Dice odds without dice - Page 3

Anthony · 05-31-2018, 04:26 PM

Quote:

Originally Posted by evileeyore

Very nice! Hmmm. I wonder if there are print shops that could do a run of cards specifically for this...

Alternately, take two identical decks of cards (say, a Canasta set), remove 1-6 from each of them, and shuffle them together. The result is a 48 card deck. Your odds are still slightly distorted (for any given combination, odds range from 1/308 to 1/203, instead of a constant 1/216), but the more cards you have the less your numbers get distorted.

ericbsmith · 05-31-2018, 04:29 PM

Quote:

Originally Posted by evileeyore

Very nice! Hmmm. I wonder if there are print shops that could do a run of cards specifically for this...

If you're going to go that far... you might as well make your own version of the GURPS Combat Cards which includes the Die Roll Results as a symbol in the corners.

zuljita · 06-01-2018, 11:53 AM

There's also the A Deck of Dice article in Pyramid #3/34: Alternate GURPS. There's a discussion thread about using such a system on Mook's page.

Brandy · 06-03-2018, 12:25 PM

I was musing around with an alternative that could get the desired result with a smaller number of cards. I noticed that you get pretty good results - not perfect -- with just 12 cards numbered 0-1-2-2-3-3-4-4-5-5-6-7. Take three cards at random and add them together.

Here's how that compares to 3d6:

Code:

	Freq	Pct	3d6%
3	12	0.9%	0.5%
4	18	1.4%	1.4%
5	42	3.2%	2.8%
6	66	5.0%	4.6%
7	96	7.3%	6.9%
8	120	9.1%	9.7%
9	150	11.4%	11.6%
10	156	11.8%	12.5%
11	156	11.8%	12.5%
12	150	11.4%	11.6%
13	120	9.1%	9.7%
14	96	7.3%	6.9%
15	66	5.0%	4.6%
16	42	3.2%	2.8%
17	18	1.4%	1.4%
18	12	0.9%	0.5%

ericbsmith · 06-03-2018, 01:11 PM

Quote:

Originally Posted by Brandy

I noticed that you get pretty good results - not perfect -- with just 12 cards numbered 0-1-2-2-3-3-4-4-5-5-6-7. Take three cards at random and add them together.

That's brilliant. I hadn't even thought about using an asymmetrical set of cards. You can actually tighten up the results by using 14 cards, numbered 0-1-2-2-3-3-3-4-4-4-5-5-6-7 (this adds in an extra 3 & 4).

Code:

    Freq     Pct    3d6%      Pct     3d6%
                              Cum      Cum
 3    12   0.55%   0.46%    0.55%    0.46%
 4    24   1.10%   1.39%    1.65%    1.85%
 5    60   2.75%   2.78%    4.40%    4.63%
 6   102   4.67%   4.63%    9.07%    9.26%
 7   156   7.14%   6.94%   16.21%   16.20%
 8   204   9.34%   9.72%   25.55%   25.93%
 9   258  11.81%  11.57%   37.36%   37.50%
10   276  12.64%  12.50%   50.00%   50.00%
11   276  12.64%  12.50%   62.64%   62.50%
12   258  11.81%  11.57%   74.45%   74.07%
13   204   9.34%   9.72%   83.79%   83.80%
14   156   7.14%   6.94%   90.93%   90.74%
15   102   4.67%   4.63%   95.60%   95.37%
16    60   2.75%   2.78%   98.35%   98.15%
17    24   1.10%   1.39%   99.45%   99.54%
18    12   0.55%   0.46%  100.00%  100.00%

That same 14-card deck also works pretty well as a 2d6 simulator for damage, although it does allow for a result of 1 or 13 (either just allow the results or treat a 1 as a 2 and a 13 as a 12; either works fine).

