For quite some time there has been a discussion in my board game group whether is better:

Scenario A: (The 47 Method)

  • Roll 4 * 6 sided dice
  • Pick the 3 best dice that were rolled
  • This generates a a total from 3 to 18

Perform this task 7 times, pick the 6 best sets.

Scenario B: (The 56 Method)

  • Roll 5 * 6 sided dice
  • pick the 3 best dice that were rolled
  • this generates a total from 3 to 18

perform this task 6 times

 

The benefits of each one is clear, with scenario A you can remove 1 terribly rolled set but with scenario B you have a better chance of getting good sets but take the risk of getting a terrible set you can’t get rid of.

 

We are perfectly aware that we could google this but where is the fun in that ?

 

One member of our group planned on doing a mathematical proof but hasn’t gotten around to it and I decided to simply perform a mathematical experiment.

I though I would get away with using bash but when I realized the calculations would take ~35 hours for just 100K simulations I decided to rewrite more efficient code. I ended up writing this Python code that performs 1M simulations in less then 4 minutes:
(expand code section to read the code)

The results of this program were consistent with earlier version of it which had less detail. Yes, the 56 Method produces higher overall stats with a considerable higher average score and a higher highest score and we could therefor say: The 56 method won, experiment over.

But on the downside the 56 Method has a lower lowest score and it is up to personal taste whether it is better to get a higher highest stat at the expanse of the lowest stat or not

Here is the data side by side.

As we can see, the difference is the lowest in the high/low range but highest in the mid-range

 

Set 47 Method AVG 56 Method AVG Difference
Set 1 15,86 16,44 0,58
Set 2 14,49 15,21 0,72
Set 3 13,39 14,14 0,75
Set 4 12,37 13,06 0,69
Set 5 11,30 11,80 0,50
Set 6 10,05 9,94 -0,12
 Average: 0,52

Here we have the number distribution curve from each generation visualized with a great tool called permeter

47 Method:

47meth

56 Method:

56methid

 

Final words:

Having rolled 58 million dice I am not sure which I would pick, I am however pretty sure when I decide to play D&D again, a single dice toss will not care what I calculated.

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