struggle session: review of (d6-d6) resolution system

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i’m sick, missing class, and laying in bed. i’m bored. so, gonna critique the resolution system i came up with a couple days ago. read the original post for my inspiration and context.

i’m going to criticize the original version of the idea, where stats are generated by 2d6. here are some problematic facts about the resolution system with respect to this stat distribution.

  • the maximal score 2 can win against is 7 (2.78%)

  • the minimal score 7 can lose against is 3 (2.78%)

  • the maximal score 7 can win against is 12 (2.78%)

  • the minimal score 12 can lose against is 8 (2.78%)

in other words, only scores >= 7 have a chance > 0 to win against 12, while only scores <= 6 have a chance to lose against 2.

what this means:

  • 58.33% of players have zero chance of losing against score 2

  • 41.67% of players have zero chance of winning against score 12

this system can only be improved by letting there be less possible stat scores than there are possible rolls. for instance, FUDGE has 7 possible stat “scores” and a roll distribution of |{-4, -3, ..., 3, 4}| = 9. whereas our stat scores are generated by 2d6 (11 possible results), but our rolls have a distribution of |{-5, -4, ..., 4, 5}| = 11. too much variation!

let this be improved by having basically the same number of possible stat scores as FUDGE, which for us will range from 4 to 10 (median/mean = 7). this results in the following:

  • score 4 has a zero percent chance to win against score 10

  • score 10 has a zero percent chance to lose against score 4

  • score 4 has a 2.78% chance to win against score 9

  • score 10 has a 2.78% chance to lose against score 5

certain results are thereby restricted to only the most extreme stat scores. as in FUDGE, this method probably works best with stat score assignment instead of random generation.

that is why the method i published on this blog is a vast improvement over that which i posted originally to twitter.

reason why i post this after making a vent thread that discussion about mechanics and their superiority? this is the nitty gritty; i’m not talking about different systems being objectively qualitatively better, but which version of a system’s premise is most mathematically fair and viable for players. this boils down to essentially why a FUDGE system cannot be easily reconciled with stat generation.

Comments

  1. Joaquin OlloMarch 29, 2021 at 12:36 PM

    The shadow of yesterday, an indie game from 2005 aprox that featured 3dF (rolling 3 fudge dice) for resolution, had only 5 possible stat scores: 0, +1, +2, +3, +4. Fudge doesn't allow for many stat scores. Obviously, no random generation.
    Same for Apocalypse World. Having a bell distribution curve, can't trust randomness for the stats.

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    Replies
    1. Marcia B.March 29, 2021 at 12:55 PM

      that's fascinating how all the stat scores in the shadow of yesterday are positive! that must be another trend in these sorts of games.

      i think you're totally right about randomness for bell curves! and when you do try to add randomness, you're either overly restricted or you have too much variance.

      Delete
  2. Joaquin OlloMarch 29, 2021 at 5:34 PM

    Well, those scores in TSoY are actually skills, because stats are pools you spend to aid your rolls, so that might be a reason for only positive scores. Another example I know of is Diaspora, based on FATE 3rd edition, where you either have 0 at a skill, or a positive score.
    I'd posit that, if you must do with only 5 scores, you should pick them carefully. Low scores are not as interesting and inspiring for narrative as positive ones, perhaps, although there's the example of Apocalypse World with -1 and -2. In my experience, though, you avoid rolling negative stats, if possible.

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