Difference between revisions of "Template VI1/Intrusion on the 3rd row"
m (Updated a link.) |
(Trying to complete the proof. The last case should be simplified.) |
||
| Line 35: | Line 35: | ||
E a:g3 b:h3 c:f4 d:g4 e:e5 f:f5 g:g5 h:d6 i:e6 j:f6 k:g6 x:f3" | E a:g3 b:h3 c:f4 d:g4 e:e5 f:f5 g:g5 h:d6 i:e6 j:f6 k:g6 x:f3" | ||
/> | /> | ||
| − | If Blue plays at c, e, h, | + | If Blue plays at c, e, h, j or k, Red responds at d and gets a 2nd row ladder, which connects. |
If Blue plays at b, Red plays at x and connects by [[edge template IV1a]]. | If Blue plays at b, Red plays at x and connects by [[edge template IV1a]]. | ||
If Blue plays at d, Red plays at x and gets a 2nd row ladder, which connects. | If Blue plays at d, Red plays at x and gets a 2nd row ladder, which connects. | ||
| − | This leaves a, f, i, g, k. | + | This leaves a, f, g, i. |
| + | |||
| + | <hexboard size="6x14" | ||
| + | coords="none" | ||
| + | edges="bottom" | ||
| + | visible="area(i1,c4,a6,o6,o4,k1)" | ||
| + | contents="R j1 B h4 R h2 R 1:h3 | ||
| + | E a:g3 d:g4 f:f5 g:g5 k:g6 y:i4" | ||
| + | /> | ||
| + | If Blue plays at a,f or g, then Red plays at b. | ||
| + | Note that Red connect down from the left by playing d, and connect down from the right by playing y. | ||
| + | The only way for Blue to block both is to play k, but Red with the same strategy on the left would produce a 2nd row ladder toward the right. | ||
| + | |||
| + | <hexboard size="6x14" | ||
| + | coords="none" | ||
| + | edges="bottom" | ||
| + | visible="area(i1,c4,a6,o6,o4,k1)" | ||
| + | contents="R j1 B h4 R h2 B e6 R 1:g4 B 2:g5 R 3:f5 B 4:f6 R 5:d5 B 6:e5 R 7:e4 B 8:f4 R 9:f3 | ||
| + | E a:g3 b:h3 y:i4" | ||
| + | /> | ||
| + | |||
| + | Finally if Blue plays at i, then Red plays at d. Suppose Blue don't intrude the bridge at a or b, then Red has the forcing sequence shown in the picture. | ||
| + | |||
| + | Now if the bridge was intruded by blue at a at some moment before 9, then Red should respond at b, forcing Blue to block on the right part (against Red y) and Red can win with one more move on the left. | ||
| + | If the bridge was intruded at b, then Red should respond at a and can win with a capped flank on the left. | ||
| + | These claims have to be checked on each turn. | ||
| + | |||
| + | |||
{{stub}} | {{stub}} | ||
[[category:edge templates]] | [[category:edge templates]] | ||
Revision as of 15:49, 19 September 2023
This article deals with a special case in the defense of edge template VI1a, namely the intrusion on the 3rd that is not eliminated by sub-templates threats.
Basic situation
In this situation, there are only 3 possible winning moves for Red, and they are "a", "b", and "c". Of these, "a" is the easiest to verify, so we will assume Red plays there.
Before continuing the analysis, we first note that Red can escape all 2nd row ladders coming from the left, as follows:
Apart from attacking the bridge, which Red defends, Blue's next move must be in the shaded blue area, or else Red plays at d and connects.
If Blue plays at c, e, h, j or k, Red responds at d and gets a 2nd row ladder, which connects. If Blue plays at b, Red plays at x and connects by edge template IV1a. If Blue plays at d, Red plays at x and gets a 2nd row ladder, which connects. This leaves a, f, g, i.
If Blue plays at a,f or g, then Red plays at b. Note that Red connect down from the left by playing d, and connect down from the right by playing y. The only way for Blue to block both is to play k, but Red with the same strategy on the left would produce a 2nd row ladder toward the right.
Finally if Blue plays at i, then Red plays at d. Suppose Blue don't intrude the bridge at a or b, then Red has the forcing sequence shown in the picture.
Now if the bridge was intruded by blue at a at some moment before 9, then Red should respond at b, forcing Blue to block on the right part (against Red y) and Red can win with one more move on the left. If the bridge was intruded at b, then Red should respond at a and can win with a capped flank on the left. These claims have to be checked on each turn.
