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Testing Dices

Discussion in 'General' started by Evillevi, May 9, 2015.

  1. Evillevi

    Evillevi Shadow Pika!

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    Testing . Feel free to post and roll 13 dice to expand the pool
    Evillevi rolled 15 die of 100 faces, total: 853
    For: Testing
    Rolled on: May-09-2015, 07:41am
    35
    91
    27
    17
    71
    21
    55
    97
    93
    64
    77
    61
    79
    46
    19
     
    Evillevi, May 9, 2015
    #1
  2. Evillevi

    Evillevi Shadow Pika!

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    2nd test
    Evillevi rolled 13 die of 100 faces, total: 668
    For: test
    Rolled on: May-09-2015, 07:42am
    61
    17
    94
    5
    38
    27
    48
    35
    74
    98
    88
    22
    61
     
    Evillevi, May 9, 2015
    #2
  3. Evillevi

    Evillevi Shadow Pika!

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    Boop
    Evillevi rolled 13 die of 100 faces, total: 708
    For: PIka
    Rolled on: May-09-2015, 07:43am
    21
    74
    47
    88
    65
    3
    36
    49
    88
    93
    55
    7
    82
     
    Evillevi, May 9, 2015
    #3
  4. Evillevi

    Evillevi Shadow Pika!

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    4th test
    Evillevi rolled 13 die of 100 faces, total: 691
    For: sss
    Rolled on: May-09-2015, 07:44am
    16
    78
    81
    49
    8
    19
    46
    7
    95
    24
    92
    80
    96
     
    Evillevi, May 9, 2015
    #4
  5. Evillevi

    Evillevi Shadow Pika!

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    5th test
    Evillevi rolled 13 die of 100 faces, total: 722
    Rolled on: May-09-2015, 07:46am
    25
    45
    90
    33
    24
    94
    77
    43
    97
    74
    47
    43
    30
     
    Evillevi, May 9, 2015
    #5
  6. Evillevi

    Evillevi Shadow Pika!

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    6th test
    Evillevi rolled 13 die of 100 faces, total: 614
    Rolled on: May-09-2015, 07:48am
    6
    49
    45
    8
    43
    6
    94
    37
    99
    23
    63
    93
    48
     
    Evillevi, May 9, 2015
    #6
  7. Evillevi

    Evillevi Shadow Pika!

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    7th test
    Evillevi rolled 13 die of 100 faces, total: 371
    Rolled on: May-09-2015, 07:48am
    11
    17
    95
    15
    28
    51
    4
    53
    18
    7
    37
    22
    13
     
    Evillevi, May 9, 2015
    #7
  8. Evillevi

    Evillevi Shadow Pika!

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    8th test
    Evillevi rolled 13 die of 100 faces, total: 630
    Rolled on: May-09-2015, 07:48am
    86
    51
    30
    76
    66
    8
    57
    14
    15
    75
    60
    22
    70
     
    Evillevi, May 9, 2015
    #8
  9. Evillevi

    Evillevi Shadow Pika!

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    9th test
    Evillevi rolled 13 die of 100 faces, total: 754
    Rolled on: May-09-2015, 07:49am
    46
    14
    56
    86
    75
    24
    91
    93
    8
    83
    47
    85
    46
     
    Evillevi, May 9, 2015
    #9
  10. Evillevi

    Evillevi Shadow Pika!

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    10th test
    Evillevi rolled 13 die of 100 faces, total: 584
    Rolled on: May-09-2015, 07:49am
    73
    2
    8
    11
    33
    99
    96
    43
    63
    40
    6
    51
    59
     
    Evillevi, May 9, 2015
    #10
  11. Evillevi

    Evillevi Shadow Pika!

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    1-10 >> 15
    11-20 >>14
    21-30 >> 15
    31-40 >> 9
    41-50 >>18
    51-60 >> 10
    61-70 >> 8
    71-80 >> 13
    81-90 >> 9
    91-100 >> 19


    Average = 49.6


    End result of 130 data points with the QQ roller for those interested. My hypothesis seems likely though not conclusively so


    Essentially there's a high tendency for the dice to roll at the low end of the range and when it rolls high there's a tendency to roll really high
     
    Evillevi, May 9, 2015
    #11
  12. wayne82444

    wayne82444 Experienced.

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    That first roll was 15 die, so you actually tested 132 times. I'd imagine you found the average based on 130, so that one isn't right.
    wayne82444 rolled 13 die of 100 faces, total: 757
    For: Might as well
    Rolled on: May-09-2015, 09:23am
    49
    81
    36
    83
    90
    50
    69
    15
    32
    56
    95
    54
    47
     
    wayne82444, May 9, 2015
    #12
  13. Evillevi

    Evillevi Shadow Pika!

