Dice
From ThorxWiki
(Difference between revisions)
(link info) |
(link to coffee graphs) |
||
| (21 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | = Dice = |
||
| − | |||
Dice are an essential part of many games. |
Dice are an essential part of many games. |
||
| − | This is an exploration of probabilities of D6. The faces are generilised to A,B,C,D,E,F |
+ | 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 |
||
{| class="wikitable" |
{| class="wikitable" |
||
|- |
|- |
||
| − | ! Requirement !! 1D6 !! 2D6 !! 3D6 !! 4D6 !! 5D6 !! 6D6 !! 7D6 !! 8D6 !! 9D6 !! 10D6 !! 11D6 !! 12D6 !! 13D6 !! 14D6 !! 15D6 |
+ | !| Requirement !! 1D6 !! 2D6 !! 3D6 !! 4D6 !! 5D6 !! 6D6 !! 7D6 !! 8D6 !! 9D6 !! 10D6 !! 11D6 !! 12D6 !! 13D6 !! 14D6 !! 15D6 |
|- |
|- |
||
| − | | A OR B OR C || 3/6 || || || || || || || || || || || || || || |
+ | | 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 || 2/6 || || || || || || || || || || || || || || |
+ | | 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 || || || || || || || || || || || || || || |
+ | | 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 B) OR (C AND D) || n/a || || || || || || || || || || || || || || |
||
| + | |- |
||
| + | | A AND (A OR B) || n/a || || || || || || || || || || || || || || |
||
|- |
|- |
||
| A AND (B OR C) || n/a || || || || || || || || || || || || || || |
| A AND (B OR C) || n/a || || || || || || || || || || || || || || |
||
| + | |- |
||
| + | | A AND A || n/a || || || || || || || || || || || || || || |
||
|- |
|- |
||
| A AND B || 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 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 || || || || || || || || || || || || |
| A AND B AND C || n/a || n/a || 1/36 || || || || || || || || || || || || |
||
| + | |||
|} |
|} |
||
| − | == Info == |
+ | The above incomplete table is calculated exact. |
| − | * Useful site https://anydice.com/ |
||
| − | Can craft custom functions there, such as |
+ | 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 |
||
<pre> |
<pre> |
||
function: SEQUENCE:s has N:n and NN:n or NNN:n{ |
function: SEQUENCE:s has N:n and NN:n or NNN:n{ |
||
| − | result: (SEQUENCE=N) & ((SEQUENCE = N) | (SEQUENCE = NN)) > 0 |
+ | result: (SEQUENCE=N) & ((SEQUENCE = NN) | (SEQUENCE = NNN)) > 0 |
} |
} |
||
| − | output [2d6 has 4 and 6 or 3] |
+ | output [2d6 has 2 and 4 or 3] |
</pre> |
</pre> |
||
| + | |||
| + | |||
Latest revision as of 22:36, 11 February 2020
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
[edit] 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]
