thanks to our friends at rec.games.backgammon we learned that there are 2 extra shots that hit us with the blot on the 5 pt. 4-2 and 4-1. It is a beginner mistake and I am embarassed I would make such an error
Yeah, so counting shots is a pain.
But basically a direct shot for one number is 11 rolls. So here if the blot is on the 4 pt, any 4 hits, [4-1] [4-2] [4-3] [4-4] [4-5] [4-6] [1-4] [2-4] [3-4] [5-4] [6-4] that is 11 rolls. So even if some of them are virtual duplicates like 3-4 and 4-3. We still count them as separate rolls for calculation convenience since 6x6 is 36. And 3-1 hits so total hits on the 4 pt is 12 rolls. If the blot is on the 5 pt we have the 11 rolls for a direct shot as shown for the direct 4. And 3-2 hits for 12 shots AND we also hit with 4-1 and 4-2 for total of 14 shots. So we are leaving 2 extra shots if the blot is on the 5 pt. Since we don't gain anything by leaving those extra shots, it is a mistake. So this type of position is easy to remember. To minimize your shots, scoot as far to the right side edge as possible.