Difference between revisions of "Tom's move"

From HexWiki
Jump to: navigation, search
(Better description and examples)
(Improved proof of template.)
Line 9: Line 9:
 
   edges="bottom"
 
   edges="bottom"
 
   coords="none"
 
   coords="none"
  contents="R a1--a4 b2 b4 c2 B a5 b3 b5 c3 E *:e3"
 
 
   visible="-a1--c1 g1 h1 h2"
 
   visible="-a1--c1 g1 h1 h2"
 +
  contents="R a1--a4 b2 b4 c2 B a5 b3 b5 c3 E *:e3"
 
   />
 
   />
 
Then Red can connect by playing at "*", the so-called "Tom's move".
 
Then Red can connect by playing at "*", the so-called "Tom's move".
Line 72: Line 72:
 
== Why Tom's move is connected ==
 
== Why Tom's move is connected ==
  
Red has three main threats:
+
Let us compute Blue's [[mustplay region]]. Red has several main threats:
  
<hexboard size="5x11"
+
<hexboard size="5x8"
  coords="hide"
+
  edges="bottom"
  edges="bottom"
+
  coords="none"
  visible="area(g1,c5,k5,k3,i1)"
+
  visible="-a1--c1 g1 h1 h2"
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 E *:f1 E *:j1 E *:k1 E *:a2 E *:b2 E *:c2 E *:d2 R f2 E *:k2 E *:a3 E *:b3 R d3 E +:g3 R h3 E *:a4 B c4 R d4 R e4 R 1:f4 E +:g4 R 3:h4 B c5 B d5 B e5 B 2:f5 E +:g5 E +:h5"
+
  contents="R a1--a4 b2 b4 c2 B a5 b3 b5 c3 R e3 R 1:c4 B 2:c5 R 3:e4 S area(d3,c4,c5,e5,e3)"
  />
+
  />
 
+
<hexboard size="5x11"
+
  coords="hide"
+
  edges="bottom"
+
  visible="area(g1,c5,k5,k3,i1)"
+
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 E *:f1 E *:j1 E *:k1 E *:a2 E *:b2 E *:c2 E *:d2 R f2 R 1:g2 E +:h2 E *:k2 E *:a3 E *:b3 R d3 E +:g3 R h3 E +:i3 E *:a4 B c4 R d4 R e4 E +:g4 E +:h4 E +:i4 B c5 B d5 B e5 E +:f5 E +:g5 E +:h5 E +:i5"
+
  />
+
using the [[ziggurat]] and
+
  
<hexboard size="5x11"
+
<hexboard size="5x8"
  coords="hide"
+
  edges="bottom"
  edges="bottom"
+
  coords="none"
  visible="area(g1,c5,k5,k3,i1)"
+
  visible="-a1--c1 g1 h1 h2"
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 E *:f1 E *:j1 E *:k1 E *:a2 E *:b2 E *:c2 E *:d2 R f2 E +:g2 E *:k2 E *:a3 E *:b3 R d3 R h3 E *:a4 B c4 R d4 R e4 E +:f4 R 1:g4 B c5 B d5 B e5"
+
  contents="R a1--a4 b2 b4 c2 B a5 b3 b5 c3 R e3 R 1:c4 B 2:c5 R 3:d4 B 4:d5 R 5:f4 S area(e3,c4,c5,f5,f3)"
  />
+
  />
where the group containing 1 is connected to the left via one of the spots marked with + and trivially to the bottom.
+
  
The overlap in which Blue has to play:
 
  
<hexboard size="5x11"
+
<hexboard size="5x8"
  coords="none"
+
  edges="bottom"
  edges="bottom"
+
  coords="none"
  visible="area(g1,c5,k5,k3,i1)"
+
  visible="-a1--c1 g1 h1 h2"
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 E *:f1 E *:j1 E *:k1 E *:a2 E *:b2 E *:c2 E *:d2 R f2 E *:k2 E *:a3 E *:b3 R d3 E a:g3 R h3 E *:a4 B c4 R d4 R e4 E b:g4 B c5 B d5 B e5 E c:f5 E d:g5"
+
  contents="R a1--a4 b2 b4 c2 B a5 b3 b5 c3 R e3 R 1:d2 S area(d2,d4,c5,f5,f3,e2)"
  />
+
  />
 
+
The 4 different moves are now considered one by one.
+
  
If Blue moves at a:
+
<hexboard size="5x8"
<hexboard size="5x11"
+
  edges="bottom"
  coords="hide"
+
  coords="none"
  edges="bottom"
+
  visible="-a1--c1 g1 h1 h2"
  visible="area(g1,c5,k5,k3,i1)"
+
  contents="R a1--a4 b2 b4 c2 B a5 b3 b5 c3 R e3 R 1:d4 S area(d2,c4,c5,d5,e3,e2)"
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 E *:f1 E *:j1 E *:k1 E *:a2 E *:b2 E *:c2 E *:d2 R f2 E *:k2 E *:a3 E *:b3 R d3 B 1:g3 R h3 E *:a4 B c4 R d4 R e4 R 2:f4 R 4:g4 B c5 B d5 B e5 B 3:f5"
+
  />
  />
+
The group containing 4 is now connected to the bottom via the template [[Edge_template_III2b|III-2-b]] 
+
  
