User:StillYetAnother11 - Revision history

Selinger: Minor typos

2026-03-20T18:58:57Z

Minor typos

StillYetAnother11 at 11:00, 20 March 2026

2026-03-20T11:00:33Z

StillYetAnother11 at 10:43, 20 March 2026

2026-03-20T10:43:24Z

StillYetAnother11: /* g3 is probably losing on 13x13 */

2026-01-15T17:31:49Z

‎g3 is probably losing on 13x13

StillYetAnother11 at 19:42, 20 October 2025

2025-10-20T19:42:36Z

StillYetAnother11 at 14:58, 20 August 2025

2025-08-20T14:58:23Z

StillYetAnother11 at 13:54, 20 August 2025

2025-08-20T13:54:08Z

StillYetAnother11 at 19:21, 8 March 2025

2025-03-08T19:21:54Z

Tommah: Creating user page for new user.

2024-10-05T00:06:21Z

Creating user page for new user.

New page

← Older revision		Revision as of 18:58, 20 March 2026
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	== log2(1.5) ratio ==		== log2(1.5) ratio ==

−	I was thinking about why katahex evaluates a7 as the most balanced opening on 12x12 which is very anomalous because openings in the middle of the 1st column tend to be quite strong, although in Hayward's 2003 paper, a4 on 7x7 has the highest number of nodes of all solved openings. The smallest board size after 12x12 where such an opening seems quite playable is 17x17 since katahex evaluates a10 as more balanced than ~~it's~~ neighbors and is still one of the most balanced openings on the first column. A pattern starts to emerge where if you encode the acute corner as 0 and the obtuse corner as 1 you'll find that these openings match ratios that well approximate a particular ratio namely log2(1.5). The first semiconvergents of log2(1.5) are 1/1, 1/2, 2/3, 3/5, 4/7, 7/12, 10/17, 17/29, 24/41, 31/53 and 55/94. The next fraction after 10/17 is 17/29 so is a17 on 29x29 more balanced than ~~it's~~ neighbors? I've run 200 engine games for each opening: a16, a17 and a18 and the results were 110 wins for a16, 102 wins for a17 and 112 wins for a18. I also ran 100 games on 41x41 for each of the following openings. The results were 57 wins for a23, 49 wins for a24 and 56 wins for a25 so the pattern seems to be consistent. This has a benefit when it comes to opening variety because most balanced openings in hex are predominantly on your own edge and not on your opponent's edge. I believe that having the denominators of semiconvergents of log2(1.5) as board sizes is the most logical and consistent way of deriving board sizes in hex.	+	I was thinking about why katahex evaluates a7 as the most balanced opening on 12x12 which is very anomalous because openings in the middle of the 1st column tend to be quite strong, although in Hayward's 2003 paper, a4 on 7x7 has the highest number of nodes of all solved openings. The smallest board size after 12x12 where such an opening seems quite playable is 17x17 since katahex evaluates a10 as more balanced than its neighbors and is still one of the most balanced openings on the first column. A pattern starts to emerge where if you encode the acute corner as 0 and the obtuse corner as 1 you'll find that these openings match ratios that well approximate a particular ratio namely log2(1.5). The first semiconvergents of log2(1.5) are 1/1, 1/2, 2/3, 3/5, 4/7, 7/12, 10/17, 17/29, 24/41, 31/53 and 55/94. The next fraction after 10/17 is 17/29 so is a17 on 29x29 more balanced than its neighbors? I've run 200 engine games for each opening: a16, a17 and a18 and the results were 110 wins for a16, 102 wins for a17 and 112 wins for a18. I also ran 100 games on 41x41 for each of the following openings. The results were 57 wins for a23, 49 wins for a24 and 56 wins for a25 so the pattern seems to be consistent. This has a benefit when it comes to opening variety because most balanced openings in hex are predominantly on your own edge and not on your opponent's edge. I believe that having the denominators of semiconvergents of log2(1.5) as board sizes is the most logical and consistent way of deriving board sizes in hex.

@@ Line 1: / Line 1: @@
 == The best way for red to fight in c2 opening on 11x11 ==
@@ Line 39: / Line 44: @@
     contents="R 1:g3 E +:g4 B 6:i5 E *:d8 R 3:j9 B 2:d10 R 5:i10 B 4:j10"
     />

← Older revision		Revision as of 10:43, 20 March 2026
Line 39:		Line 39:
	contents="R 1:g3 E +:g4 B 6:i5 E *:d8 R 3:j9 B 2:d10 R 5:i10 B 4:j10"		contents="R 1:g3 E +:g4 B 6:i5 E *:d8 R 3:j9 B 2:d10 R 5:i10 B 4:j10"
	/>		/>
		+
		+	== log2(1.5) ratio ==
		+
		+	I was thinking about why katahex evaluates a7 as the most balanced opening on 12x12 which is very anomalous because openings in the middle of the 1st column tend to be quite strong, although in Hayward's 2003 paper, a4 on 7x7 has the highest number of nodes of all solved openings. The smallest board size after 12x12 where such an opening seems quite playable is 17x17 since katahex evaluates a10 as more balanced than it's neighbors and is still one of the most balanced openings. A pattern starts to emerge where if you encode the acute corner as 0 and the obtuse corner as 1 you'll find that these openings match ratios that well approximate a particular ratio namely log2(1.5). The first semiconvergents of log2(1.5) are 1/1, 1/2, 2/3, 3/5, 4/7, 7/12, 10/17, 17/29, 24/41, 31/53 and 55/94. The next fraction after 10/17 is 17/29 so is a17 on 29x29 more balanced than it's neighbors? I've run 200 engine games for each opening: a16, a17 and a18 and the results were 110 wins for a16, 102 wins for a17 and 112 wins for a18. I also ran 100 games on 41x41 for each of the following openings. The results were 57 wins for a23, 49 wins for a24 and 56 wins for a25 so the pattern seems to be consistent. This has a benefit when it comes to opening variety because most balanced openings in hex are predominantly on your own edge and not on your opponent's edge. I believe that having the denominators of semiconvergents of log2(1.5) as board sizes is the most logical and consistent way of deriving board sizes in hex.

