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Old 05-30-2018, 02:39 PM   #11
evileeyore
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Default Re: Dice odds without dice

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Originally Posted by Anthony View Post
According to OP: 'We have no dice and no digital tech.' Otherwise, yes, it's by far the easiest solution.
Oops. Missed the 'no digital' line.



Another possibility: Do you have a deck of cards? Take the Ace and 2-6 from each suit. This gives you four 'dice'.
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Old 05-30-2018, 03:02 PM   #12
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Default Re: Dice odds without dice

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Another possibility: Do you have a deck of cards? Take the Ace and 2-6 from each suit. This gives you four 'dice'.
It's statistically poor unless you reshuffle after each card pull, which is a hassle (the odds of rolling three on 3d6 is 1/216. The odds of pulling three aces from a deck of 24 cards is 1/552).
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Old 05-30-2018, 03:12 PM   #13
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Default Re: Dice odds without dice

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Originally Posted by Anthony View Post
It's statistically poor unless you reshuffle after each card pull, which is a hassle (the odds of rolling three on 3d6 is 1/216. The odds of pulling three aces from a deck of 24 cards is 1/552).
Keep separate piles. Or keep one pile and draw until you have cards from a number of suits equal to the number of dice - two suits foe 2d, three suits for 3d, four suits for 4d, using only the first card drawn from each suit for your "roll."
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Old 05-30-2018, 03:37 PM   #14
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Default Re: Dice odds without dice

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Keep separate piles. Or keep one pile and draw until you have cards from a number of suits equal to the number of dice - two suits foe 2d, three suits for 3d, four suits for 4d, using only the first card drawn from each suit for your "roll."
Basically this, I just didn't feel like writing it out. Thanks ericbsmith!


Also, if you need more cards (for ease of shuffling, smoother statistical spread, etc) just ditch the Ace from each suit and the two Jokers. Assign the King 13, Queen as 12, the Jack as 11, and then divide by two, round down. Viola, 1-6 distribution (but with more maths).



Basically I mention this method (deck of cards) since I always have a deck of cards on me* when going on a trip, and more importantly, many 'rest stop' style gas stations sell decks of cards, but not often dice.


* I also always have dice, but that's less relevant at the moment.

Last edited by evileeyore; 05-30-2018 at 03:41 PM.
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Old 05-30-2018, 04:29 PM   #15
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Default Re: Dice odds without dice

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Originally Posted by ericbsmith View Post
Keep separate piles. Or keep one pile and draw until you have cards from a number of suits equal to the number of dice - two suits foe 2d, three suits for 3d, four suits for 4d, using only the first card drawn from each suit for your "roll."
I was going to suggest putting numbers on slips of paper and drawing from a cup, but cards are far more elegant (and they're pretty cheap.)
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Old 05-30-2018, 04:34 PM   #16
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Default Re: Dice odds without dice

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Ultimately, it's clearly better to use a randomizing tool. (And thanks for the great suggestions along those lines.) We got to musing about the possibility of guessing numbers in the car, which then got me interested in the theory of how one could use guessing numbers as a randomizer.
Deck of cards?
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Old 05-30-2018, 07:00 PM   #17
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Default Re: Dice odds without dice

Something with a Popomatic Bubble (TM)?
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Old 05-30-2018, 08:13 PM   #18
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Default Re: Dice odds without dice

I've been in this situation before and thought about how I would handle it. My solution was to use the english language as my source of randomness.

I explain it here, including links to the tables.

Ironically, I haven't had a chance to use it: I've either had electronics or dice with me ever since.
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Old 05-31-2018, 03:55 PM   #19
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Default Re: Dice odds without dice

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Originally Posted by evileeyore View Post
Another possibility: Do you have a deck of cards? Take the Ace and 2-6 from each suit. This gives you four 'dice'.
I've been running some numbers, and if you take a standard 54 card deck of cards (w/2 jokers) and you take a sharpie to them, you can number the cards 1-6 nine times. If you draw 1,2,3, even 6 cards from the deck to represent a roll of that number of dice the distribution of results is off from rolling the same number of dice by less than 1% for any given result, with the overall bell curve is almost the same shape. Any inaccuracies are reflected on both sides of the distribution curve (so on 3d6 a reduction in the number of 3's from being "rolled" is mirrored by the same reduction in 18's being "rolled"). It's close enough that I personally wouldn't worry about it, and the added convenience of being able to use a deck of cards when dice aren't available certainly makes up for it.

