Difference between revisions of "Talk:Wheel"
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(Can intrusion into the center of a wheel ever be the unique winning move?) |
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This pattern is not what I would call a Wheel. It is at most a Broken wheel. I think somebody called it a U-turn. — taral | This pattern is not what I would call a Wheel. It is at most a Broken wheel. I think somebody called it a U-turn. — taral | ||
:Yes, granted. My initial feeling was that it was important to point out that this related position is weak, but maybe it's not important enough to merit mention on this page. We could always create a "U-turn" page, or just refer to the example in the tutorial. [[User:Turing|turing]] 08:18, 10 Feb 2005 (CET) | :Yes, granted. My initial feeling was that it was important to point out that this related position is weak, but maybe it's not important enough to merit mention on this page. We could always create a "U-turn" page, or just refer to the example in the tutorial. [[User:Turing|turing]] 08:18, 10 Feb 2005 (CET) | ||
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| + | ''Blue should never attempt to intrude by playing at B.'' I believe this is false. Here's a simple example (Blue to move) where Blue's only winning moves are at one of (*). In particular, d2 is winning for Blue, while all of the hexes marked A are losing. | ||
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| + | <hexboard size="5x5" | ||
| + | coords="show" | ||
| + | edges="show" | ||
| + | contents="R d1 e2 c3 e5 B c1 b3 b5 E *:(d2 d4) A:(e1 c2 d3)" | ||
| + | /> | ||
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| + | Now, this might not be very interesting because playing at d2 just delays the "real" winning d4 move. A more interesting question: is there a position where playing at B is the ''unique'' winning move? This seems trickier than it looks, in many winning positions there's a useless bridge intrusion that also preserves the win for instance, so the move at B isn't unique. Intuitively, I think that in order for the intrusion at B to be better than all intrusions at A, the intrusion at B needs to serve the function of asking a [[question]]. | ||
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| + | "lazyplayer" from LittleGolem showed me [https://hexworld.org/board/#13n,c2d10j9j4c8g7b10b11l4l3k4k3f8g9i7f11e9d9e7f6i8h7d5e6g8h8c7f7e8e10 a position] loosely based from [https://littlegolem.net/jsp/game/game.jsp?gid=2359962 this game]. I was surprised when I put this in KataHex, because it was the first position I saw where an intrusion at B (specifically, f10) was winning but intrusions at A were losing. But, f10 might not be unique; KataHex thinks c11 or i5 could also win. I played around a bit to see if I could make f10 unique — it was tricky to get KataHex to not think c11 was also winning or close to 50%. Eventually, I found [https://hexworld.org/board/#13n,c2d10j9j4c8g7b10b11l4l3k4k3f8g9i7f11e9d9e7f6i8h7d5e6g8h8c7f7e8e10i5i2i3j2h3d4 a position] where KataHex thinks, after about 50k visits, that f10 is winning (90.3% win rate), and the second best move has only an 8.6% win rate. So it appears that this last position has a unique winning move at B, but I only have KataHex evaluations and not a solid proof. | ||
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| + | It would be nice if someone could come up with an example small enough that one can ''prove'' the intrusion at B is the unique winning move. I suspect the smallest example might not even fit on a 5x5 or 6x6 board, since it's a fickle matter getting the condition to hold. [[User:Hexanna|Hexanna]] ([[User talk:Hexanna|talk]]) 01:09, 17 April 2023 (UTC) | ||
Revision as of 01:09, 17 April 2023
This pattern is not what I would call a Wheel. It is at most a Broken wheel. I think somebody called it a U-turn. — taral
- Yes, granted. My initial feeling was that it was important to point out that this related position is weak, but maybe it's not important enough to merit mention on this page. We could always create a "U-turn" page, or just refer to the example in the tutorial. turing 08:18, 10 Feb 2005 (CET)
Blue should never attempt to intrude by playing at B. I believe this is false. Here's a simple example (Blue to move) where Blue's only winning moves are at one of (*). In particular, d2 is winning for Blue, while all of the hexes marked A are losing.
Now, this might not be very interesting because playing at d2 just delays the "real" winning d4 move. A more interesting question: is there a position where playing at B is the unique winning move? This seems trickier than it looks, in many winning positions there's a useless bridge intrusion that also preserves the win for instance, so the move at B isn't unique. Intuitively, I think that in order for the intrusion at B to be better than all intrusions at A, the intrusion at B needs to serve the function of asking a question.
"lazyplayer" from LittleGolem showed me a position loosely based from this game. I was surprised when I put this in KataHex, because it was the first position I saw where an intrusion at B (specifically, f10) was winning but intrusions at A were losing. But, f10 might not be unique; KataHex thinks c11 or i5 could also win. I played around a bit to see if I could make f10 unique — it was tricky to get KataHex to not think c11 was also winning or close to 50%. Eventually, I found a position where KataHex thinks, after about 50k visits, that f10 is winning (90.3% win rate), and the second best move has only an 8.6% win rate. So it appears that this last position has a unique winning move at B, but I only have KataHex evaluations and not a solid proof.
It would be nice if someone could come up with an example small enough that one can prove the intrusion at B is the unique winning move. I suspect the smallest example might not even fit on a 5x5 or 6x6 board, since it's a fickle matter getting the condition to hold. Hexanna (talk) 01:09, 17 April 2023 (UTC)
