Advanced (strategy guide) - Revision history

Selinger: Capitalization

2022-02-09T00:58:56Z

Capitalization

Selinger: Italics

2022-02-09T00:57:24Z

Italics

Selinger: Added a link to the original.

2022-02-09T00:55:41Z

Added a link to the original.

Selinger: minor edit (forking ladder escape -> ladder escape fork)

2021-09-05T15:27:07Z

minor edit (forking ladder escape -> ladder escape fork)

Selinger: Updated a link.

2021-06-20T21:53:46Z

Updated a link.

Selinger: Converted to new hexboard diagrams. Some copy-editing.

2021-03-09T03:53:58Z

Converted to new hexboard diagrams. Some copy-editing.

Show changes

Hyperpape: /* The minimax principle */ phrasing

2017-03-27T14:01:55Z

‎The minimax principle: phrasing

Pworth: /* Example 1 */

2016-09-13T11:22:45Z

‎Example 1

Richyfourtytwo: /* Template IVc */ renaming to IV-2-a and linking

2016-05-13T19:30:30Z

‎Template IVc: renaming to IV-2-a and linking

Roland Illig (Admin): /* Third row ladder to a3 and its symmetric analogues */ added move numbers

2012-11-03T13:06:04Z

‎Third row ladder to a3 and its symmetric analogues: added move numbers

← Older revision		Revision as of 00:58, 9 February 2022
Line 1:		Line 1:
−	''Adapted from: [http://www.gcrhoads.byethost4.com/GamesPuzzles/Advanced.html Glenn C. Rhoads's ~~Advanced Strategy Guide~~].''	+	''Adapted with permission from: [http://www.gcrhoads.byethost4.com/GamesPuzzles/Advanced.html Glenn C. Rhoads's advanced strategy guide].''

	== Advanced edge templates ==		== Advanced edge templates ==

← Older revision		Revision as of 00:57, 9 February 2022
Line 1:		Line 1:
−	Adapted from: [http://www.gcrhoads.byethost4.com/GamesPuzzles/Advanced.html Glenn C. Rhoads's Advanced Strategy Guide].	+	''Adapted from: [http://www.gcrhoads.byethost4.com/GamesPuzzles/Advanced.html Glenn C. Rhoads's Advanced Strategy Guide].''

	== Advanced edge templates ==		== Advanced edge templates ==

← Older revision		Revision as of 00:55, 9 February 2022
Line 1:		Line 1:
		+	Adapted from: [http://www.gcrhoads.byethost4.com/GamesPuzzles/Advanced.html Glenn C. Rhoads's Advanced Strategy Guide].
		+
	== Advanced edge templates ==		== Advanced edge templates ==
	=== Template [[Edge_template_IV2a\|IV-2-a]] ===		=== Template [[Edge_template_IV2a\|IV-2-a]] ===

