From Buffon's Needle to Buffon's Noodle

I'm wary of asking questions (my curiosity is bounded), but what changes if you limit the range of allowed angles to multiples of, say, 10°? How about 90°, does pi go away then?

Pretty neat! However, if you wanted to know the _probability_ of a noodle crossing any line in the long noodle case (L/W > 1), the expression is more complex (and I believe would require an integral) :).

It's interesting that the number of crossings is independent of whether L/W is less than or greater than 1, but the probability of crossings is equal to 2pi * L/W only in the short case. This makes sense since in the short case the noodle can at most cross a single line.