Code:

    Freq     Pct    2d6%      Pct     2d6%
                              Cum      Cum
 1     2   1.10%   0.00%    1.10%    0.00%
 2     4   2.20%   2.78%    3.30%    2.78%
 3    10   5.49%   5.56%    8.79%    8.33%
 4    14   7.69%   8.33%   16.48%   16.67%
 5    22  12.09%  11.11%   28.57%   27.78%
 6    24  13.19%  13.89%   41.76%   41.67%
 7    30  16.48%  16.67%   58.24%   58.33%
 8    24  13.19%  13.89%   71.43%   72.22%
 9    22  12.09%  11.11%   83.52%   83.33%
10    14   7.69%   8.33%   91.21%   91.67%
11    10   5.49%   5.56%   96.70%   97.22%
12     4   2.20%   2.78%   98.90%  100.00%
13     2   1.10%   0.00%  100.00%    0.00%

Brandy · 06-03-2018, 01:25 PM

Quote:

Originally Posted by ericbsmith

That's brilliant. I hadn't even thought about using an asymmetrical set of cards. You can actually tighten up the results by using 14 cards, numbered 0-1-2-2-3-3-3-4-4-4-5-5-6-7 (this adds in an extra 3 & 4).
[/code]

That's a surprisingly good match for the 3d6 curve. Very nice.

ericbsmith · 06-03-2018, 03:50 PM

I just ran 4d6 and 6d6 probabilities using the 14-card deck, and while the bell curve isn't a great fit to rolling dice it does provide a reasonably good bell curve with a perfectly fair spread of results - and the same average result - for computing damage. In a pinch I wouldn't have an issue using that deck for damage results through 6d6. I'm pretty sure it would be fine for results through 9d6 or more; it's just that the more cards you pull the more the bell curve begins to look less and less like a bell, tending towards producing the average. The again, the same happens when rolling lots of dice, just not at quite as quickly a rate. On 9d6 you will roll between 26-37 (avg+/-5.5) a full 66% of the time.

And since the 14-card deck only includes, at most, 3 of the same card you could use a single deck of playing cards to set it up as well as a separate 1d6 deck using the cards A-6. Or you could use the same 14-card deck to draw 1d6 from; it produces a fair bell-curve of results with the same average, it's just a different curve than 1d6 would.

Code:

    Freq     Pct    4d6%     Pct    4d6%
                             Cum     Cum
 4     0   0.00%   0.08%   0.00%   0.08%
 5    24   0.10%   0.31%   0.10%   0.39%
 6   144   0.60%   0.77%   0.70%   1.16%
 7   288   1.20%   1.54%   1.90%   2.70%
 8   600   2.50%   2.70%   4.40%   5.40%
 9   984   4.10%   4.32%   8.49%   9.72%
10  1512   6.29%   6.17%  14.79%  15.90%
11  1920   7.99%   8.02%  22.78%  23.92%
12  2448  10.19%   9.65%  32.97%  33.56%
13  2664  11.09%  10.80%  44.06%  44.37%
14  2856  11.89%  11.27%  55.94%  55.63%
15  2664  11.09%  10.80%  67.03%  66.44%
16  2448  10.19%   9.65%  77.22%  76.08%
17  1920   7.99%   8.02%  85.21%  84.10%
18  1512   6.29%   6.17%  91.51%  90.28%
19   984   4.10%   4.32%  95.60%  94.60%
20   600   2.50%   2.70%  98.10%  97.30%
21   288   1.20%   1.54%  99.30%  98.84%
22   144   0.60%   0.77%  99.90%  99.61%
23    24   0.10%   0.31% 100.00%  99.92%
24     0   0.00%   0.08% 100.00% 100.00%

Code:

