Difference between revisions of "User:Wurfmaul"
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| − | + | ==A lemma (as seen on discord!)== | |
| + | |||
| + | A: <hexboard size="3x4" | ||
| + | float="inline" | ||
| + | edges="bottom" | ||
| + | coords="none" | ||
| + | visible="area(a4, c4, c3, d2, d1)" | ||
| + | contents="R d1 B d2 E x:c2 y:b3 z:c3" | ||
| + | /> | ||
| + | B: <hexboard size="3x4" | ||
| + | float="inline" | ||
| + | edges="bottom" | ||
| + | coords="none" | ||
| + | visible="area(a4, c4, c3, d2, d1)" | ||
| + | contents="R d1 c2 B d2 b3" | ||
| + | /> | ||
| + | |||
| + | 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. | ||
Revision as of 18:24, 20 February 2023
Contents
A lemma (as seen on discord!)
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.
