# Dice

From ThorxWiki

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]