      Freq      Pct    6d6%       Pct      6d6%
                                  Cum       Cum
 6       0   0.000%  0.002%    0.000%    0.002%
 7       0   0.000%  0.013%    0.000%    0.015%
 8       0   0.000%  0.045%    0.000%    0.060%
 9       0   0.000%  0.120%    0.000%    0.180%
10       0   0.000%  0.270%    0.000%    0.450%
11    2160   0.100%  0.540%    0.100%    0.990%
12    7920   0.366%  0.977%    0.466%    1.968%
13   20160   0.932%  1.620%    1.399%    3.588%
14   37440   1.732%  2.488%    3.130%    6.076%
15   66240   3.064%  3.571%    6.194%    9.647%
16   96480   4.462%  4.816%   10.656%   14.463%
17  136800   6.327%  6.121%   16.983%   20.585%
18  170640   7.892%  7.354%   24.875%   27.939%
19  204480   9.457%  8.372%   34.332%   36.310%
20  221760  10.256%  9.047%   44.589%   45.358%
21  234000  10.823%  9.285%   55.411%   54.642%
22  221760  10.256%  9.047%   65.668%   63.690%
23  204480   9.457%  8.372%   75.125%   72.061%
24  170640   7.892%  7.354%   83.017%   79.415%
25  136800   6.327%  6.121%   89.344%   85.537%
26   96480   4.462%  4.816%   93.806%   90.353%
27   66240   3.064%  3.571%   96.870%   93.924%
28   37440   1.732%  2.488%   98.601%   96.412%
29   20160   0.932%  1.620%   99.534%   98.032%
30    7920   0.366%  0.977%   99.900%   99.010%
31    2160   0.100%  0.540%  100.000%   99.550%
32       0   0.000%  0.270%    0.000%   99.820%
33       0   0.000%  0.120%    0.000%   99.940%
34       0   0.000%  0.045%    0.000%   99.985%
35       0   0.000%  0.013%    0.000%   99.998%
36       0   0.000%  0.002%    0.000%  100.000%

ericbsmith · 06-03-2018, 06:15 PM

One last data dump post on this. I continued looking at this and you can get slightly better results is you use 20 cards. This can, of course, be built using a standard deck of playing cards since the maximum number of cards is 4x of the same.
1x = 0 (Joker?)
2x = 1 (Ace)
3x = 2
4x = 3
4x = 4
3x = 5
2x = 6
1x = 7

Compared to the 14-card deck the 20-card deck gets only slightly better results for a 3d6 roll, but it gets far better results for other die rolls, with 2d6 and 4d6 being very close, and higher die rolls being better bell curves.

Worth noting, on a 3d6 roll you can draw a 2 or 19; for skill rolls just treat them as a 3 or 18.

For damage rolls, on 1d6 you can draw a 0 or 7. On 2d6 you can draw a 1 or 13. On 3d6 you can draw a 2 or 19. You need to decide whether to just use the resulting draw or to bump the result into the range of the actual die roll. Either way will be statistically similar results, but you should use the same method consistently.

Code:

Roll    2d6   20 Card     2d6%   20 Card       2d6   20 Card
       Freq      Freq                  %      Cum%      Cum%
   1                4    0.00%     1.05%     0.00%     1.05%
   2      1         8    2.78%     2.11%     2.78%     3.16%
   3      2        20    5.56%     5.26%     8.33%     8.42%
   4      3        30    8.33%     7.89%    16.67%    16.32%
   5      4        46   11.11%    12.11%    27.78%    28.42%
   6      5        52   13.89%    13.68%    41.67%    42.11%
   7      6        60   16.67%    15.79%    58.33%    57.89%
   8      5        52   13.89%    13.68%    72.22%    71.58%
   9      4        46   11.11%    12.11%    83.33%    83.68%
  10      3        30    8.33%     7.89%    91.67%    91.58%
  11      2        20    5.56%     5.26%    97.22%    96.84%
  12      1         8    2.78%     2.11%   100.00%    98.95%
  13                4    0.00%     1.05%   100.00%   100.00%

Code:

