Just my two
, but I would say the unupped should be reduced to 4
to put it in line with the
equivalent. I would also suggest the following probabilities. Based on a bell shaped distribution, e.g. each potential point of reduction treated as a coin flip with a 50% chance of success. The upped version was made using a 7 coins and automatic +1 reduction.
Unupped - 0 -> 1.56%
- 1 -> 9.38%
- 2 -> 23.44%
- 3 -> 31.25%
- 4 -> 23.44%
- 5 -> 9.38%
- 6 -> 1.56%
| Upped - 1 -> 0.78%
- 2 -> 5.47%
- 3 -> 16.41%
- 4 -> 27.34%
- 5 -> 27.34%
- 6 -> 16.41%
- 7 -> 5.47%
- 8 -> 0.78%
|
This can easily be adjusted to set the average to any value in the range by adjusting the success rate (like a loaded coin). I.e. with a 33% chance the unupped version will have an average reduction of 2 instead of 3.
The standard deviation will be Sqrt(number coins * success chance * (1 - success chance))
You can use wolfram alpha to generate the table using: BinomialDistribution[6,.5]