@@ Line 124: / Line 124: @@
 <hex>R10 C10 Q1 Va3 Vc6 Vb8 Vc8 Vd8 Ve8 Vg6 Vg7 Vg8 Hf5 Hf7 Hf8 He9 Hd9 Hc9 Hb9 Hd7</hex>
-In this position, I was the vertical player and was expecting f6 to which h4 would give me an excellent position (with best play, this position would in fact be winning though this is not obvious). Instead my opponent played the excellent minimax move f4. This move fights in both directions and is in fact a killer move. I can't block the f4-f5 pair from the right due to the forking ladder escape at h9. Thus, I must meekly submit to the forcing sequence f6, e7, e6, d5 yielding
+In this position, I was the vertical player and was expecting f6 to which h4 would give me an excellent position (with best play, this position would in fact be winning though this is not obvious). Instead my opponent played the excellent minimax move f4. This move fights in both directions and is in fact a killer move. I can't block the f4-f5 pair from the right due to the ladder escape fork at h9. Thus, I must meekly submit to the forcing sequence f6, e7, e6, d5 yielding
 <hex>R10 C10 Q1 Va3 Vc6 Vb8 Vc8 Vd8 Ve8 Vg6 Vg7 Vg8 Hf5 Hf7 Hf8 He9 Hd9 Hc9 Hb9 Hd7 MH Mf4 Mf6 Me7 Me6 Md5</hex>
-The game is over.  The f4-f5 pair is connected to d5 which in turn threatens to connect to left in two non-overlapping ways, c5 (a 3rd row template) and d6, hence the pair is connected to the left. If I try to block at the right, the best I can do is yield a ladder (e.g. h4, h3, j2, i3 and H has a second row ladder) and then the forking ladder escape at h9 wins the game.
+The game is over.  The f4-f5 pair is connected to d5 which in turn threatens to connect to left in two non-overlapping ways, c5 (a 3rd row template) and d6, hence the pair is connected to the left. If I try to block at the right, the best I can do is yield a ladder (e.g. h4, h3, j2, i3 and H has a second row ladder) and then the ladder escape fork at h9 wins the game.
 === Example 3 ===
@@ Line 184: / Line 184: @@
 <hex>R9 C9 Q1 Vg2 Vf3 Ve4 Vd5 Vd6 Vh3 Vh4 Vf7 Hi4 Hc6 Hb8 Hc8 He6 Hf6 Hg6</hex>
-Red can win by laddering 1. d7 d8 2. e7. Suppose instead Red plays 1.h5 intruding on the g6 edge template. If Blue reconnects with h6, then Red would have nothing else to do except play the winning line. So Blue reconnects with g7 making the win tougher. (Red could still win by d7, d8, e7, e9, f8, f9, h8! &mdash; a forking ladder escape which decides the issue).
+Red can win by laddering 1. d7 d8 2. e7. Suppose instead Red plays 1.h5 intruding on the g6 edge template. If Blue reconnects with h6, then Red would have nothing else to do except play the winning line. So Blue reconnects with g7 making the win tougher. (Red could still win by d7, d8, e7, e9, f8, f9, h8! &mdash; a ladder escape fork which decides the issue).
 Now suppose that Red again intrudes on the edge template with 2. h6. Now the game continues 2...g8 (again reconnecting by playing parallel to the edge) 3. h7 (persistent) h8, 4. d7 d8, 5. e7 e9! and now Blue has an unbreakable winning chain at the bottom. By reconnecting with the parallel moves instead of the direct reconnection, Blue's group had a new way to connect to the left and this extra possibility turned a defeat into a win.
@@ Line 192: / Line 192: @@
 <hex>R9 C9 Q1 Vh3 Vg2 Vf3 Ve4 Vd5 Vd6 Hc6 Hb8 Hc8 He6 Hg5 Hi3</hex>
-With best play Blue wins, so Red tries 1. h4.  If Blue responds with the direct reconnection h5, then the win is assured and Red may as well resign. Suppose instead that Blue reconnects with 1... g6. Then Red can respond with 2.h7! &mdash; this forking ladder escape is a killer. Red now has two disjoint winning threats, laddering from d7 to h7 and play i5 (This double two-chain cutoff threat occurs in situations besides cutting off third row edge templates.  It is well worth being familiar with this idea.). Blue cannot stop them both so Red wins.
+With best play Blue wins, so Red tries 1. h4.  If Blue responds with the direct reconnection h5, then the win is assured and Red may as well resign. Suppose instead that Blue reconnects with 1... g6. Then Red can respond with 2.h7! &mdash; this ladder escape fork is a killer. Red now has two disjoint winning threats, laddering from d7 to h7 and play i5 (This double two-chain cutoff threat occurs in situations besides cutting off third row edge templates.  It is well worth being familiar with this idea.). Blue cannot stop them both so Red wins.
 But this doesn't exhaust the reconnection possibilities. There is a third way to reconnect; a way that most players don't seem to discover.
@@ Line 281: / Line 281: @@
 <hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9   Vb4   N:on Hc3 Vb5 Hb3 Va4 Hb1 Vd2</hex>
-d2 is a forking ladder escape; it threatens d3 and it provides an escape to the 2nd row ladder starting with b2. Blue cannot stop both winning threats with a single move, thus Red wins.
+d2 is a ladder escape fork; it threatens d3 and it provides an escape to the 2nd row ladder starting with b2. Blue cannot stop both winning threats with a single move, thus Red wins.
 a3/j8 is a common opening move. If you frequently play it or play against somebody who does, then you will run into these 3rd row ladder situations and hence, it will be beneficial to learn how to play them.

@@ Line 33: / Line 33: @@
 If Blue intrudes at 1, Red responds with 2, which forces Blue to respond at 3. (Blue could also first intrude on Red's bridge, but this would not change anything). Now Red connects at 4 using a [[trapezoid]]. Alternatively, Red can also play 4 before 2.
-=== [[Defending_against_intrusions_in_template_1-Va|Template Va]] ===
+=== [[Edge template V1a|Template V1a]] ===
 <hexboard size="5x10"

@@ Line 65: / Line 65: @@
 (See also the page [[Minimax]])
-Suppose you have multiple ways of establishing/maintaining a connection to an edge. A move that maintains as strong a connection as possible is not preferable to other connection moves because you only need to get some connection; you don't win extra points by connecting more strongly.
+Suppose you have multiple ways of establishing/maintaining a connection to an edge. A move that maintains the strongest possible connection is not necessarily preferable to other connection moves because you only need to get some connection; you don't win extra points by connecting more strongly.
 In fact it is generally better to play a move that maintains as ''weak'' a connection as possible; the reason being that such a piece may help you extend the connection towards the opposite edge. This principle is sometimes called "mini-maxing."