Roll    3d6   20 Card     3d6%   20 Card       3d6   20 Card
       Freq      Freq                  %      Cum%      Cum%
   2                6    0.00%     0.09%     0.00%     0.09%
   3      1        36    0.46%     0.53%     0.46%     0.61%
   4      3        84    1.39%     1.23%     1.85%     1.84%
   5      6       180    2.78%     2.63%     4.63%     4.47%
   6     10       318    4.63%     4.65%     9.26%     9.12%
   7     15       480    6.94%     7.02%    16.20%    16.14%
   8     21       648    9.72%     9.47%    25.93%    25.61%
   9     25       798   11.57%    11.67%    37.50%    37.28%
  10     27       870   12.50%    12.72%    50.00%    50.00%
  11     27       870   12.50%    12.72%    62.50%    62.72%
  12     25       798   11.57%    11.67%    74.07%    74.39%
  13     21       648    9.72%     9.47%    83.80%    83.86%
  14     15       480    6.94%     7.02%    90.74%    90.88%
  15     10       318    4.63%     4.65%    95.37%    95.53%
  16      6       180    2.78%     2.63%    98.15%    98.16%
  17      3        84    1.39%     1.23%    99.54%    99.39%
  18      1        36    0.46%     0.53%   100.00%    99.91%
  19                6    0.00%     0.09%   100.00%   100.00%

Code:

Roll    4d6   20 Card     4d6%   20 Card       4d6   20 Card
       Freq      Freq                  %      Cum%      Cum%
   4      1        72    0.08%     0.06%     0.08%     0.06%
   5      4       240    0.31%     0.21%     0.39%     0.27%
   6     10       768    0.77%     0.66%     1.16%     0.93%
   7     20      1560    1.54%     1.34%     2.70%     2.27%
   8     35      2976    2.70%     2.56%     5.40%     4.83%
   9     56      4776    4.32%     4.11%     9.72%     8.94%
  10     80      7152    6.17%     6.15%    15.90%    15.09%
  11    104      9336    8.02%     8.03%    23.92%    23.12%
  12    125     11592    9.65%     9.97%    33.56%    33.09%
  13    140     12888   10.80%    11.08%    44.37%    44.17%
  14    146     13560   11.27%    11.66%    55.63%    55.83%
  15    140     12888   10.80%    11.08%    66.44%    66.91%
  16    125     11592    9.65%     9.97%    76.08%    76.88%
  17    104      9336    8.02%     8.03%    84.10%    84.91%
  18     80      7152    6.17%     6.15%    90.28%    91.06%
  19     56      4776    4.32%     4.11%    94.60%    95.17%
  20     35      2976    2.70%     2.56%    97.30%    97.73%
  21     20      1560    1.54%     1.34%    98.84%    99.07%
  22     10       768    0.77%     0.66%    99.61%    99.73%
  23      4       240    0.31%     0.21%    99.92%    99.94%
  24      1        72    0.08%     0.06%   100.00%   100.00%

Code:

   Roll    5d6   20 Card     5d6%   20 Card       5d6   20 Card
          Freq      Freq                  %      Cum%      Cum%
      5      1         0    0.01%     0.00%     0.01%     0.00%
      6      5       360    0.06%     0.02%     0.08%     0.02%
      7     15      1680    0.19%     0.09%     0.27%     0.11%
      8     35      5160    0.45%     0.28%     0.72%     0.39%
      9     70     12120    0.90%     0.65%     1.62%     1.04%
     10    126     24720    1.62%     1.33%     3.24%     2.37%
     11    205     43080    2.64%     2.32%     5.88%     4.68%
     12    305     68400    3.92%     3.68%     9.80%     8.36%
     13    420     98640    5.40%     5.30%    15.20%    13.66%
     14    540    131160    6.94%     7.05%    22.15%    20.71%
     15    651    161520    8.37%     8.68%    30.52%    29.39%
     16    735    185280    9.45%     9.96%    39.97%    39.35%
     17    780    198120   10.03%    10.65%    50.00%    50.00%
     18    780    198120   10.03%    10.65%    60.03%    60.65%
     19    735    185280    9.45%     9.96%    69.48%    70.61%
     20    651    161520    8.37%     8.68%    77.85%    79.29%
     21    540    131160    6.94%     7.05%    84.80%    86.34%
     22    420     98640    5.40%     5.30%    90.20%    91.64%
     23    305     68400    3.92%     3.68%    94.12%    95.32%
     24    205     43080    2.64%     2.32%    96.76%    97.63%
     25    126     24720    1.62%     1.33%    98.38%    98.96%
     26     70     12120    0.90%     0.65%    99.28%    99.61%
     27     35      5160    0.45%     0.28%    99.73%    99.89%
     28     15      1680    0.19%     0.09%    99.92%    99.98%
     29      5       360    0.06%     0.02%    99.99%   100.00%
     30      1         0    0.01%     0.00%   100.00%   100.00%

