Difference between revisions of "Forcing move"

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A '''forcing move''' is a move that makes a threat that your opponent must reply to on their next [[turn]]. Common forcing moves include playing in one of the [[Empty hex|open hex]]es in a two-chain (threatening to break the link), intrusion into an [[edge template]], or [[threat]]ening an immediate [[strong connection]] or [[win]].  Consider the following position with the [[red|vertical player]] to move.
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A '''forcing move''' is a move that makes a threat that your opponent must reply to on their next turn. Common forcing moves include playing in one of the empty hexes of a [[bridge]], intruding into an [[edge template]], or threatening to complete an immediate [[strong connection]] or [[win]].  Consider the following position with Red to move.
  
 
<hex>R9 C9 Q1 Vg3 Vg4 Vf5 Vh5 Hc7 Hd8 Hf7 Hh7</hex>
 
<hex>R9 C9 Q1 Vg3 Vg4 Vf5 Vh5 Hc7 Hd8 Hf7 Hh7</hex>
  
At first glance, the position looks bad for [[Red (player)|Red]], but Red can win by making a couple of forcing moves. He plays at e8 threatening to play at e7 on his next turn which would create an unbeatable [[winning chain]]. [[Blue (player)|Blue]] has little choice but to stop this threat by playing e7 (there is nothing better). The move e8 is a forcing move.
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At first glance, the position looks bad for Red, but she can win by making a couple of forcing moves. She plays at e8, threatening to play at e7 on her next turn which would create a winning connection. Blue has little choice but to stop this threat by playing e7, since there are no better options. The move e8 is a forcing move.
  
The forcing nature of the move allows Red to place a piece on the other side of Blue's line without giving Blue any time to do anything constructive. The e8 piece on the other side is connected to the [[Bottom edge|bottom]] and is of critical importance.
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The forcing nature of the move allows Red to place a piece on the other side of Blue's line without giving Blue time to do anything constructive. The e8 piece on the other side is connected to the bottom and is extremely useful to Red.
  
Red continues by playing another [[forcing move]] at g7. The only move that stops this piece from immediately [[connection|connecting]] to the bottom edge is f9. But after f9, Red completes the win by playing at f8.
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Red continues by playing another forcing move at g7. The only move that stops this piece from immediately [[connection|connecting]] to the bottom edge is f9. But after f9, Red completes the win by playing at f8.
  
<hex>R9 C9 Q1 Vg3 Vg4 Vf5 Vh5 Hc7 Hd8 Hf7 Hh7   Ve8 He7 Vg7 Hf9 Vf8</hex>
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<hex>R9 C9 Q1 Vg3 Vg4 Vf5 Vh5 Hc7 Hd8 Hf7 Hh7 N:on  Ve8 He7 Vg7 Hf9 Vf8</hex>
  
The group of red pieces near the bottom are connected to the bottom edge. These pieces are connected via [[chain|two-chains]] to the group g3-g4-f5 which is in turn connected to the [[top edge]] via [[edge template IIIa]].
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The group of red pieces near the bottom are connected to the bottom edge. These pieces are connected via [[bridge]]s to the group g3-g4-f5 which is in turn connected to the top edge via a [[ziggurat]].
  
''(Note: the two forcing moves could just as easily be played in the reverse order. That is Red plays g7, Blue is forced to respond with f9, and then Red plays e8 which threatens to form an unbeatable chain [[Double threat|in two distinct ways]].)''
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''(Note: the two forcing moves could just as easily be played in the reverse order. That is Red plays g7, Blue is forced to respond with f9, and then Red plays e8 which threatens to form a connection [[Double threat|in two distinct ways]].)''
  
In general terms, you have three options when responding to a forcing move in a two-chain.
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In general terms, the opponent has three options when responding to a forcing move.
  
# [[Saving a connection|Save]] the link by playing the other move in the two-chain.
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# ''Defend'' against the threat, by saving the connection, restoring the template, etc.;
# [[Ignoring a threat|Play elsewhere]] (e.g. playing another move may give another way of meeting the threat thus rendering it harmless)
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# ''Ignore'' the threat and play elsewhere (see also [[tenuki]]);
# [[Counterthreat|Respond]] with a forcing move of your own.
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# ''Counter'' the threat by making a forcing move of their own.
  
