probability issue)
 

I suspect you already realize this, but I'll throw it out there just in case; this doesn't produce truly independent results for your three dice "rolls".

As an example, suppose the 3d6 roll comes up 18. There's no variation in the results for your 2d6 and 1d6 rolls; you know the results. Same with 3, of course. As you get closer to the middle of the bell curve, you'll get more possible variation in your 2d6 & 1d6 "rolls."

Re: Retooled dice mechanic (probability issue)
 

I suppose it depends on what you're trying to do, and how independent you wish these results to be. If this is, as you say, a standard GURPS dice roll, then the player critically succeeds on a 3 and critically fails on an 18. Suppose, for the sake of argument, that you're simply rolling against a 10.

There are 216 combinations of 3 6-sided dice, and 16 results for the 3-dice total, ranging from 3-18.

If you look at the subset of dice that represent a 3-die success against a difficulty of 10 — that is, 111, 112, 121, 211, 122, 212, 221, 123, etc — and count the second and third digit as "red dice," you'll find something interesting.

You'd expect that the two red dice would have an average roll of 7. However, when you only count the red dice on a success roll vs 10 (all 3 dice total 10 or fewer), the average of the red dice is only 5.39.

Why is this? Because if the total of all dice must be less than 10, the total of the red dice cannot be more than 9 (because the non-red die must be at least 1).

Similarly, on a failure vs 10 (all 3 dice total 11 or more), the average of the red dice is 8.61. Again, this is because in order to total 11, the red dice cannot be less than 5, because the non-red die can be at most 6.

Let's look at the result of the non-red die. You'd expect an average roll of 3.5 from a single d6, but if you extract the subset of success vs. 10, that non-red die averages 2.69. On a failure vs. 10, the non-red die has an average of 4.30.

The results, therefore, are not truly independent. When you roll a success vs. 10, your "red dice" subset and "non-red die" will tend to a lower average result.

Re: Retooled dice mechanic (probability issue)
 

I see what you're saying; in the instance of using a subset to determine hit location successful to-hit rolls will necessarily require a certain range of results that I must take into account. It depends on what rolls I need to combine and whether they are related. I will keep that in mind.

Re: Retooled dice mechanic (probability issue)
 

Heh... sounds a bit like Yatzhee... 'WOO! I got four 5s!'

Would be interesting to see how such a system might work. I can understand the extrapolation of multiple results from a single roll beyond just rolling 2 sets of 3d6 at the same time... maybe rolling 6D6 with two red dice, two blue dice, one white die and one green.... then you could determine one result from red + white, another from red + green, yet another from blue + white...

As for overall roll you could just sum them all and half result. That would gravitate more towards the middle of the curve and make critical results even less probable than with standard 3d6.

One application I could see of this would be to combine attack and damage roll... would make it pretty interesting because low rolls are good on attack but bad on damage. You'd tend to see only highly skilled people hitting for decent damage and critical successes would be minimal damage (assuming the damage roll was extrapolated from the same three dice the attack was).

I can't see much use for the first part in GURPS though... finding matches like out of 6D6 you get two 2s, three 4s and one 6.... That'd take some work to incorporate meaning... unless you wanted to use it for some the LT hit location parts... like determining if an arm hit was the shoulder, elbow or forearm... or determining left or right on limb/extremity hits... maybe breakage chance for parries.

Re: Retooled dice mechanic (probability issue)
 

These kinds of double dice would take some getting used to, but could be an easy way to get two separate 3d6 rolls from a single throw of three dice.