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Problem of Scality (Preserving the 1d6)

2003-09-27
2004-02-05
  • Benjamin F. Galbraith

    We have a massive size scale variating, which ranges from approximatley size level -5 to size level 15 (for a total likely range of about 20,) for Characters likely to be used in a game.  Interestingly enough, our scale was the minimum possible size we could come up with when it was developed.

    The problem is also that we want to keep the system based on a 1D6 for success rolls.  If the range is about 20 for size levels, ability levels range in about half that amount, most character bonuses ranging from about 1 to 10.  Size level 12 characters cannot hit size level 1 characters, unless we allow for special rolling rules (like you get a plus 1D6 if you roll a six), and even then it's very unlikely, because if a size level 12 character can have an ability bonus of 5, so can the size level 2 character (and because of the nature of PPV it's likely the smaller character will have even a larger bonus.)

    What solutions are there?

     
    • Benjamin F. Galbraith

      If the scale is has size bonus range of about 20, then the ability bonus is likely to creep up  (like it has been, for example our latest experimental ability scale) that it will be possible for larger characters to be able to hit smaller characters (and to provide more opportunity for character development, an ability range of 10 does not provide a lot of character development opportunity.)  Of course, then the smaller character can just get a higher ability as well, and then there's a huge difference between ability levels as well, so that it very quickly gets impossible to damage highly skilled characters, because of the small range of the 1D6 roll.

      So the obvious culprit is the 1D6 roll.  Tempting alternatives include 2D6, 0-10+(2d6 w/ 6's as Zero, adding additional rolls each time a 10 is rolled,) 1D10, 1d12 and d20.

       
      • Benjamin F. Galbraith

        In light of the fact that A) The size scale is just as about as narrow as it can get, and B) a broader ability bonus range allows for more character development options, I think it's time we change our fundamental dice roll.

        One option that has been mentioned that is much better than just 1D6 is using a 1D6 plus another 1D6 each time a 6 is rolled.  But still, this gives us a fairly narrow likely range.  We could go this way, but it would be keeping the random element very narrow.

        If we use 2D6, adding an additional 2D6 each time a 12 is rolled, it would be very similar to what we get out of the above 1d6 roll, but the average roll would be higher.  The 2D6 has a more predictabillity than a D10, D12 or D20.

        What other optons do we have?

         
        • Benjamin F. Galbraith

          I think the best range we can get out of a cube-shaped dice (D6,) is to multiply the result instead of using multiple dice.

          If we used 1d6 x3, that would give us a range from 0 to 15 in a single roll (18 -3  = 15.) But it would also make the difference between ability level 3 and ability level 5 fairly insignificant.  So what I'm thinking is:

          1D6, + 1D6 when a 6 is rolled, and multiply to total final roll by 2.  (In other words, the "Grade School" roll doubled.)

          So if I roll a 3 it's a bonus of 6.  If I roll a 6, then I add an addional roll, and if I got a 5, that would give me a total of 11, for a total bonus of 22.  Now THAT would make it possible, and still less-likely, for large character to stomp smaller ones. 

           
          • Benjamin F. Galbraith

            I think Hit point bonuses would have to be added to the roll before it was doubled.

             
            • Benjamin F. Galbraith

              I've changed my mind on this.  It would be better to have more hitpoints than to complicate the roll any further.  I believe we are going to have more hitpoints now with our latest ability PPV scale anyhow, and if that's not enough hit point influence, we could just change the hit point formula to add more hit points than it does now.

              So what I'm saying here is that with the latest experimental PPV scale (the one that doubles every two levels starting at level 4,) we will have more hit points anyways, so there's no need to effectively double the bonus of each hit point like I applied in the message this is replying too.  (And we have many other ways of adding extra hit points if we need to.)

               
      • Benjamin F. Galbraith

        Instead of multiplying the role by 2, or adding a 1D6 each time a 6 is rolled, we could:

        Multiply the 1D6 roll by 1D6 if a 6 is rolled (for a maximum of +36 from the roll, but a roll of 1-5 being 5 times as likely as a roll from 6 to 26.)

        what you rolled ~ the bonus it gives:

        1 ~ 1
        2 ~ 2
        3 ~ 3
        4 ~ 4
        5 ~ 5
        6 & 1 ~ 6
        6 & 2 ~ 12
        6 & 3 ~ 18
        6 & 4 ~ 24
        6 & 5 ~ 30
        6 & 6 ~ 36

        We could keep our current size, hitpoint AND ability scales with this roll !!

