Double 4-card run

Seems like double runs come in two flavors: a double run of 3 (e.g. 3-4-4-5 with any cut) or a double run of 4 (e.g. T-J-Q-Q with K cut).

I see two ways to score such a double 4-card run: as multiple 3-card runs, or multiple 4-card runs.

Example using the above TJQQK: either four 3-card runs (TJQ twice = 6 and JQK twice = 6) makes 12, and a pair is 14 total. Or, two 4-card runs for 8 (TJQK twice = 8), and a pair is only 10 total.

Wha? Which one is correct, and why? I'm just guessing I'm required to score this the second way. But I don't see why it should be one way or the other.

Re: Double 4-card run

It's a perfectly good point. You could argue the same about a 4-card run with no doubles: should it be scored as a 4-card run, or two overlapping 3-card runs?

However, as you rightly say, this doesn't happen in Cribbage. 4-card runs are scored as 4-card runs. That's just the way it is!