Dice

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= Dice =
 
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Dice are an essential part of many games.
 
Dice are an essential part of many games.
   
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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 || || || || || || || || || || || || || ||
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| 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 || || || || || || || || || || || ||
  +
 
|}
 
|}
  +
  +
  +
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)
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  +
http://nemo.house.cx/~nemo/slumberland/coffee.html
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  +
  +
== 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
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  +
<pre>
  +
function: SEQUENCE:s has N:n and NN:n or NNN:n{
  +
result: (SEQUENCE=N) & ((SEQUENCE = NN) | (SEQUENCE = NNN)) > 0
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}
  +
  +
output [2d6 has 2 and 4 or 3]
  +
</pre>
  +
  +
  +
   
 
[[Category:Games]]
  
[[Category:Games]]

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 

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]
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