If Blue moves at b:
+
<hexboard size="5x8"
<hexboard size="5x11"
+
  edges="bottom"
  coords="hide"
+
  coords="none"
  edges="bottom"
+
  visible="-a1--c1 g1 h1 h2"
  visible="area(g1,c5,k5,k3,i1)"
+
  contents="R a1--a4 b2 b4 c2 B a5 b3 b5 c3 R e3 R 1:d4 S area(d2,c4,d5,f5,f3,e2)"
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 E *:f1 E +:h1 E *:j1 E *:k1 E *:a2 E *:b2 E *:c2 E *:d2 R f2 R 4:i2 E *:k2 E *:a3 E *:b3 R d3 E +:g3 R h3 E *:a4 B c4 R d4 R e4 R 2:f4 B 1:g4 B c5 B d5 B e5 B 3:f5"
+
  />
  />
+
 
The group containing 4 is now connected to the left by one of the threads marked with + and to the bottom via the template [[Edge_template_IV2b|IV-2-b]]
+
<hexboard size="5x8"
 +
  edges="bottom"
 +
  coords="none"
 +
  visible="-a1--c1 g1 h1 h2"
 +
  contents="R a1--a4 b2 b4 c2 B a5 b3 b5 c3 R e3 R 1:d4 S area(d2,c4,c5,f5,f3,e2)-d5"
 +
  />
 +
 
 +
Blue's [[mustplay region]] consists of the intersection of the carriers of these threats, which means that Blue's only hope is to play at 1.
 +
<hexboard size="5x8"
 +
  edges="bottom"
 +
  coords="none"
 +
  visible="-a1--c1 g1 h1 h2"
 +
  contents="R a1--a4 b2 b4 c2 B a5 b3 b5 c3 R e3 B 1:d4"
 +
  />
 +
Red responds like this:
 +
<hexboard size="5x8"
 +
  edges="bottom"
 +
  coords="none"
 +
  visible="-a1--c1 g1 h1 h2"
 +
  contents="R a1--a4 b2 b4 c2 B a5 b3 b5 c3 R e3 B 1:d4 R 2:c4 B 3:c5 R 4:f2 E *:e1 *:d3"
 +
  />
  
If Blue moves at c:
+
The group containing 4 is now connected to the bottom via [[Edge_template_III2b|edge template III2-b]], and to
<hexboard size="5x11"
+
Red's main group by double threat at the cells marked "*". Note that 2 and 3 do not actually need to be played; these moves have been included for clarity.
  coords="hide"
+
  edges="bottom"
+
  visible="area(g1,c5,k5,k3,i1)"
+
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 E *:f1 E *:j1 E *:k1 E *:a2 E *:b2 E *:c2 E *:d2 R f2 R 4:g2 E *:k2 E *:a3 E *:b3 R d3 R h3 E *:a4 B c4 R d4 R e4 B 3:f4 R 2:g4 R 6:i4 B c5 B d5 B e5 B 1:f5 B 5:g5"
+
  />
+
If Blue plays 3 before 5, Red can play 4 before 6.
+
 
+
If Blue moves at d:
+
<hexboard size="5x11"
+
  coords="hide"
+
  edges="bottom"
+
  visible="area(g1,c5,k5,k3,i1)"
+
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 E *:f1 E *:j1 E *:k1 E *:a2 E *:b2 E *:c2 E *:d2 R f2 E *:k2 E *:a3 E *:b3 R d3 R h3 E *:a4 B c4 R d4 R e4 R 2:f4 R 4:i4 B c5 B d5 B e5 B 3:f5 B 1:g5"
+
  />
+
So all of Blue's blocking attempts fail.
+
  
 
== See also ==
 
== See also ==

Revision as of 16:57, 11 September 2021

Introduction

Tom's move is a trick that enables a player to make a connection from a 2nd-and-4th row parallel ladder. It can also be used to break through a 2nd row ladder using a single stone on the 4th row, or to connect a single stone on the 4th row to the edge. Its name originates from Tom Ace (player Tom239), who devised it during a game against dj11, on 15 December 2002 on Playsite. This was not its first use ever, just how it came to be known among Hex players on Playsite.

Description

Suppose Red has a 2nd-and-4th row parallel ladder and the amount of space shown here:

Then Red can connect by playing at "*", the so-called "Tom's move".

Usage examples

Connecting a 2nd row ladder using an isolated stone on the 4th row

Red to move and win:

The solution is to push the ladder to 3 and then play Tom's move:

51324

A single stone on the 4th row is connected

Consider a single stone on the 4th row, with the amount of space shown:

Then Red can connect as follows:

216435

Red squeezes through the bottleneck at 2, starts a 2nd row ladder at 4, then plays Tom's move at 6. Note that all of Blue's moves are forced; if Blue plays differently, Red connects outright.

In a game

Red to move:

abcdefghijkabcdefghijk12345678910111234567891011

Red's d4 group is already connected to the top edge by edge template IV1-a. To connect to the bottom, Red plays as follows:

abcdefghijkabcdefghijk12345678910111234567891011129357468

Now Red is connected by Tom's move. Note that d8 is already connected to Red's group by double threat at c8 and d9.


Why Tom's move is connected

Let us compute Blue's mustplay region. Red has several main threats:

132
13524


1
1
1
1

Blue's mustplay region consists of the intersection of the carriers of these threats, which means that Blue's only hope is to play at 1.

1

Red responds like this:

4213

The group containing 4 is now connected to the bottom via edge template III2-b, and to Red's main group by double threat at the cells marked "*". Note that 2 and 3 do not actually need to be played; these moves have been included for clarity.

See also