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mathformulaprobabilitydice

Formula to calculate chance (probability) of a dice side based on its value


So I am making a simple Dice that has 6 sides, but I want to modify the chances of those 6 sides.

Now my dice can have N sides, it grows, so you start with 6 sided dice and you may get up to 10 sided dice. The chances for a specific side to come up on a roll depends on its value. Chances should decrease depending on the value on a side so if side value is 1 its chance is higher than the side numbered 6 whose chance would be much lower.

Example (6 Sided):

Side   :   Chance
 1     :   35  %
 2     :   25  %
 3     :   20  %
 4     :   11  %
 5     :   6.5 %
 6     :   2.5 %

So as sides increase the chances should decrease never going over 100.

I tried making formula depend on the side and divide the current chance by number of sides but did not work.

Edit:

Side 6 should have 6 times less probability than side 1 and 5 times less probability than side 2 and 4 times less probability than side 3 etc... My example does not match this because I could not come up with numbers so they would add up to 100 and qualify the conditions.


Solution

  • If I understand you correctly, you want this equation:

    If the dice has N sides, the total "weight" is (N/2)*(n+1).1 For 6 sides, the total "weight" is (6/2)*(6+1) = 3*7 = 21.

    Then the math is simple

    1 -> 6 / 21 = 0.28571428571
    2 -> 5 / 21 = 0.23809523809
    3 -> 4 / 21 = 0.19047619047
    4 -> 3 / 21 = 0.14285714285
    5 -> 2 / 21 = 0.09523809523
    6 -> 1 / 21 = 0.04761904761
    

    Obviously 6/21 is 6 times as big as 1/21, so that part holds up. And the summation:

      0.28571428571      6/21
    + 0.23809523809     +5/21
    + 0.19047619047     +4/21
    + 0.14285714285     +3/21
    + 0.09523809523     +2/21
    + 0.04761904761     +1/21
    ---------------     -----
      0.99999999996     21/21
    

    well, the left side is close enough to 100% anyway. Rounding being what it is. Right side shows that this is a rounding thing and not an error thing.

    *this equation (and the variant (N/2)*(N-1)) are seriously handy equations. It's a shortcut for 1+2+3+4+5+6...