Difference between revisions of "User:Wurfmaul"
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| − | [[ | + | ==An automatic peep lemma?== |
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| + | A: <hexboard size="4x4" | ||
| + | float="inline" | ||
| + | edges="none" | ||
| + | coords="none" | ||
| + | visible="area(a4, c4, c3, d2, c2)" | ||
| + | contents="B d2 E x:c2 y:b3 z:c3 R a4--c4" | ||
| + | /> | ||
| + | B: <hexboard size="4x4" | ||
| + | float="inline" | ||
| + | edges="none" | ||
| + | coords="none" | ||
| + | visible="area(a4, c4, c3, d2, c2)" | ||
| + | contents="B d2 b3 R c2 a4--c4" | ||
| + | /> | ||
| + | |||
| + | From blue's perspective, A is at least as good as B. | ||
| + | ===Proof=== | ||
| + | ====When red plays first==== | ||
| + | The best red can do in A is to play at x, capturing the two cells below. When red plays at the empty cell in B, it kills the blue cell to the left of it, so the result is equivalent to the result in A. | ||
| + | ====When blue plays first==== | ||
| + | When blue plays at y in A, the result is at least as good for blue as when blue plays at the empty cell in B. To see this, note that if blue plays at x next, it kills z, and this implies that locally, red's only sensible move is at x, making the position identical to B. | ||
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| + | reply by [[User:Demer|Demer]]: | ||
| + | |||
| + | That does not need the top red stone. Also, it still works with a line of 3 red stones instead of the edge. See [[Peep#Automatic_peep|automatic peep]]. | ||
| + | |||
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| + | Wurfmaul: Thanks for the pointers. I actually thought an edge looks nicer than three stones but it's true stones are more accurate. | ||
Latest revision as of 02:31, 21 February 2023
Contents
An automatic peep lemma?
A: B:From blue's perspective, A is at least as good as B.
Proof
When red plays first
The best red can do in A is to play at x, capturing the two cells below. When red plays at the empty cell in B, it kills the blue cell to the left of it, so the result is equivalent to the result in A.
When blue plays first
When blue plays at y in A, the result is at least as good for blue as when blue plays at the empty cell in B. To see this, note that if blue plays at x next, it kills z, and this implies that locally, red's only sensible move is at x, making the position identical to B.
reply by Demer:
That does not need the top red stone. Also, it still works with a line of 3 red stones instead of the edge. See automatic peep.
Wurfmaul: Thanks for the pointers. I actually thought an edge looks nicer than three stones but it's true stones are more accurate.
