Counting Crawls

1st line crawl  

We suppose that the White territory extends infinitely far to the right. How much does gain?
Plainly, 1 point, as it reduces White's potential by that much.^[1]
If White's territory is finite, gains less than that. If the White stones extended only one point beyond the Black stones, it would be worth nothing, merely filling a dame. If they extended 2 points beyond, it would gain ``1/2`` point. If they extended 3 points beyond, it would gain ``3/4`` point, etc. The asymptotic value is 1 point, the exact value is ``1-1/2^n`` with n+1 being the length of the corridor.

2nd line crawl  

Now gains 3 points: it adds 1 point of Black territory and takes away 2 points of White territory.
OC, on an infinite board the crawl is not the best play. The Monkey Jump is. However, on a finite board the crawl is sometimes better. Then it is usually worth 2+ points.

3rd line crawl  

This is easy. It gains 5 points.
In fact this kind of crawl on the ``N``th line gains ``2N - 1`` points in the limit, up to some N where the opponent can play underneath your wall to some effect.

This is not of any great practical value, since this kind of crawl is typically wrong. But it does illustrate the idea behind miai counting, which asks how much a play gains in comparison to the original position.