Since I started keeping stats on the pins left standing after the first throw, I have recorded 334 pin configurations. Of these, 110 are unique. It is possible to increase this number to 150 with the current count by making a symmetry assumption: if a particular spare combination has been observed, then the mirror image about the midline is also possible. For example, if a 6-7 leave has been observed, then it is assumed that a 4-10 leave is also possible.
To date, I have observed every possible single pin spare opportunity. There are ten of these. Among the bowlers I have observed, the 5 pin is most likely to be left standing when a score of 9 is received on the first ball. A standing 1 pin is the rarest.
This post concerns two pin leaves. There are 45 theoretically possible combinations of two pins remaining after the first ball. Of these, I have recorded a total of 35 when symmetrical pairs are included. I have divided the ten that I have not yet recorded into two groups, symmetrical and asymmetrical. The symmetrical leaves are symmetrical about the midline. The asymmetrical are not:
Symmetrical leaves not observed: 1-5, 2-3, 8-9, 7-10
Asymmetrical leaves not observed: 1-7, 1-10, 2-6, 2-9, 3-4, 3-8
So here’s the question. Have these not been observed because they are impossible to leave, or because they are rare? One of these is obviously possible because we have all seen it, and it is probably the most famous leave in all of bowling, the 7-10 split. It is apparently not particularly common. Is the same true of the others? My hunch is that all of these are possible but one, the 2-3. It is hard to imagine how this could be accomplished without some crazy pin action. Anyone else care to venture a guess? Has anyone seen a 1-5 or an 8-9?
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