@@ Line 88: / Line 88: @@
 <hex>R10 C10 Q1 Va3 Hf5 Vc6 Hf4 Vd5   MH M6c7 Me6</hex>
-In fact, the c7, e6 sequence occurred in the actual game. I eventually won after a close hard fought battle.
+In fact, the c7, e6 sequence occurred in the actual game. I eventually won after a close, hard-fought battle.
 === Example 2 ===

@@ Line 1: / Line 1: @@
 == Advanced edge templates ==
-=== Template IVc ===
+=== Template [[Edge_template_IV2a|IV-2-a]] ===
 <hex>R4 C4 Q1 1:BBRR 2:B_+_ 3:B**_ 4:_+__</hex>

@@ Line 204: / Line 204: @@
 I am Blue and it is my move. Red's e6-f6(-f4-g4) group is connected to bottom via template Vb. Red's i2 piece is connected to the top via edge template II.  In order to stop these two groups from connecting to each and completing a win, I must start laddering down column H. So I ladder down to h6 forcing Red to follow down column I to i6 yielding the following position.
-<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6</hex>
+<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   N:on Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6</hex>
 My h10 piece is ''not'' a valid ladder escape. If I ladder all the way down to h10, then Red follows down to i8 and his response to h9 is not i9 but j9!
-<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6   Hh7 Vi7 Hh8 Vi8 Hh9 Vj9</hex>
+<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6   N:on Hh7 Vi7 Hh8 Vi8 Hh9 Vj9</hex>
 Red has a winning chain on the right side. You might think I could win by instead laddering down one more hex, and then double two-chain to the h10 piece yielding the following position.
-<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6   Hh7 Vi7 Hg9</hex>
+<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6   N:on Hh7 Vi7 Hg9</hex>
 This may appear to settle the matter in my favor but in actuality, Red has a winning position! Red can win by 1. h8 (h9 also works but h8 is slightly more deceptive). If I respond by saving the link, i.e. by 1...g8, then Red wins by playing 2.h9 g10 (forced) 3. j9.
-<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6   Hh7 Vi7 Hg9   Vh8 Hg8 Vh9 Hg10 Vj9</hex>
+<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6   Hh7 Vi7 Hg9   N:on Vh8 Hg8 Vh9 Hg10 Vj9</hex>
 Red has an unbreakable winning chain down the right. Instead it is better for me to respond to Red's 1.h8 with 1...h9.  My g9-h9-h10 group is now solidly connected to the right but Red can continue 2.g8 and I cannot stop g8 from connecting to the bottom because of the help provided by Red's e6-f6 pieces (work it out!)
@@ Line 222: / Line 222: @@
 In the initial position I cannot afford to ladder down any farther than g6.  If I ladder down one more hex, I lose against best play no matter what. If there are no other pieces in the area, as is the case here, then the strongest way to play it is to ladder down one hex short of the hex that could double two-chain to the "almost-escape" piece, and then two chain up from the almost-escape piece which in our present case yields the following position.
-<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6   Hg9</hex>
+<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6   N:on Hg9</hex>
 Red has three tries to stop the connection between the h6 and g9 pieces.
@@ Line 234: / Line 234: @@
 In the actual game my opponent played h7 and I responded with f8. f8 threatens to connect with with h6 through g7. So my opponent played g7 to which I responded with f7. Again this threatens a winning connection from f7 to h6 through g6. So my opponent played g6 and I responded with c9 with a winning position.
-<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6   Hg9   Vh7 Hf8 Vg7 Hf7 Vg6 Hc9</hex>
+<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10   Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6   Hg9   N:on Vh7 Hf8 Vg7 Hf7 Vg6 Hc9</hex>
 Further play no longer concerns the topic under discussion but the remaining moves were d9, e7, d7, d8, b9, c8, a8, b8, a9, b7, a7, d6, resigns.  My opponent doesn't need to see g8, f9, h9, g10, j9, i8
@@ Line 244: / Line 244: @@
 Red has a chain running from the bottom at c9 up to d4. The only way Red can win is to connect this group to the top. Red can ladder d3, c3, b3 but as we saw earlier, the a3 piece is not a valid ladder escape. But Red can still win by two-chaining from a3 to b4.
-<hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9   Vb4</hex>
+<hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9   N:on Vb4</hex>
 This threatens a winning connection to c5 through b5. If Blue blocks this with b5, then Red plays the ladder because now the pair a3-b4 are a valid ladder escape. If instead Blue blocks off the ladder with say c3, then Red wins with the line b5, b3, a4 (forced), b1, d2!
-<hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9   Vb4   Hc3 Vb5 Hb3 Va4 Hb1 Vd2</hex>
+<hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9   Vb4   N:on Hc3 Vb5 Hb3 Va4 Hb1 Vd2</hex>
 d2 is a forking ladder escape; it threatens d3 and it provides an escape to the 2nd row ladder starting with b2. Blue cannot stop both winning threats with a single move, thus Red wins.