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    Thread: Geeky math help requested.

    1. 04-10-2012 03:46 AM #1
      I couldn't figure out how to properly phrase this in google, so I'm curious if one of you math nuts can explain this to me.

      I was calculating percentages of some dice rolls (putting together a game). I am using the following.

      1) D4 (four sided dice)
      2) D6 (six sided dice)
      3) D8 (eight sided dice).

      Each dice, when rolled, is "open ended" meaning if a value of 4, 6 or 8 (the highest possible value) is rolled, you may roll the dice again, adding to the original value. This can continue indefinitely.

      I am trying to establish the percentage chance of rolling the following values:

      4+
      5+
      6+
      7+

      The D6 and D8 are quite simple.

      D6
      4+ = 50%
      5+ = 33%
      6+ = 16%
      7+ = 16% (if a 6 is needed, and rolled, the minimum total will be 7)

      D8
      4+ = 63%
      5+ = 50%
      6+ = 38%
      7+ = 25%

      ...now the D4 is what I can't figure out (it's been a few too many years since my last math class).

      D4
      4+ = 25%
      5+ = 25% (Again, if a 4 is needed, and rolled, the minimum value is 5)
      6+ = a 25% chance, followed by a 75% chance ---- what overall chance does this equate to?
      7+ = a 25% chance, followed by a 50% chance ---- what overall chance does this equate to?

      I don't remember the formular to combine two percentage chances into one number - anyone?

      Thanks.

      PS: Part of me wants to simply say the chance is 75% of 25%...or 18.75% --- but it's not that simple right?
      Last edited by Elbows; 04-10-2012 at 03:49 AM.

    2. Member GeoffD's Avatar
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      04-10-2012 06:27 AM #2
      A pair of D4 gives you the following 16 possible combinations:
      1-1
      1-2
      1-3
      1-4
      2-1
      2-2
      2-3
      2-4
      3-1
      3-2
      3-3
      3-4
      4-1
      4-2
      4-3
      4-4

      Just add them up and divide by 16 to get your percentage
      4+ is 12 out of 16 or 75% odds
      5+ is 10 out of 16 or 62.5% odds
      6+ is 6 out of 16 or 37.5% odds

      My university probability theory course was back in 1978. The math behind this is long gone.

    3. 04-10-2012 02:02 PM #3
      I agree, but I'm not initially rolling two dice at once - a second dice is only rolled if the initial result is a 4.

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      04-10-2012 04:23 PM #4


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      04-10-2012 04:26 PM #5

      Done!!
      /thread

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      04-10-2012 04:39 PM #6
      Quote Originally Posted by Elbows View Post
      D4
      4+ = 25%
      5+ = 25% (Again, if a 4 is needed, and rolled, the minimum value is 5)
      6+ = a 25% chance, followed by a 75% chance ---- what overall chance does this equate to?
      7+ = a 25% chance, followed by a 50% chance ---- what overall chance does this equate to?

      I don't remember the formular to combine two percentage chances into one number - anyone?

      Thanks.

      PS: Part of me wants to simply say the chance is 75% of 25%...or 18.75% --- but it's not that simple right?
      I think it is that simple. I believe you just multiply the odds of the first roll (1/4) times the odds of the second roll.

      The odds of a 4 on the first roll are 1/4, and then the combined odds are then conditional on the second roll:
      5+: 25% (1/1 x 1/4 = 1/4)
      6+: 18.75% (3/4 x 1/4 = 3/16)
      7+: 12.5% (2/4 x 1/4 = 1/8)
      8: 6.25% (1/4 x 1/4 = 1/16)

      Similar to how if you roll two dice, your odds of rolling a 2 (1/6 x 1/6) are the same as rolling a 12 (1/6 x 1/6) or 1/36.

    7. 04-10-2012 05:51 PM #7
      Gotcha. I actually just called my mother, the accountant/super math wiz and we came to the same conclusion. Thank ye kindly.


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      04-10-2012 06:27 PM #8
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      04-10-2012 10:16 PM #9
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