[Cryptography] Throwing dice for "random" numbers

[Tom Mitchell]

On Sun, Aug 12, 2018 at 4:01 AM, Dave Horsfall <dave at horsfall.org> wrote:

> I know that I should know the answer to this, but for some reason my brain
> appears to be in neutral (call it early senility, as I turn 66 soon).
>
> I picked up a a pack of 12 dice from one of those discount stores for the
> princely sum of AU$2 (so we can safely assume that they are not exactly
> casino-quality[*], but at least the pattern of dots is correct).
>
> So, the obvious question is: how unpredictable (not "random") would their
> sum be, modulo N, given that each individual source is numbered 1-6?


Ignoring the quality of the dice for now.

With twelve common dice the numbers will range from 6 to 72.
With 12 and 72 being quite rare.

The number 13 is has twelve  ways of happening  a single 2 and 11 ones.

The number 14 has ways with  a pair of 2s and 12 ways with a single 3.

There are a lot of ways the dice can roll. 6^12 but a short list of sum
values (66)
so a value of 6 would be uncommon

.....
The value 33 would be very common compared to 6 or 72.
Now what is N?
Mod N of all the possible sum values is fixed.  The integer sum value can
be safely scaled
so it 6=0 or 6 & 72 are equal distant +/- from zero or any value (pi?).
The extreme 6&72
uncommon but the middle values near 33 very common and thus very
predictable..

Two dice is easy... snake eyes 1 in 36  boxcars 1 in 36.
Sums of 6,7,8 account for almost 45% if the rolls and 5,6,7,8,9 two thirds.
https://wizardofodds.com/gambling/dice/


https://wizardofodds.com/gambling/dice/2/  <-- no table for 12 but set two
aside and use the table for 10.

10 Dice
TOTALCOMBINATIONSPROBABILITY
10 1 0.000000016538172
11 10 0.000000165381717
12 55 0.000000909599443
13 220 0.000003638397771
14 715 0.000011824792757
15 2002 0.000033109419719
16 4995 0.000082608167581
17 11340 0.000187542866941
18 23760 0.000392946959305
19 46420 0.000767701929753
20 85228 0.001409515296618
21 147940 0.002446657119511
22 243925 0.004034073528976
23 383470 0.006341892697167
24 576565 0.009535330959246
25 831204 0.013746594459686
26 1151370 0.019041554736321
27 1535040 0.025386755067825
28 1972630 0.032623693616742
29 2446300 0.040457329400159
30 2930455 0.048464367913724
31 3393610 0.056124104821843
32 3801535 0.062870438507638
33 4121260 0.068158105450558
34 4325310 0.071532719383478
35 4395456 0.072692805974699
36 4325310 0.071532719383478
37 4121260 0.068158105450558
38 3801535 0.062870438507638
39 3393610 0.056124104821843
40 2930455 0.048464367913724
41 2446300 0.040457329400159
42 1972630 0.032623693616742
43 1535040 0.025386755067825
44 1151370 0.019041554736321
45 831204 0.013746594459686
46 576565 0.009535330959246
47 383470 0.006341892697167
48 243925 0.004034073528976
49 147940 0.002446657119511
50 85228 0.001409515296618
51 46420 0.000767701929753
52 23760 0.000392946959305
53 11340 0.000187542866941
54 4995 0.000082608167581
55 2002 0.000033109419719
56 715 0.000011824792757
57 220 0.000003638397771
58 55 0.000000909599443
59 10 0.000000165381717
60 1 0.000000016538172
Total 60466176 1.000000000000000








-- 
  T o m    M i t c h e l l
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