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SHG Dice Revisited - Fixed?

Posted By: NJ
Date: Tuesday, 6 October 2009, at 5:21 p.m.

In Response To: SHG Dice Revisited - Fixed? (Michael Petch)

I'm going to take a wild guess at what was wrong with the dice. Here's a reasonable way to generate the dice:

1. Generate a random number between 1 and 36.
2. For each number, have a preassigned 2-dice combo: 1-1, 1-2, ..., 6-5, 6-6

Here's a similar but wrong way to generate the dice:

1. There are 30 non doubles rolls and 6 doubles rolls.
2. I know that non doubles are twice as likely to be rolled as doubles.
3. Given #2, let's weigh the nondoubles by 2 and doubles by 1.
4. With the weights, we have 60 nondoubles chances (30 * 2) and 6 doubles chances.
5. Generate a random number from 1 to 66.
6. If the number is between 1 and 60, generate one of 30 non doubles rolls.
7. If the number is between 61 and 66, generate one of 6 doubles rolls.

Given that erroneous algorithm, the chance of generating a double would be 6 out of 66, or 9.09%. That would be close to the observed frequency of 9.1-9.2%. Of course, this is just speculation but it's the only reasonable explanation I can come up with for dice that are fair for nondoubles but with a 9.1% doubles rate.

Messages In This Thread

• SHG Dice Revisited - Fixed?
  Michael Petch -- Saturday, 3 October 2009, at 7:33 a.m.
  • SHG Dice Revisited - Fixed?
    Michael Petch -- Saturday, 3 October 2009, at 10:58 a.m.
    • SHG Dice Revisited - Fixed?
      W Womack -- Saturday, 3 October 2009, at 12:36 p.m.
      • SHG Dice Revisited - Fixed?
        Michael Petch -- Saturday, 3 October 2009, at 12:41 p.m.
    • SHG Dice Revisited - Fixed?
      neilkaz -- Saturday, 3 October 2009, at 3:15 p.m.
  • SHG Dice Revisited - Fixed?
    Timothy Chow -- Sunday, 4 October 2009, at 6:32 p.m.
    • SHG Dice Revisited - Fixed?
      Michael Petch -- Monday, 5 October 2009, at 11:39 a.m.
      • SHG Dice Revisited - Fixed?
        NJ -- Tuesday, 6 October 2009, at 5:21 p.m.
        • SHG Dice Revisited - Fixed?
          Rich Munitz -- Tuesday, 6 October 2009, at 7:28 p.m.
          • SHG Dice Revisited - Fixed?
            W Womack -- Tuesday, 6 October 2009, at 8:11 p.m.
            • SHG Dice Revisited - Fixed?
              Rich Munitz -- Tuesday, 6 October 2009, at 8:45 p.m.
              • SHG Dice Revisited - Fixed?
                W Womack -- Tuesday, 6 October 2009, at 8:58 p.m.