Dice

Dice are an essential part of many games.

This is an exploration of probabilities of D6.

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

Name	Requirement	1D6	2D6	3D6	4D6	5D6	6D6	7D6	8D6	9D6	10D6	11D6	12D6	13D6	14D6	15D6
tripleor	A OR B OR C	1/2	3/4	7/8	15/16
simpleor	A OR B	2/6
simplesingle	A	1/6
	(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
simpleand-twin	A AND A	n/a
simpleand	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
tripleand-doubleor	A AND (B OR C) AND (D OR E)	n/a	na
tripleand-parallelor	A AND ((B AND C) OR (D AND E))	n/a	na
tripleand-whichtwin	A AND B AND (A or B)	n/a	na
tripleand-maybetwin	A AND B AND (B or C)	n/a	na
tripleand-twinandor	A AND A AND (C or D)	n/a	na
tripleand-singleor	A AND B AND (C or D)	n/a	na
tripleand-triplet	A AND A AND A	n/a	n/a	1/36
tripleand-twin	A AND A AND B	n/a	n/a
tripleand	A AND B AND C	n/a	n/a	1/36

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]