Dice

Dice are an essential part of many games.

This is an exploration of probabilities of D6 (note: Normal D6, not https://en.wikipedia.org/wiki/Sicherman_dice)

The faces are generalised to A,B,C,D,E,F and order is not important

Requirement	1D6	2D6	3D6	4D6	5D6	6D6	7D6	8D6	9D6	10D6	11D6	12D6	13D6	14D6	15D6
A OR B OR C	1/2	3/4	7/8	15/16	31/32	63/64	127/128	255/256	511/512	1023/1024	2047/2048	4095/4096	8191/8192	16383/16384	32767/32768
A OR B	1/3	5/9	19/27	65/81	212/243	665/729	2059/2187	6305/6561	19171/19683	58025/59049	175099/177147	527345/531441	99.49%	99.66%	99.77%
A	1/6	11/36	91/216	671/1296	4561/7776	31031/46656	201811/279936	1288991/1679616	8124571/10077696	83.85%	86.54%	88.78%	90.65%	92.21%	93.51%
(A OR B) AND (A OR B)	n/a
(A OR B) AND (B OR C)	n/a
(A OR B) AND (C OR D)	n/a
(A AND B) OR (C AND D)	n/a
A AND (A OR B)	n/a
A AND (B OR C)	n/a
A AND A	n/a
A AND B	n/a
A AND (A OR B) AND (C OR D)	n/a	na
A AND (A OR B) AND (A OR C)	n/a	na
A AND (A OR B) AND (B OR C)	n/a	na
A AND (B OR C) AND (C OR D)	n/a	na
A AND (B OR C) AND (D OR E)	n/a	na
A AND ((B AND C) OR (D AND E))	n/a	na
A AND B AND (A or B)	n/a	na
A AND B AND (B or C)	n/a	na
A AND A AND (C or D)	n/a	na
A AND B AND (C or D)	n/a	na
A AND A AND A	n/a	n/a	1/36
A AND A AND B	n/a	n/a
A AND B AND C	n/a	n/a	1/36

The above incomplete table is calculated exact.

The graphs at this link are experimental based on thousands of simulated dice rolls (relying on linux /dev/urandom for randomness)

http://nemo.house.cx/~nemo/slumberland/coffee.html

Infos

• http://www.semistable.com/dicelab/ - local tool with own language to craft results and calculate probabilities

• https://anydice.com/ - Can craft custom functions there, such as

function: SEQUENCE:s has N:n and NN:n or NNN:n{
 result: (SEQUENCE=N) & ((SEQUENCE = NN) | (SEQUENCE = NNN)) > 0
}

output [2d6 has 2 and 4 or 3]