== Breaking edge templates via forcing moves ==
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A player who attempts a forcing move usually expects the opponent to defend. However, if the threat is not strong enough, the opponent may decide to do something unexpected, such as ignoring or countering the threat, or even defending it but not in the expected way. Therefore, care must be taken to ensure that the potential forcing move really forces the intended response.
  
Forcing moves are also the only way to successfully defeat an [[edge template]]. This is done by making a [[template intrusion]] that is also a more threatening forcing move. After the opponent responds to the [[greater threat]], you can play another move within the template and destroy the connection to the edge. For example, consider the following position with the [[vertical player]] to move.
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Some forcing moves are better played early than late. For example, with very few pieces on the board, the opponent might typically answer a bridge intrusion, because they expect that the bridge may become important later in the game. Later in the game, it may turn out that the bridge is no longer important to the opponent's connection, and the opponent would likely not defend it at that point.
  
<hex>R9 C9 Q1 Hc3 Hd3 He3 Hf2 Hg1 Hg3 Vd7 Ve6 Ve5 Ve4 Vf3 Vh5 Si1 Si2 Si3 Si4 Sh2 Sh3 Sh4 Sg4</hex>
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== Breaking edge templates via forcing moves ==
  
The piece on g3 is connected to the [[right edge]] via [[Edge template IIIa|template IIIa]] indicated by the '*'s. Red's best move is to play at h2. This intrudes on the edge template, is connected to the top via [[edge template II]], and threatens to complete an unbeatable chain by playing at g2 next turn. Blue can stop this threat only by playing at g2. Then Red Plays i3 breaking Blue's connection to the [[Right edge|right]].
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Forcing moves are the only way to successfully defeat a [[template]]. This is done by making a template [[intrusion]] that is also a more threatening forcing move. After the opponent responds to the greater threat, the attacker can play another move within the template and destroy the connection. For example, consider the following position with Red to move.
  
<hex>R9 C9 Q1 Hc3 Hd3 He3 Hf2 Hg1 Hg3 Vd7 Ve6 Ve5 Ve4 Vf3 Vh5    Vh2 Hg2 Vi3</hex>
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<hexboard size="5x5"
 +
  coords="top left"
 +
  edges="all"
 +
  contents="B a3 b2 c1 c3 R a5 a4 b3 d5 S e1 e2 e3 e4 d2 d3 d4 c4 c3"
 +
  />
 +
 
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The piece on c3 is connected to the right edge by a [[ziggurat]], as shown. If Red moves at d2, she intrudes on the ziggurat while also threatening to connect via c2. Blue can only stop this threat by playing at c2. Then Red Plays e3, breaking Blue's connection to the right.
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<hexboard size="5x5"
 +
  coords="top left"
 +
  edges="all"
 +
  contents="B a3 b2 c1 c3 R a5 a4 b3 d5 S e1 e2 e3 e4 d2 d3 d4 c4 c3 R 1:d2 B 2:c2 R 3:e3"
 +
  />
  
 
== Using forcing moves to steal territory ==
 
== Using forcing moves to steal territory ==
  
I'll define [[territory]] to be the number of [[empty hex]]es adjacent to your pieces. By playing a forcing move in one of the empty hexes in a two-chain, a player can [[Stealing territory|steal territory]] at no cost.
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By playing a forcing move inside the opponent's template, a player can sometimes steal [[territory]] at no cost.
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 +
<hexboard size="5x5"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(b1,a2,a5,d5,e4,e1)"
 +
  contents="B c2 b4 R d2 d3 E *:(b3 c3)"
 +
  />
 +
 
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In this position, if Red intrudes on the left side of the bridge and Blue defends the connection, Red gains territory on the left, while giving up nothing of value on the right, and without disturbing either player's connections.
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 +
<hexboard size="5x5"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(b1,a2,a5,d5,e4,e1)"
 +
  contents="B c2 b4 R d2 d3 R 1:b3 B 2:c3"
 +
  />
 +
 
 +
Significantly, the additional territory is on the other side of Blue's connection where it may potentially be used for a future threat. The additional territory can't hurt and sometimes makes a crucial difference.
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A forcing move is harmless if it gains no territory for the opponent. You should not be worried at all about leaving harmless forcing moves available for your opponent.  
  