@@ Line 24: / Line 24: @@
 At this point red can try a bunch of different moves. Blue needs to know that the cell marked with + is the only winning move to a lot of red's responses. You should continue to analyze this position yourself with katahex.
-== g3 is probably losing on 13x13 ==
+== g3 opening on 13x13 ==
-I calculated g3 opening to 81 million nodes with katahex and the evaluated winrate was 60.9 percent for blue. These are the only winning opening moves for blue. If red plays * then + is the only winning response.
 <hexboard size="13x13"
     coords="hide"
-    contents="R 1:g3 E +:g4 B 6:i5 E *:d8 R 3:j9 B 2:d10 R 5:i10 B 4:j10"
+    contents="R 1:g3 R 3:i7 B 2:d10"
     />
-Katahex high depth continuation goes as follows:
+While j9 is losing for red. If red plays * then + is the only winning response for blue.
 <hexboard size="13x13"
     coords="hide"
-    contents="R g3 B i5 R 3:d6 B 2:e6 B 4:d7 R 5:d9 R 7:e9 R j9 R 1:b10 B d10 R i10 B j10 B 6:b12 B 8:e12"
+    contents="R 1:g3 E +:g4 B 6:i5 E *:d8 R 3:j9 B 2:d10 R 5:i10 B 4:j10"
     />

← Older revision		Revision as of 19:42, 20 October 2025
Line 23:		Line 23:

	At this point red can try a bunch of different moves. Blue needs to know that the cell marked with + is the only winning move to a lot of red's responses. You should continue to analyze this position yourself with katahex.		At this point red can try a bunch of different moves. Blue needs to know that the cell marked with + is the only winning move to a lot of red's responses. You should continue to analyze this position yourself with katahex.
		+
		+	== g3 is probably losing on 13x13 ==
		+	I calculated g3 opening to 81 million nodes with katahex and the evaluated winrate was 60.9 percent for blue. These are the only winning opening moves for blue. If red plays * then + is the only winning response.
		+
		+	<hexboard size="13x13"
		+	coords="hide"
		+	contents="R 1:g3 E +:g4 B 6:i5 E *:d8 R 3:j9 B 2:d10 R 5:i10 B 4:j10"
		+	/>
		+
		+	Katahex high depth continuation goes as follows:
		+
		+	<hexboard size="13x13"
		+	coords="hide"
		+	contents="R g3 B i5 R 3:d6 B 2:e6 B 4:d7 R 5:d9 R 7:e9 R j9 R 1:b10 B d10 R i10 B j10 B 6:b12 B 8:e12"
		+	/>

← Older revision		Revision as of 14:58, 20 August 2025
Line 22:		Line 22:
	/>		/>

−	At this point red can try a bunch of different moves. Blue needs to know that the cell marked with + is the only winning move to a lot of red's responses. You should continue to analyze this ~~positions~~ yourself with katahex.	+	At this point red can try a bunch of different moves. Blue needs to know that the cell marked with + is the only winning move to a lot of red's responses. You should continue to analyze this position yourself with katahex.

← Older revision		Revision as of 13:54, 20 August 2025
Line 1:		Line 1:
−	~~My ideal board~~ size is ~~53x53~~ but ~~most players think~~ it's ~~too large~~.	+	== The best way for red to fight in c2 opening on 11x11 ==
		+
		+	<hexboard size="11x11"
		+	coords="hide"
		+	contents="R 1:c2 E :c4 E :d5 R 3:b8 B 2:d8 R 5:c9 B 4:f9"
		+	/>
		+
		+	I prefer to play 5.c9 here even though it's not the best move according to katahex. Moves marked with * are the only moves winning for blue.
		+
		+
		+	<hexboard size="11x11"
		+	coords="hide"
		+	contents="R 1:c2 R 7:j4 B 6:d5 E :f5 E :f7 R 3:b8 B 2:d8 R 5:c9 B 4:f9"
		+	/>
		+
		+	7.j4 is again not the top engine move but here is why I prefer it. Moves marked with * are the only winning moves for blue but there are still ways for blue to lose if they don't play this very concrete position correctly.
		+
		+
		+	<hexboard size="11x11"
		+	coords="hide"
		+	contents="R 1:c2 R 7:j4 B 6:d5 B 8:f5 E +:b7 R 3:b8 B 2:d8 R 5:c9 B 4:f9"
		+	/>
		+
		+	At this point red can try a bunch of different moves. Blue needs to know that the cell marked with + is the only winning move to a lot of red's responses. You should continue to analyze this positions yourself with katahex.

← Older revision	Revision as of 19:21, 8 March 2025
Line 1:	Line 1:
−	+	My ideal board size is 53x53 but most players think it's too large.