User:Fwilson/Villagergame delay probabilities
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If safes are alive, this is the delay after all safes have acted. If safes are dead, the delay is the total night length.
The probability is of the exact timing occurring (probability mass function), whereas cumulative is the probability that any time less than or equal to the specified time occurs (cumulative distribution function).
The delay is a normal distribution with a mean of a 5 second delay and a standard deviation of 1.5 seconds. When safes are alive, all negative delays are equivalent to a 0 second delay. When safes are dead, the absolute value of the delay is taken, transforming it into a folded normal distribution. These modifications are not represented in the table below (edits welcome!)
| Delay | Probability | Cumulative |
|---|---|---|
| -2 seconds | < 0.0005% | < 0.0005% |
| -1 second | 0.009% | 0.003% |
| 0 seconds | 0.103% | 0.043% |
| 1 second | 0.760% | 0.383% |
| 2 seconds | 3.599% | 2.275% |
| 3 seconds | 10.934% | 9.121% |
| 4 seconds | 21.297% | 25.249% |
| 5 seconds | 26.596% | 50.000% |
| 6 seconds | 21.297% | 74.751% |
| 7 seconds | 10.934% | 90.879% |
| 8 seconds | 3.599% | 97.725% |
| 9 seconds | 0.760% | 99.617% |
| 10 seconds | 0.103% | 99.957% |
| 11 seconds | 0.009% | 99.997% |
| 12 seconds | < 0.0005% | ≥ 99.9995% |