<hex>R5 C5 Hc2 Hb4 Vd2 Vd3 Sb3</hex>
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When you have more than one way of completing a connection, e.g. when completing a [[loose connection]], you should consider which move leaves the least valuable forcing move for your opponent. Consider the following position with Red to play.
  
In this position, Blue has two more hexes of territory than Red (9 vs. 7 adjacent hexes). Suppose Red makes the forcing move at the indicated hex and Blue [[Saving a connection|saves the link]].
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<hexboard size="6x6"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(d1,a4,a6,c6,f3,f1)"
 +
  contents="R d2 d4 B b4 b5 e3 E c:c3 b:c4 a:d3 x:c2 y:b3 S c3 c4 d3"
 +
  />
  
<hex>R5 C5 Hc2 Hb4 Vd2 Vd3    Vb3 Hc3</hex>
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Red wants to connect her two pieces. There are three distinct moves that accomplish this, a, b, and c.
  
Now Red has two more hexes of territory; i.e. Red has stolen 4 hexes of territory without disturbing either player's connections. Significantly, the additional territory is on the other side of Blue's connection where it may potentially be used for a future threat. The additional territory can't hurt and sometimes it makes a crucial difference.
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There is not much to be said about a; it directly connects without altering anything else.  
  
A forcing move is [[Irrelevant move|harmless]] if it gains no territory for the opponent. You should not be worried at all about leaving harmless forcing moves available for your opponent. When you have more than one way of completing a connection with a two-bridge, e.g. when completing the [[loose connection]] described previously, you should consider which forcing move is least valuable for your opponent. Consider the following position with Red to play.
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b connects, but gives a potentially useful forcing move to Blue. Blue can respond at c. If Red saves the connection at a, Blue has gained a free hex of territory. The hex x is now directly adjacent to Blue's group when it wasn't previously. Hence, b is worse than a.
  
<hex>R5 C6 Q1 Vd2 He3 Hb4 Vd4 Hb5</hex>
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Now consider the last remaining possibility, c. This leaves two forcing moves for Blue, but both of them are completely harmless! If after c, Blue plays one of the forcing moves a or b, then Red can save the link and Blue will not have gained any territory at all &mdash; any empty hexes adjacent to the forcing piece were already adjacent to Blue's existing pieces. Hence, c is just as safe as a but significantly, c ''gains'' one hex! &mdash; y is now adjacent to Red's group when it wasn't before. Thus, c is better than a and is the best of three choices.
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In other words, c [[dominated cell|dominates]] a and b.
  
Red wants to connect the d4 piece to the d2 piece. There are three distinct moves that accomplish this, d3, c4 (two-chaining to d2), and c3 (two-chaining to d4).
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== See also: ==
  
There is not much to be said about d3; it [[Direct connection|directly connects]] without altering anything else. c4 connects but gives a potentially useful forcing move to Blue. Blue can respond with c3 and suppose Red saves the connection with d3. Now Blue has gained a free hex of territory, the hex c2 is now directly adjacent to the c3/b4/b5 group when it wasn't previously. Hence, c4 is worse than d3.
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* [[Peep]]
  
Now consider the last remaining possibility, c3. This leaves two forcing moves for Blue but both of them are completely harmless! If after c3, Blue plays one of the forcing moves c4 or d3, then Red can save the link and Blue will not have gained any territory at all &mdash; any empty hexes adjacent to the forcing piece were already adjacent to Blue's existing pieces. Hence, c3 is just as safe as d3 but significantly, c3 ''gains'' one hex! &mdash; b3 is now adjacent to Red's d2/b3 group when it wasn't before. Thus, c3 is better than d3 and is the best of three choices.
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[[category:strategy]]

Latest revision as of 15:33, 7 October 2023

A forcing move is a move that makes a threat that your opponent must reply to on their next turn. Common forcing moves include playing in one of the empty hexes of a bridge, intruding into an edge template, or threatening to complete an immediate strong connection or win. Consider the following position with Red to move.

abcdefghi123456789

At first glance, the position looks bad for Red, but she can win by making a couple of forcing moves. She plays at e8, threatening to play at e7 on her next turn which would create a winning connection. Blue has little choice but to stop this threat by playing e7, since there are no better options. The move e8 is a forcing move.

