Difference between revisions of "Tom's move"
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| + | This is a special case of a [[Theorems_about_templates#Alternative_connection_up|general theorem]]. | ||
=== Tall variant === | === Tall variant === | ||
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R 1:e3 B 2:d4 R 3:c4 B 4:c5 R 5:f2 E *:d3 *:e1 | R 1:e3 B 2:d4 R 3:c4 B 4:c5 R 5:f2 E *:d3 *:e1 | ||
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Now Red is connected by the (ordinary) Tom's move. | Now Red is connected by the (ordinary) Tom's move. | ||
See [[Tom's move for 3rd and 5th row parallel ladders]] for more details. | See [[Tom's move for 3rd and 5th row parallel ladders]] for more details. | ||
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| + | === Tall variant === | ||
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| + | Tom's move for 3rd-and-5th row parallel ladders also has a tall version. It works in the same way as the tall version of Tom's move for 2nd-and-4th row parallel ladders above, given the appropriate amount of space. | ||
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== See also == | == See also == | ||
Latest revision as of 21:44, 20 April 2024
Contents
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 connect 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, but it is 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:
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:
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. This is edge template IV1d.
In a game
Red to move:
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:
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
To compute Blue's mustplay region, we consider two red threats:
These leaves only blue moves in the ziggurat.
If Blue plays there other than at a, then Red plays at a.
In that case, Red's 2 connects back via either of the cells marked "*", and since the piece Blue just played is in only one of the x,y,z regions, Red's 2 also connects down via either of the remaining two of those three regions.
Thus Blue's only remaining hope is to play at a.
Red responds like this:
Red's 4 is now connected to the bottom via edge template IV2b, 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.
Pushing the 4th row ladder first
Sometimes, there is not enough room to play Tom's move right away, but enough room can be created by first pushing the 4th row ladder. For a typical example, consider the following situation. It is Blue's turn, and Red wants to connect her stone to the bottom edge.
If Red tries to play Tom's move immediately, it doesn't work, because 8 does not connect back to Red's main group.
What Red can do instead is start by pushing the 4th row ladder twice.
Of course this only works if after pushing the ladder, there is still enough room for Tom's move.
It is not actually necessary to push the 2nd row ladder (moves 6–13 can be omitted), but they have been included for clarity.
Note that when Red pushes the 4th row ladder, Blue cannot yield, as this would give Red a ladder escape fork for the below 2nd row ladder. Also, as explained in more detail in the article on parallel ladders, the 4th row ladder must be pushed before the 2nd row ladder has caught up to it. If Red starts by first pushing the 2nd row ladder, then it is too late to push the 4th row ladder.
Variants
Alternative connection up
Tom's move also works when the hex marked "a" is not empty, provided that "b" connects to Red's main group.
For example, Tom's move works in this situation:
This is a special case of a general theorem.
Tall variant
If "d" is empty, there is a variant of Tom's move that does not require a connection via "b", or even for "b" to be empty; it merely requires "c" and "e" to threaten to connect to Red's main group. An example is this situation:
In this version of Tom's move, Red's 4 is different than usual (the usual move 4 does not work here). As before, moves 2 and 3 don't need to be played, but make it easier to see how the connection works.
Note that "x" is connected to Red's main group without requiring "y", and "4" is also connected to Red's main group without requiring "y". (However, Red cannot guarantee to connect both "x" and "4" to her main group without requiring "y"). If Blue tries to cut Red off from the edge, Red responds as follows:
Now no matter how Blue plays, Red can connect to the edge by a sequence of forcing moves. The situation is analogous to the hammock template.
Tom's move for 3rd-and-5th row parallel ladders
Main article: Tom's move for 3rd and 5th row parallel ladders.
There is a version of Tom's move that works for parallel ladders on the 3rd and 5th rows. It requires a large amount of space:
By playing at "1", Red can connect to the edge. Verifying this requires a lot of steps, but here is the basic idea:
Notice that Red's 3 is connected left by double threat at the two cells marked "*", and connected right by edge template V2m. The latter template is itself based on Tom's move at "x". It works, for example, like this:
Now Red is connected by the (ordinary) Tom's move.
See Tom's move for 3rd and 5th row parallel ladders for more details.
Tall variant
Tom's move for 3rd-and-5th row parallel ladders also has a tall version. It works in the same way as the tall version of Tom's move for 2nd-and-4th row parallel ladders above, given the appropriate amount of space.
