OW describes the "Zeroing Effect" for Begginers

[Pehmyt]

Originally Posted by Agema

If anyone wants to check this sort of phenomenon mathematically, I've attached an MS Excel file I made months ago. I don't know programming, so I constructed it longhand with Excel, and it's accurate up to DRN rolls about 40-50, which means it's over 99.99% accurate.

I think I should comment that as far as I can understand your spreadsheet, the results are ~10% off as soon as the open-ended rolls enter the picture. Did you take into account that 6 equals "5 +extra roll"? Not that it matters for the present discussion.

For example, the probability of getting 7 should be that of throwing one of (2;5), (3;4), (4;3), (5;2), (6,1;1), (1;6,1) (with ";" separating the two dice), that is 4/36 + 2/216 = 13/108 = 0.1204.

The results corresponding your column A can be computed exactly by writing the value of DRN roll as X=5k+r+1, with r between 0 and 4, and using

P(DRN = 5k+r+1) =  ((6-r)5k +r )/6^(k+2)

The chances of DRN being at least as large as a given number X=5k+r+1 can also be computed exactly, although this is not directly useful. It could be practical for generating a table similar to that in manual without losing too much precision. For 6-sided dice it reads

P(DRN >= 5k+r+1) = ( (48 - 13r + r^2)5k + 72 + r - r^2 )/( 2 * 6^(k+2) )