The forcing nature of the move allows Red to place a piece on the other side of Blue's line without giving Blue time to do anything constructive. The e8 piece on the other side is connected to the bottom and is extremely useful to Red.

Red continues by playing another forcing move at g7. The only move that stops this piece from immediately connecting to the bottom edge is f9. But after f9, Red completes the win by playing at f8.

abcdefghi12345678923154

The group of red pieces near the bottom are connected to the bottom edge. These pieces are connected via bridges to the group g3-g4-f5 which is in turn connected to the top edge via a ziggurat.

(Note: the two forcing moves could just as easily be played in the reverse order. That is Red plays g7, Blue is forced to respond with f9, and then Red plays e8 which threatens to form a connection in two distinct ways.)

In general terms, the opponent has three options when responding to a forcing move.

  1. Defend against the threat, by saving the connection, restoring the template, etc.;
  2. Ignore the threat and play elsewhere (see also tenuki);
  3. Counter the threat by making a forcing move of their own.

A player who attempts a forcing move usually expects the opponent to defend. However, if the threat is not strong enough, the opponent may decide to do something unexpected, such as ignoring or countering the threat, or even defending it but not in the expected way. Therefore, care must be taken to ensure that the potential forcing move really forces the intended response.

Some forcing moves are better played early than late. For example, with very few pieces on the board, the opponent might typically answer a bridge intrusion, because they expect that the bridge may become important later in the game. Later in the game, it may turn out that the bridge is no longer important to the opponent's connection, and the opponent would likely not defend it at that point.

Breaking edge templates via forcing moves

Forcing moves are the only way to successfully defeat a template. This is done by making a template intrusion that is also a more threatening forcing move. After the opponent responds to the greater threat, the attacker can play another move within the template and destroy the connection. For example, consider the following position with Red to move.

abcde12345

The piece on c3 is connected to the right edge by a ziggurat, as shown. If Red moves at d2, she intrudes on the ziggurat while also threatening to connect via c2. Blue can only stop this threat by playing at c2. Then Red Plays e3, breaking Blue's connection to the right.

abcde12345213

Using forcing moves to steal territory

By playing a forcing move inside the opponent's template, a player can sometimes steal territory at no cost.

In this position, if Red intrudes on the left side of the bridge and Blue defends the connection, Red gains territory on the left, while giving up nothing of value on the right, and without disturbing either player's connections.

12

Significantly, the additional territory is on the other side of Blue's connection where it may potentially be used for a future threat. The additional territory can't hurt and sometimes makes a crucial difference.

A forcing move is harmless if it gains no territory for the opponent. You should not be worried at all about leaving harmless forcing moves available for your opponent.

When you have more than one way of completing a connection, e.g. when completing a loose connection, you should consider which move leaves the least valuable forcing move for your opponent. Consider the following position with Red to play.

xycab

Red wants to connect her two pieces. There are three distinct moves that accomplish this, a, b, and c.

There is not much to be said about a; it directly connects without altering anything else.

b connects, but gives a potentially useful forcing move to Blue. Blue can respond at c. If Red saves the connection at a, Blue has gained a free hex of territory. The hex x is now directly adjacent to Blue's group when it wasn't previously. Hence, b is worse than a.

Now consider the last remaining possibility, c. This leaves two forcing moves for Blue, but both of them are completely harmless! If after c, Blue plays one of the forcing moves a or b, then Red can save the link and Blue will not have gained any territory at all — any empty hexes adjacent to the forcing piece were already adjacent to Blue's existing pieces. Hence, c is just as safe as a but significantly, c gains one hex! — y is now adjacent to Red's group when it wasn't before. Thus, c is better than a and is the best of three choices. In other words, c dominates a and b.

See also: