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A few probability calculations

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  • A few probability calculations

    I got curious about how big the differences between the various dice tricks were, so I went on AnyDice and cooked up a comparison. You can see it here.

    We've got Mortimer the Mortal, rolling ten dice.

    We've got Sidney the Sidereal, rolling ten dice against TN 4.

    We've got Solomon the Solar, rolling ten dice with double 7s.

    We've got Abby the Abyssal, rolling sixteen dice.

    We've got Godfrey the God, rolling ten dice and adding three successes.

    Each of the supernaturals gets 8 successes on average. But their results are distributed quite differently.

    Sidney is 97% likely to hit difficulty 5. Solomon is only 83% likely. But Solomon has a 17% chance of hitting difficulty 12, while Sidney only has a 3% chance. Godfrey's results are quite similar to Sidney's, while Abby hangs in between Solomon and the others.

    Mortimer is left behind in the dust, obviously.

    There are no real surprises in the output, but I think the numbers are interesting enough to share. I encourage y'all to go in there and play with the system, see what you can see. Check out the graphs and try a few sample rolls.

    I set it up so that you can vary everyone's roll at once by changing the value of X. Plus or minus some rounding errors, all the magical folks will get the same number of average successes for any X.

    Personally, I think Solomon gets the best end of the deal. The differences shrink as the number of dice increases, but when I think about actual play situations I think his bonus is the most likely to be really useful.

    PS: Anyone know how to program rerolls into AnyDice?


    EX3 Craft Rewrite

    Sanctaphrax is not a person
    -Chejop Kejak

  • #2
    From their wiki;

    Code:
    function: explode ROLLEDVALUE:n {
    if ROLLEDVALUE = 4 { result: 4 + [explode d4] }
    result: ROLLEDVALUE
    }
    
    output [explode d4] named "explode on 4"

    Messing with the ' if rolled value' well let you do those odd "reroll 10's and 6's only" tricks.


    Code:
    function: explode ROLLEDVALUE:n {
    if ROLLEDVALUE = 3 { result: 1 + [explode Xd{0,0,0,0,0,3,2,2,2,4}] }
    if ROLLEDVALUE = 4 { result: 2 + [explode Xd{0,0,0,0,0,3,2,2,2,4}] }
    result: ROLLEDVALUE
    }
    
    X:10
    output Xd{0,0,0,0,0,0,2,2,2,2} named "Solomon the Solar"
    output [explode Xd{0,0,0,0,0,3,2,2,2,4}] named "Solomon the Exploding Solar"
    Last edited by Elkovash; 11-17-2015, 03:46 AM.


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    • #3
      That helps, thanks.

      Presents another problem, though. If I make 6s give a result of 3, it'll throw off the final success count.

      For "reroll Xs until Xs no longer appear" I think it's best to just remove that entry from the die. So rerolling 6s would give you d{ 0,0,0,0,0,1,1,1,2 }.

      And "reroll up to X dice that failed" is the same as X extra dice the vast majority of the time unless X is very large, so I'm not interested in modelling it.

      It's "reroll all dice that failed" and "if you fail, roll again" that are giving me trouble.

      Maybe I should just handle it manually. A die which you reroll when it fails is d{ 0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2 }, if my napkin math is correct. And if you've got an X% chance of making a roll, I'm pretty sure you've got an [X + X(1-X)]% chance of making it with a reroll.


      EX3 Craft Rewrite

      Sanctaphrax is not a person
      -Chejop Kejak

      Comment


      • #4
        Originally posted by Sanctaphrax View Post
        That helps, thanks.

        Presents another problem, though. If I make 6s give a result of 3, it'll throw off the final success count.
        that's what the result function is for; Result = 1 or 2 + new exploded dice on any given numeral you assign.

        So re rolling something that is not a success is 'Result = 0 + Explode dice'

        You'd just need to assign unique numerals to each instance of reroll potential while keeping 1 for numerals that don't explode but are still successes.


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        • #5
          Oh, I see. Thanks.


          EX3 Craft Rewrite

          Sanctaphrax is not a person
          -Chejop Kejak

          Comment


          • #6
            I actually like this info, TBH without doing any maths on the subject, I figured that TN4 would give you the best bang for your buck, especially with increasing numbers of dice, but once you think about it, it makes sense Double 7s gets you the real kaboom for your jade scrip.

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