         
        • Benjamin F. Galbraith

          36 seems a bit high as a maximum roll, and 18-24 seems to be a bit high of an average (that's the neighboorhood I'de be looking for maximum.)  So what if we instead simply squared the re-roll, counting 6 as zero and re-rolling on a 5:

          6 ~ 0
          1 ~ 1
          2 ~ 2
          3 ~ 3
          4 ~ 4
          5 & 6 ~ 0
          5 & 1 ~ 1
          5 & 2 ~ 4
          5 & 3 ~ 9 (Within normal ability range.)
          5 & 4 ~ 16 (Low enough to be size scale)
          5 & 5 ~ 25 (High enough for a maximum roll)

           
          • P J

            P J - 2003-09-30

            We are really going to have to playtest ALL of these to see what works...  It sounds like a real pain, but its going on the list.

             
            • P J

              P J - 2003-10-06

              We recently playtested the rolling method where if a six is rolled another d6 is added to the roll.  It seemed to work fairly well for up to a size level difference of 4, but the range is still fairly limited.  The "Grade vs. Old solution" might be just what we need to expand the possible size level combat range.  It increases the range while keeping the range of common rolls within a close range. The problem that arrises is that smaller characters will be able to do more damage than otherwise expected, because their success levels could be very great, but as long as we limit the success based damage to 5 at level 10 we shouldn't have much of a problem.   I plan to playtest this solution soon.

               
    • Benjamin F. Galbraith

      Perhaps what we could do is change the size level range for how it effects the roll.  There is Size Level, the damage bonus it gives, the protection bonus it gives, and the encumberance disadvantage it gives.  It's the Encumberance from size that is throwing off the whole 1D6 range.

      Perhaps what should be done is to half encumberance.  However, this means that every 1/2 size level would be worth more PPV than the next full size level, because it would give a damage bonus without getting encumberance disadvantage.

      Size~Encumberance~armor/damge bonus
      0.0 ~ 0.0 ~ 0.0
      0.5 ~ 0.0 ~ 0.5
      1.0 ~ 0.5 ~ 1.0
      1.5 ~ 0.5 ~ 1.5
      2.0 ~ 1.0 ~ 2.0
      2.5 ~ 1.0 ~ 2.5
      3.0 ~ 1.5 ~ 3.0
      3.5 ~ 1.5 ~ 3.5
      4.0 ~ 2.0 ~ 4.0
      4.5 ~ 2.0 ~ 4.5

      So what would this do to Size PPV?
      Size ~ PPV (+1 per half level*,+ 0.5for full levels**)
      0.0 ~ 0.0
      0.5 ~ 1.0*
      1.0 ~ 1.5**
      2.5 ~ 2.5*
      3.0 ~ 3.0**
      3.5 ~ 4.0*
      4.0 ~ 4.5**
      4.5 ~ 5.5*
      5.0 ~ 6.0**
      5.5 ~ 7.0*

       
    • Benjamin F. Galbraith

      The problem with "Grade School" verses "Old School" is that with grade school there is only a 1 in 6 chance of there being a value outside of the 1-6 range, but with old school there is a 1 in 3 chance of this, making the over all range much greater.

      I suggest that we use the Grade school system, except for that we subract 1D6 if a 1 is rolled besides just addding a 1D6 if a 6 is rolled.

       
    • Benjamin F. Galbraith

      A)It's critical for hit-points and the die-roll to be comparable, because they are the variable things that happen durring combat. 

      B)Size and Ability Level, on the other hand, are things that have to be comparable, because they are things that happen durring character development. 

      C)The balance between A and B is simply a difference between how powerful an individual game allows character to get compared to other characters.

      Therefore, I think our latest balance* is actualy quite nice.

      *our "latest balance" is using a 1D6 roll (-1D6 on a 1 and +1D6 on a 6,) an ability scale that doubles PPV at every even level after level 4 (4 is 4 PPV, 5 is 6 PPV, 6 is 8 PPV...), hit points is strength +1, "Skills" add full bonus (instead of half, maximum of 2 abilities per action generally,) and using the same old size-scale.

