Does this look like a bug to anyone? d1 can be fed into Plot function and it shows uninterrupted line suggesting Wolfram treats it as continuous distribution.

Here is another problem (maybe related) -- here it looks like TransformedDistribution can't apply to itself:

p = DiscreteUniformDistribution[{1,6}];
y = TransformedDistribution[a + b, {a \[Distributed] p, b\[Distributed]p}];
w = TransformedDistribution[c + d, {c \[Distributed] y, d \[Distributed]p}];

pdf1 = PDF[y]
DiscretePlot[pdf1[s1], {s1, 0, 20}, ExtentSize -> 0.8]

pdf2 = PDF[w]
DiscretePlot[pdf2[s2], {s2, 0, 20}, ExtentSize -> 0.8]

pdf2 refuses to be evaluated to anything meaningful (to me).

Thank you for helping me with case #1. Do you reckon it is a bug or I am missing some important distinction between a and {a} in this context?

About case #2 -- I am using Wolfram Programming Lab (free subscription), no idea about backend it uses and version. I need to run few simple calcs involving throwing dices -- ended up spending my evenings for more than a week, fighting weird syntax issues and digging in help pages. :)

Here is what I get when running second part:

It is correct, but I must point out that actual amount of underlying computations is minuscule -- we are talking about probability mass function of discrete variable in a very small range ([0, 100] tops). That distribution is defined by array of values no longer than 100 elements -- transforming it (e.g. calculating distribution of Max[x1 - x2, 0]) is trivial convolution of two short arrays, modern CPU can do thousands of these per second.

I suspect Wolfram Lab backend spends all this time in logic that attempts to comprehend and simplify symbolic representation of related functions, but it seems that it is very inefficient. Probably because the same thing PDF is used for both discrete and continuous distributions. Probably a reason behind these bugs too.