However, what makes sense would be to look at the first set of rolls one die at a time. Essentially, there are 5 cases worth looking at.
- 1st Roll
- 2nd Roll
- Last Roll
- 2nd to Last Roll
- Other Roll
The odds of any individual roll in any case being a 20 are 5%. The odds of either of the ones adjacent to them being a 20 are 1-(.95^2), except for in the case of 1st and last roll, where there is only 1 adjacent roll. From here, you look at the cases left.
- Neither Adjacent is a 20.
- One Adjacent is a 20.
- Both Adjacent are 20.
The first of these cases means the roll is not part of a 3 20s set, the last of these means it is a 3 or more 20 set. Calculating the odds of it being more than 20 is another step, and one I'll ignore in the explanation, suffice to say it is there. Its also important to note which of the adjacent is a 20, as in the 2nd or 2nd to last case if it is the 1st or last only it is not a 3 20 set. For everything else, another specific roll must be a 20, which is a 5% chance. For it to only be 3 20s in a row, the next must not be a 20, which is a 95% chance, ignoring the cases where the first roll was the 3rd or the 3rd to last, and the first adjacent was the 2nd or 2nd to last.
One must then look at the 2 remaining cases, both of which act as the first. Moreover, one must note that much of the specifics were left unsaid, as that is dependent on the original case.
*And it assumes entirely fair dice, which is unlikely given the shoddy manufacturing in most cases.