       
    • Benjamin F. Galbraith

      Our latest solution that we are currently playtesting, is that we are taking advantage of the Size and Encumberance scales being different, and making the Encumberance scale have half of the effect of the Size scale.  (In other words, we sort of changed the "Encumberance" scale back to the "original" size scale.)

       
    • Benjamin F. Galbraith

      Last Saturday, we playtested with encumberance being half of what the current size is, we found the encumberance to be working much better, but it was still "impossible to hurt creatures bigger than yourself."

      The obvious solution is to totally revert to our old size-scale (current playtested encumberace [1/2 of what it is now.])

      However, I think most of us feel that the size scale does NOT do enough damage at half of what it is.  In the same breath, I wonder if, as it is now, size is not enough of a factor (our large character was fairly nimble, let's put it that way.)

      About 3 years ago, Seth suggested to me that we might want to consider a doulbing-every-1.5 size levels instead of every level or every-two-levels.

      Now I'de like to try it.  According to my calculations, this is what that new size level scale would be (it doubles every 1.5 size levels... I kinda like it, though we might want to boost it up a half-level):

      Size  kg/lbs
      -6    3.8/8
      -5.5  5.0/12
      -5    6.3/14
      -4.5  7.5/16
      -4   10.0/22
      -3.5 12.5/26
      -3     15/33
      -2.5   20/44
      -2     25/55
      -1.5   30/66
      -1     40/88
      -0.5   50/110
      0     60/132 
      0.5   80/176
      1    100/220
      1.5  120/264 
      2    160/352  
      2.5  200/440
      3    240/528 
      3.5  320/704
      4    400/880
      4.5  480/1056
      5    640/1408
      5.5  800/1760
      6    960/2112
      6.5 1280/2816
      7   1600/3520
      7.5 1920/4224
      8   2560/5632
      8.5 3200/7040
      9   3840/8448
      9.5 5120/11264
      10   6400/14080
      10.5 7680/16896
      11   10240/22528
      11.5 12800/28160
      12   15360/33792
      12.5 20480/45056
      13   25600/56320
      13.5 30720/67584
      14   40960/90112
      14.5 51200/112640
      15   61440/135168

       
      • Benjamin F. Galbraith

        We found the size scale that doubles every 1.5 levels (instead of every one or two levels) to be very favorable, as both a size scale and as an encumberance scale.  Basically, it fits the 1D6 better than the double-every-2-levels-scale, AND it gives better percision than the doubles-every-1-level-scale.

        We found that with some hit-point adjustment, we have been able to make this "1.5" scale work.  However, we are not clear if the adjustment we made is quite enough to balance out the scale in all likely situations.  (I personally am very not-convinced.)

        Best Solution:

        The next thing I want to try, is resolving the Hit Point balance question.  This is what I think we should try next:

        The new hit point formula, should be, in my opinion: strenth times 2, plus one.  (So, if your strength was 0.5, you would double that to get 1, and add one to get 2.  If your stregnth was 4, you would double it to get 8, plus one would be 9.  If your strength was 0, you would double it to get zero, plus one would be one.)

        But of course, this makes it so that we have too many hit points, too fast, so that the hit points themselves comprimise the 1D6.  But is this really a problem with the hit point formula I have proposed, or is it a problem with the ability scale we currently have, already comprimising the 1D6?  Skills add full bonus to general abilities, so the easily obtained potential bonus is actually double of whatever it would seem to be from our ability PPV scale.  So if it seems like it's easy to get a +5 bonus, it's not so much a problem of getting +11 hit points, so much as it is actually getting a +10 bonus (+5 from skill and +5 from general ability) in the first place!

        So, I think our new ability scale should be:
        Level = PPV
        0.5 = 1 PPV
        1.0 = 2 PPV
        1.5 = 3 PPV
        2.0 = 4 PPV
        2.5 = 6 PPV
        3.0 = 8 PPV
        3.5 = 12 PPV
        4.0 = 16 PPV
        (and after this point, it only goes up 8 PPV every half level)
        4.5 = 24 PPV
        5.0 = 32 PPV
        5.5 = 40 PPV
        6.0 = 48 PPV

        So this way, the "average character" would have 7 or 8 hit points (instead of 10 to 12 hit points).  That's about how many hit points I think it's going to take for our 1.5 scale to really work out in most situations when big warriors take on smaller ones.  Also, this ability scale works out better with our new skill bonus rules (where they give a full bonus instead of a half bonus.)