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    I got rid of two dice from the first 15
     
    Evillevi, May 9, 2015
    #13
  14. kinglugia

    kinglugia A Randy Avian

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    Someone is bored I see...
    kinglugia rolled 10 die of 100 faces, total: 501
    For: ???
    Rolled on: May-09-2015, 11:49am
    38
    8
    88
    24
    53
    45
    29
    75
    69
    72
     
    kinglugia, May 9, 2015
    #14
  15. Evillevi

    Evillevi Shadow Pika!

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    Not that difficult.

    Also there's a somewhat higher than normal possibility that the RNG for the QQ dice is borked.
     
    Evillevi, May 9, 2015
    #15
  16. pepperjack

    pepperjack A Variety of Cheese

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    I'm new to this sort of thing, but I looked up what a chi-square test was and tried to apply that here.


    i OiEiOi −Ei(Oi −Ei )2(Oi −Ei )2/Ei
    1-101513240.31
    11-201413110.08
    21-301513240.31
    31-40913-4161.23
    41-5018135251.92
    51-601013-390.62
    61-70813-5251.92
    71-801313  0.00
    81-90913-4161.23
    91-10019136362.77
        Sum10.46
    Given nine degrees of freedom, the critical value to establish even 70% confidence that the dice roller has bias would be 10.66; that is, by this standard, a fair die would fail more than 30% of the time. The critical value for 95% confidence would be 16.92.

    I'm going to maintain that these are not statistically significant results.
     
    pepperjack, May 12, 2015
    #16
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  17. Evillevi

    Evillevi Shadow Pika!

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    Thanks for the link. It's been a looooong while since I did stats.
     
    Evillevi, May 12, 2015
    #17
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  18. Evillevi

    Evillevi Shadow Pika!

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    Also it's been a long while but a question, if the hypothetical actual distribution of the QQ roller (in %) is say 12/10/.../10/8 for each group of ten would the Chi square test even notice the difference from the theoratical distribution of 10% for each group
     
    Evillevi, May 12, 2015
    #18
  19. pepperjack

    pepperjack A Variety of Cheese

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    The way you've got it set up, you're basically only testing the fidelity of the ten's place; every roll could end with 5 and the test wouldn't notice.

    One alternative would be to set up a chart with a hundred rows (one for each actual roll). One hundred and thirty rolls probably isn't a large enough number to give good data for that, though.
     
    pepperjack, May 12, 2015
    #19
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  20. pepperjack

    pepperjack A Variety of Cheese

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    Actually, I think I misunderstood your question. In my post above, I thought you were asking about percentage distribution within each group of ten. Reading you post again, I think you're asking about distribution across the groups. Like, you're asking if

    1-10 (12% of rolls)
    11-12 (10% of rolls)
    ...
    81-90 (10% of rolls)
    91-100 (8% of rolls)

    would be noticed by the test.

    If that's what you're asking, the answer is "it depends on how many rolls you make." For a lower number of rolls, this distribution might not register as biased. For a very high number of rolls, it definitely would register as biased. That's the magic of the exponent in the fifth column of the table.


    Edit: That's a feature, of course, not a bug. If you roll a d6 twenty times and get five sixes, you might just have been lucky. If you roll the same d6 two thousand times and get five hundred sixes, something is probably up.

    Edit 2: Example math

    Only two rows matter on this table since the rest are rolling as expected.

    One hundred rolls of 1d100
    iOiEiOi −Ei(Oi −Ei )2(Oi −Ei )2/Ei
    1-101210240.40
    91-100810-240.40
        Sum0.80
    Ten thousand rolls of 1d100
    iOiEiOi −Ei(Oi −Ei )2(Oi −Ei )2/Ei
    1-101200100020040,00040
    91-1008001000-20040,00040
        Sum80
    For a test of only a hundred rolls, this distribution is barely a blip; the critical value for even five percent confidence is 3.32 for nine degrees of freedom. However, for a test of ten thousand rolls, this distribution is proof positive that the die is biased: the critical value for 99.9% confidence is only 27.88.


    Edit 3:

    If you get the 12%/10%/.../10%/8% distribution over a test of 2,000 rolls, the sum is 16, which is pretty close to the critical value for confidence of 95%, but not quite there (it would need to exceed 16.92 to get a p-value of 0.05). So, you'd need more than 2,000 rolls for this distribution to be statistically significant, but not many more.
     
    Last edited: May 12, 2015
    pepperjack, May 12, 2015
    #20
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  21. Evillevi

    Evillevi Shadow Pika!

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    Interesting. Thanks for explaining it to me
     
    Evillevi, May 12, 2015
    #21
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