kmunoz · 06-03-2018, 08:01 PM

Is it a "no dice" because "NO DICE!" or because "no dice /sadface"?

If it's the latter, I'm guessing playing cards would be just as awkward (if not more so). Rolling dice inside a small box with shrink-wrap over the top would keep them from flying around. Or an empty peanut can with the transparent top on.

ericbsmith · 06-03-2018, 10:20 PM

Quote:

Originally Posted by ericbsmith

Buy a prize out of a gumball machine. Buy three dice that will fit inside of it, with one of the dice being an off-color. Instant 1d-2d-3d shaker.

On this note, I bought a ton of 12mm dice a while ago, intending to put them to another use which I never got around to doing, so they've just been sitting around. I got a brick of Chessex 36d6 and I also picked five set of dice, with 6d6 per color. After this conversation I started poking around and found these "slime storage containers" which look to be reasonably sturdy and that should hold 6d6 with enough room to allow them to shake quite nicely. At less than $3 for a set of 15 containers I decided to order them (I've spent $3 on far worse things than 15 small storage containers I can use for all sorts of things). If anyone wants to do this they could buy loose dice from their FLGS, or online somewhere, or they could get three bricks of 12mm Chessex dice in three different colors. Then you put 3d6 of one color, 2d6 of a second color, and 1d6 of a third color in a small container like those slime containers and you have an instant 1d6-6d6 dice shaker.

06-01-2018, 11:53 AM	#23
zuljita Join Date: May 2008	Re: Dice odds without dice There's also the A Deck of Dice article in Pyramid #3/34: Alternate GURPS. There's a discussion thread about using such a system on Mook's page. __________________ Running 3 GURPS games: DFRPG, Supers and a weird Evil Hogwart's (ish) game. Check out my blog: Dungeons on Automatic

06-03-2018, 12:25 PM	#24
Brandy Join Date: Aug 2004 Location: Nashville, TN	Re: Dice odds without dice I was musing around with an alternative that could get the desired result with a smaller number of cards. I noticed that you get pretty good results - not perfect -- with just 12 cards numbered 0-1-2-2-3-3-4-4-5-5-6-7. Take three cards at random and add them together. Here's how that compares to 3d6: Code: Freq Pct 3d6% 3 12 0.9% 0.5% 4 18 1.4% 1.4% 5 42 3.2% 2.8% 6 66 5.0% 4.6% 7 96 7.3% 6.9% 8 120 9.1% 9.7% 9 150 11.4% 11.6% 10 156 11.8% 12.5% 11 156 11.8% 12.5% 12 150 11.4% 11.6% 13 120 9.1% 9.7% 14 96 7.3% 6.9% 15 66 5.0% 4.6% 16 42 3.2% 2.8% 17 18 1.4% 1.4% 18 12 0.9% 0.5% __________________ I didn't realize who I was until I stopped being who I wasn't. Formerly known as Bookman- forum name changed 1/3/2018.

06-03-2018, 08:01 PM	#29
kmunoz Join Date: May 2006 Location: Seattle, Washington	Re: Dice odds without dice Is it a "no dice" because "NO DICE!" or because "no dice /sadface"? If it's the latter, I'm guessing playing cards would be just as awkward (if not more so). Rolling dice inside a small box with shrink-wrap over the top would keep them from flying around. Or an empty peanut can with the transparent top on. __________________ Natural Encyclopedia: 660 GURPS bestiary entries It Came from the Forums: A Community Bestiary with 160 entries (last updated 2009...someday I will revisit.)