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Why 2d6+1/2?

posted Jan 18, 2012, 8:22 AM by Kyle Willey
    Ok, I'm really just kinda bored right now and I'm writing a ton, but here's my explanation for the basis of the Orchestra system as well as Drifting.

    Traditionally, games use linear probability distributions-in fact, most do. Even my beloved third edition Shadowrun uses a linear die system, as does Dungeons and Dragons, Call of Cthulhu and countless others. This isn't to say that linear is bad in any way so much to say that it is not always preferable. There are times when a game just isn't bettered by linear distribution-my main gripe with Dungeons and Dragons and the d20 system is that there's always a system-mandated 5% chance of arbitrary success or failure. Even a level 1 Fighter can hit a level 20 Rogue with fancy armor and gear if they get lucky. However, that Rogue will hit the Fighter almost all the time unless they get unlucky. Shadowrun's a little better about this; there's less of a reliance on individual dice outcomes, meaning that any roll is possible for anyone at a set rate, but not in as hit-or-miss as just a 5% yes or 5% no; should there be a large difference in power there's still a chance for either party to get luckier, and though it's more luck-based there's no arbitrary success or failure mandate.

    The system I use for Orchestra, the creatively named OrchestraS, however, uses two six sided dice plus additional dice that are counted as half their face value rounded down; when more than two dice are rolled the top two are chosen at full value and the lower ones are given half value. Why? Because it works. Unless a lot of modifiers or half-dice are added on, there's never a terribly giant difference in chances to succeed, though the difference between someone throwing three dice and two is pretty noticeable as a trend but doesn't necessarily guarantee superiority. This is also why I tend to limit modifiers and half-dice gains in my systems to 3, because that leaves a estimated gain of 9 on the dice result (~2 for each half-die, 1 for each modifier), which is getting pretty broken (the difference between a near-Olympics level performance and a untrained human; the untrained person wins very, very infrequently).

    For an example of the system, the maker of AnyDice was kind enough to code me an example which can also show you all the graphs and math related stuff that the system uses, from 1 to 5 dice (which is all you really need). AnyDice