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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| + | 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 == |
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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]
