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. |
+ | 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 |
The faces are generalised to A,B,C,D,E,F and order is not important |
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{| class="wikitable" |
{| class="wikitable" |
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| − | ! Name !! 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 |
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| − | | | 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 |
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| − | | | 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% |
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| − | | | 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% |
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| − | | | (A OR B) AND (A OR B) || n/a || || || || || || || || || || || || || || |
+ | | (A OR B) AND (A OR B) || n/a || || || || || || || || || || || || || || |
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| − | | | (A OR B) AND (B OR C) || n/a || || || || || || || || || || || || || || |
+ | | (A OR B) AND (B OR C) || n/a || || || || || || || || || || || || || || |
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| − | | | (A OR B) AND (C OR D) || n/a || || || || || || || || || || || || || || |
+ | | (A OR B) AND (C OR D) || n/a || || || || || || || || || || || || || || |
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| − | | | (A AND B) OR (C AND D) || n/a || || || || || || || || || || || || || || |
+ | | (A AND B) OR (C AND D) || n/a || || || || || || || || || || || || || || |
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| − | | | A AND (A OR B) || n/a || || || || || || || || || || || || || || |
+ | | A AND (A OR B) || n/a || || || || || || || || || || || || || || |
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| − | | | A AND (B OR C) || n/a || || || || || || || || || || || || || || |
+ | | A AND (B OR C) || n/a || || || || || || || || || || || || || || |
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| − | | | A AND A || n/a || || || || || || || || || || || || || || |
+ | | A AND A || n/a || || || || || || || || || || || || || || |
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| − | | | A AND B || n/a || || || || || || || || || || || || || || |
+ | | A AND B || n/a || || || || || || || || || || || || || || |
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| − | | | A AND (A OR B) AND (C OR D) || n/a || na || || || || || || || || || || || || || |
+ | | A AND (A OR B) AND (C OR D) || n/a || na || || || || || || || || || || || || || |
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| − | | | A AND (A OR B) AND (A OR C) || n/a || na || || || || || || || || || || || || || |
+ | | A AND (A OR B) AND (A OR C) || n/a || na || || || || || || || || || || || || || |
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| − | | | A AND (A OR B) AND (B OR C) || n/a || na || || || || || || || || || || || || || |
+ | | A AND (A OR B) AND (B OR C) || n/a || na || || || || || || || || || || || || || |
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| − | | | A AND (B OR C) AND (C OR D) || n/a || na || || || || || || || || || || || || || |
+ | | A AND (B OR C) AND (C OR D) || n/a || na || || || || || || || || || || || || || |
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| − | | tripleand-doubleor | A AND (B OR C) AND (D OR E) || n/a || na || || || || || || || || || || || || || |
+ | | A AND (B OR C) AND (D OR E) || n/a || na || || || || || || || || || || || || || |
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| − | | tripleand-parallelor | A AND ((B AND C) OR (D AND E)) || n/a || na || || || || || || || || || || || || || |
+ | | A AND ((B AND C) OR (D AND E)) || n/a || na || || || || || || || || || || || || || |
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| − | | tripleand-whichtwin | A AND B AND (A or B) || n/a || na || || || || || || || || || || || || || |
+ | | A AND B AND (A or B) || n/a || na || || || || || || || || || || || || || |
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| − | | tripleand-maybetwin | A AND B AND (B or C) || n/a || na || || || || || || || || || || || || || |
+ | | A AND B AND (B or C) || n/a || na || || || || || || || || || || || || || |
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| − | | tripleand-twinandor | A AND A AND (C or D) || n/a || na || || || || || || || || || || || || || |
+ | | A AND A AND (C or D) || n/a || na || || || || || || || || || || || || || |
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| − | | tripleand-singleor | A AND B AND (C or D) || n/a || na || || || || || || || || || || || || || |
+ | | A AND B AND (C or D) || n/a || na || || || || || || || || || || || || || |
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| − | | tripleand-triplet | A AND A AND A || n/a || n/a || 1/36 || || || || || || || || || || || || |
+ | | A AND A AND A || n/a || n/a || 1/36 || || || || || || || || || || || || |
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| − | | tripleand-twin | A AND A AND B || n/a || n/a || || || || || || || || || || || || || |
+ | | A AND A AND B || n/a || n/a || || || || || || || || || || || || || |
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| − | | tripleand | A AND B AND C || n/a || n/a || 1/36 || || || || || || || || || || || || |
+ | | A AND B AND C || n/a || n/a || 1/36 || || || || || || || || || || || || |
|} |
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| + | |||
| + | |||
| + | The above incomplete table is calculated exact. |
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| + | |||
| + | 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 == |
== Infos == |
||
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]
