Trying to do percentiles with D6s, HELP!

edited January 2008 in Game Design Help
Okay, so I'm posting at 2am my time because there is a big scary storm outside that woke me up ... and also because my mind is desperately churning over a mechanic I'm trying to design and failing to do so.

I'm designing a game based on a virtual pet site I run. It's aimed at kids, quite possibly ones who have never owned pen and paper RPGs before, but who have played the web game. For this reason I think I'd like to use D6s as the dice, because it's easier than expecting them to go and buy D10s somewhere. Unfortunately the stats used in the web game are percentile, and I'd like to keep with the fact that, say, a score of 30 is not unusual for a starting character, while 80 is really good.

So the problem is, how do I simulate that using only D6s. What mechanic can I use that lets a score of 50 succeed half the time (or so, the web game is not totally percentile), while making a 10 poor and an 80 awesome. Ideally I'd like to use the units too (so 86 is better than 80), but I can live with that being used to break ties and the like.

I was toying with rolling a D6 for each 10's digit and then counting the number of 6s, or 5+s, but that's not a great approximation and doesn't do the units.

Any suggestions?


  • edited January 2008
    Edited: I totally misread that. Ignore!
  • edited January 2008
    David, it's really hard to get it exact.

    As an approximation, you could try the idea of "You win if you roll X dice and get a 6 on any of them" (where the dice are d6s). That works out something like:

    One die: 17%
    Two dice: 31%
    Three dice: 42%
    Four dice: 51%
    Five dice: 60%
    Six dice: 67%
    Seven dice: 72%
    Eight dice: 76%

    So, although it's not exact, there's pleasing gaps between the probabilities for each number of dice, and it's acceptably close to 20, 30, 40, 50, 60 and 70 percent, tailing off as you go higher.

    By the way, go to bed.

  • I went to bed ... then I went to sleep ... then the wind got worse and I think my roof started leaking, so I woke up again :(

    But cool, those probabilities look just right (well near as dammit), and ties between equal numbers of 6's can be broken by the best actual stat, units included, which gives a value to the whole number (and allows stat increases just to be in whole points, which equate to a new dice every 10 points).

    Thanks Graham!
  • You could use the first digit and add it to the dice roll, as a simple option. Second digit breaks ties? Or is just used to track advancement?
  • The problem with D6 + first digit is that it reduces the range of variation in a roll to 6 (the dice size). I did a system like that a while back (essentially like D20 tests but with a smaller dice) and I found the range of possible results unsatisfactory.

    I think I'm going with roll D6s equal to the first digit, looking for 6s. Simple tests just require 1. Extended tests require more than one, and you could accumulate them (e.g. to find something in a library you need 5 6s rolled, with one roll a day, to see how long it takes). Opposed tests, of course, require more 6s than the opponent, ties broken using the whole number (not just the second digit, since that kind of messes up it's use to track advancement :)

    Counting 6s is easy for younger kids, but it's a nice robust system for the older ones too. Sure it sort of turns a bit into the sorts of dice pools seen in shadowrun, but with less dice, which is good :) I'd like people to be able to play with the dice they already have around the house in board games, so ensuring that rolls over 5 or 6 dice are not that common helps.
  • You could roll 2d6 + digit...

    I think more dice is cooler as well, just offering options.
  • Ahh but 2d6 + digit gives you a non-liner curve, which is a whole other beast :)

    There is also the whole issue about how much is contributed to the chance of result by the stat, and how much is contributed by the stat, which is a feature of all 'add and reach a target' mechanics. I have that issue with Ars Magica for example, where the contribution of the stat (in the range 1-3) is much less than the contribution of the dice when no skill is involved.
  • Well, to be really crunchy and brute force about it, you could just take the percent chance of rolling over a given number. For example, on 1d6:

    Number........ Odds of rolling equal to or greater than
    1................. 100%
    2................. ~83%
    3................. ~66%
    4................. 50%
    5................. ~33%
    6................. ~17%

    Damn this lack of monospace font.

    Anyways, you could add or subtract one or two from the roll for helpful or complicating circumstances, respectively. Alternatively, you could have it set up so that you need to roll a lower number to succeed as your skill in something goes up and perhaps have different values where your "success number" or whatever you're going to call it changes. For example, a skill of 1-17 only succeeds on 6's, 18-33 on 5+, 34-50 on 4+, etc. and an easy skill might have it so that 1-17 succeeds on 5+, 18-33 on 4+ and so on.

    There are a few problems with this, though. This is in no way intuitive. That's just raw probability versus a stat. Next, it seems (to me) to be really arbitrary. If this is for kids, they might become a little confused as to why they succeed on 4's or higher now that their whatever is 34. It just seems a little awkward. Speaking of awkward, this system gives really volatile results, but you might want that. Lastly, if you want to have some skills "easier" than others and have their "success number" change at different values you'll probably end up with players frequently cross-referencing a huge table or index of skills or errors when characters advance.

    Personally, I would go with Graham's dice pool method for the sake of simplicity. While this method could be cleaned up a bit by having you succeed on a lower number every 20 increments in a skill (1-20 on 6's, etc.) you still get messed up leaps and bounds in your proficiency in a given task, particularly when you start succeeding all the time (84+) unless you are stuck in an unfavourable circumstance. I just wanted to throw in an alternate idea out there and perhaps a way to play with only one or two dice!
  • What about (2d6-2)*10? Gives 0 to 100, bell in the middle.
  • I'm very happy with the pool mechanism I think, it has loads of possibilities, but thanks for all of the ideas!

    Is there a website somewhere with information on the characteristics of different sorts of dice rolls? If not we should make one :)
  • ...especially for things like "roll X dice and keep the two best", or "roll X dice and drop the worst, total the rest". I can't do those with my limited math skills.
  • I'd like to see charts of probabilities, for different dice sizes and numbers, of things like "chance of at least one X" "chance of a pair of X" "chance of at least one X or Y" "chance of a pair or triple" "chance of reaching a target number"

    Also I see a fair number of lists analysing the probabilities of rolling pairs and and sets of dice, but very few to do with dice + number >= target style systems, which I find much harder to understand than, say, "roll under a number" systems.

    There are maths and gambling oriented sites with some of this information, but it's not oriented towards game design.

    It might seem silly, but I suspect (from having played them) that a lot of people get to the stage in their game where they have to "crunch the numbers" to make sure their core mechanic works, and they just don't know how to do it. I know I've done all sorts of sanity tests on mechanics in the past, what I thought covered everything, only to seem them fall apart in playtest.
  • Hi!
    You could use 3d6 to generate a number from 1-108...
    1st d6
    1 0
    2 18
    3 36
    4 54
    5 72
    6 90

    2nd d6
    1 +0
    2 +3
    3 +6
    4 +9
    5 +12
    6 +15

    3rd d6
    1-2 +1
    3-4 +2
    5-6 +3


    It creates an even distribution, uses common dice and has minimal maths.

    It isn't very elegant though...
    Dave M
  • David--

    All the ones you mention should be quite doable with relatively basic math skills, such as most people would cover in grade 9 or so.

    You can always whisper me if you need help with one of those in particular.

    I'd like to see a resource for the more tricky ones, though.
  • Hah ... I must have missed that bit in maths at school then :)

    Seriously. I did maths to a reasonable level, and have to use a fair bit in my job, but I still struggle with probabilities at times and I think lots of game authors do as well.
  • That's funny. I think Paul was suggesting that the kids should have the skills to play the game, not that you should have learnt this stuff in Grade 9.

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