1d6 vs. 1 Card: Results unchanged
Code:
Result     2d6  2 Cards      2d6  2 Cards
             %        %    Cum %    Cum %
     2   2.78%    2.52%    2.78%    2.52%
     3   5.56%    5.66%    8.33%    8.18%
     4   8.33%    8.18%   16.67%   16.35%
     5  11.11%   11.32%   27.78%   27.67%
     6  13.89%   13.84%   41.67%   41.51%
     7  16.67%   16.98%   58.33%   58.49%
     8  13.89%   13.84%   72.22%   72.33%
     9  11.11%   11.32%   83.33%   83.65%
    10   8.33%    8.18%   91.67%   91.82%
    11   5.56%    5.66%   97.22%   97.48%
    12   2.78%    2.52%  100.00%  100.00%
Code:
Result     3d6  3 Cards      3d6  3 Cards
             %        %    Cum %    Cum %
     3   0.46%    0.34%    0.46%    0.34%
     4   1.39%    1.31%    1.85%    1.64%
     5   2.78%    2.61%    4.63%    4.26%
     6   4.63%    4.58%    9.26%    8.84%
     7   6.94%    6.86%   16.20%   15.70%
     8   9.72%    9.80%   25.93%   25.50%
     9  11.57%   11.77%   37.50%   37.26%
    10  12.50%   12.74%   50.00%   50.00%
    11  12.50%   12.74%   62.50%   62.74%
    12  11.57%   11.77%   74.07%   74.50%
    13   9.72%    9.80%   83.80%   84.30%
    14   6.94%    6.86%   90.74%   91.16%
    15   4.63%    4.58%   95.37%   95.74%
    16   2.78%    2.61%   98.15%   98.36%
    17   1.39%    1.31%   99.54%   99.66%
    18   0.46%    0.34%  100.00%  100.00%
Code:
Result      6d6  6 Cards       6d6   6 Cards
              %        %     Cum %     Cum %
     6  0.0021%  0.0003%   0.0021%   0.0003%
     7  0.0129%  0.0044%   0.0150%   0.0047%
     8  0.0450%  0.0220%   0.0600%   0.0267%
     9  0.1200%  0.0712%   0.1800%   0.0979%
    10  0.2701%  0.1844%   0.4501%   0.2823%
    11  0.5401%  0.4039%   0.9902%   0.6863%
    12  0.9774%  0.7923%   1.9676%   1.4785%
    13  1.6204%  1.3988%   3.5880%   2.8773%
    14  2.4884%  2.2625%   6.0764%   5.1398%
    15  3.5708%  3.3822%   9.6472%   8.5219%
    16  4.8161%  4.7150%  14.4633%  13.2369%
    17  6.1214%  6.1558%  20.5847%  19.3927%
    18  7.3538%  7.5399%  27.9385%  26.9326%
    19  8.3719%  8.7056%  36.3104%  35.6382%
    20  9.0471%  9.4808%  45.3575%  45.1190%
    21  9.2850%  9.7619%  54.6425%  54.8810%
    22  9.0471%  9.4808%  63.6896%  64.3618%
    23  8.3719%  8.7056%  72.0615%  73.0674%
    24  7.3538%  7.5399%  79.4153%  80.6073%
    25  6.1214%  6.1558%  85.5367%  86.7631%
    26  4.8161%  4.7150%  90.3528%  91.4781%
    27  3.5708%  3.3822%  93.9236%  94.8602%
    28  2.4884%  2.2625%  96.4120%  97.1227%
    29  1.6204%  1.3988%  98.0324%  98.5215%
    30  0.9774%  0.7923%  99.0098%  99.3137%
    31  0.5401%  0.4039%  99.5499%  99.7177%
    32  0.2701%  0.1844%  99.8200%  99.9021%
    33  0.1200%  0.0712%  99.9400%  99.9733%
    34  0.0450%  0.0220%  99.9850%  99.9953%
    35  0.0129%  0.0044%  99.9979%  99.9997%
    36  0.0021%  0.0003% 100.0000% 100.0000%
Fun note: On the 2d6 table you can notice that the chance of drawing an even result goes down from rolling an even result while the chance of drawing an odd result goes up compared to rolling. This is because all even results include a chance of rolling a pair while there are no pairs in odd results, and in the card draw method the chance of drawing a pair goes down substantially. The same thing happens with drawing triplets in 3d6 or sextuplets in 6d6, however the number of possible results are so much greater in these two instances that the resulting swing is drowned out in the results. Only in the 2d6 table is this swing apparent because of the fewer number of possible results.
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Last edited by ericbsmith; 05-31-2018 at 04:25 PM.
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Old 05-31-2018, 04:18 PM   #20
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Default Re: Dice odds without dice

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I've been running some numbers...
Very nice! Hmmm. I wonder if there are print shops that could do a run of cards specifically for this...
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