         
        • P J

          P J - 2004-01-26

          This sounds like it could be a big step in the right direction.  Playtesting results should be in by next Tuesday. This will make equipment more expensive, including armor, which is something we haven't playtested enough.

           
        • Benjamin F. Galbraith

          What happened, when we playtested this again, is that we found that size was still an extreme advantage, so we decided to double Size's PPV.

          What I think we should do instead, is lower the PPV of the characters, and lowered the PPV of the abilities to this scale:
          Ability Level: PPV
          0.0: 0.0
          0.5: 0.5
          1.0: 1.0
          1.5: 1.5
          2.0: 2.0
          2.5: 3.0
          3.0: 4.0
          3.5: 6.0
          4.0: 8.0
          4.5:12.0
          5.0:16.0
          (and from here it goes up 8 PPV every half level)
          5.5:24.0
          6.0:32.0
          6.5:40.0
          7.0:48.0

          Hit points might end up a little higher on average, but that's a good thing considering some of the rules we are thinking about introducing.

           
      • Benjamin F. Galbraith

        Here's a version of this same size scale that covers a wider range, and uses Tons at the higher levels, so that it's easier to use:
        size kg/lbs
        -9.0 1.5/3
        -8.5 2.0/4
        -8.0 2.5/5
        -7.5 2.9/6
        -7.0 3.2/7
        -6.5 3.5/8
        -6.0 3.8/9
        -5.5 5.0/12
        -5.0 6.3/14
        -4.5 7.5/16
        -4.0 10.0/22
        -3.5 12.5/26
        -3.0 15/33
        -2.5 20/44
        -2.0 25/55
        -1.5 30/66
        -1.0 40/88
        -0.5 50/110
        0.0 60/132
        0.5 80/176
        1.0 100/220
        1.5 120/264
        2.0 160/352
        2.5 200/440
        3.0 240/528
        3.5 320/704
        4.0 400/880
        4.5 480/1056
        5.0 640/1408
        5.5 800/1760
        6.0 960/2112
        6.5 1280/2816
        7.0 1600/3520
        7.5 1920/4224
        8.0 2560/5632
        8.5 3200/7040

        Size Tons
        8.5 3
        9.0 4
        9.5 5
        10.0 6
        10.5 8
        11.0 10
        11.5 12
        12.0 16
        12.5 20
        13.0 24
        13.5 32
        14.0 40
        14.5 52
        15.0 64
        15.5 80
        16.0 104
        16.5 128
        17.0 160
        17.5 208
        18.0 256

         
      • Benjamin F. Galbraith

        This is a VERY ROUGH translation of our current Reach PPV scale for use with our new Size Scale (so this would be approximately the new Reach PPV scale):

        PPV  Reach
        -8.0  0.30
        -7.5  0.32
        -7.0  0.34
        -6.5  0.36
        -6.0  0.38
        -5.5  0.41
        -5.0  0.44
        -4.5  0.47
        -4.0  0.5
        -3.5  0.54
        -3.0  0.58
        -2.5  0.62
        -2.0  0.65
        -1.5  0.69
        -1.0  0.73
        -0.5  0.77
        0.0  .8
        0.5  .88
        1.0  .96
        1.5  1.04
        2.0  1.1
        2.5  1.17
        3.0  1.25
        3.5  1.32
        4.0  1.4
        4.5  1.5
        5.0  1.6
        5.5  1.7
        6.0  1.8
        6.5  1.95
        7.0  2.1
        7.5  2.25
        8.0  2.4
        8.5  2.55
        9.0  2.7
        9.5  2.85
        10.0  3.0
        10.5  3.25
        11.0  3.5
        11.5  3.75
        12.0  4.0
        12.5  4.25
        13.0  4.5
        13.5  4.75
        14.0  5.0
        14.5  5.25
        15.0  5.5 
        15.5  5.75
        16.0  6.0
        16.5  6.25
        17.0  6.5
        17.5  6.75
        18.0  7.0

         

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