Difference between revisions of "Peep"

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Sometimes it's hard to tell if a move is sufficiently [[Forcing moves|forcing]], and whether the opponent can gain by resisting, rather than just responding in the obvious way. Playing correct peeps is one of the most sophisticated aspects of Hex strategy.
 
Sometimes it's hard to tell if a move is sufficiently [[Forcing moves|forcing]], and whether the opponent can gain by resisting, rather than just responding in the obvious way. Playing correct peeps is one of the most sophisticated aspects of Hex strategy.
  
Another term for peep is '''nozoki''' (borrowed from Go).
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Another term for peep is '''nozoki''' (also borrowed from Go).
  
 
== Examples ==
 
== Examples ==
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If at least one of the shaded hexes is occupied by a piece of the corresponding color, then Blue playing * is a peep.  This is because, in such cases,
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If at least one of the shaded hexes is occupied by a piece of the indicated color, then Blue playing * is a peep.  This is because, in such cases,
  
 
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Red playing B2 instead of C2 is also a peep at Blue's ziggurat.
 
Red playing B2 instead of C2 is also a peep at Blue's ziggurat.
  
== Crucial peep ==
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== Crucial Peep ==
  
 
Playing peeps can be very useful. In certain situations, playing a peep can make the difference between winning and losing. Consider the following example:
 
Playing peeps can be very useful. In certain situations, playing a peep can make the difference between winning and losing. Consider the following example:

Revision as of 09:10, 2 January 2021

A peep is a move in specific region such that

  • Looking just at that region, it would normally be a forcing move (even if the global situation means the opponent should not respond anywhere nearby).

and

  • If the opponent does respond in that region (rather than merely close to it), then one can easily prove that the exchange does not help the opponent and can't easily prove that the exchange doesn't matter.

.


This situation occurs if one threatens to cut a connection between major groups or key stones of the opponent, or to create a connection between one's own major groups or key stones.

Sometimes it's hard to tell if a move is sufficiently forcing, and whether the opponent can gain by resisting, rather than just responding in the obvious way. Playing correct peeps is one of the most sophisticated aspects of Hex strategy.

Another term for peep is nozoki (also borrowed from Go).

Examples

If at least one of the shaded hexes is occupied by a piece of the indicated color, then Blue playing * is a peep. This is because, in such cases,

d2

Red playing * would kill d, so if Red just defends the bridge, then Blue can't do any better here than Blue playing * and Red responding with the central hex.

This is by far the most common form of peep, a "bridge peep".


Similarly, with suitable surrounding conditions, there can also be peeps at templates.

abcd12345

Here, C3 has a ziggurat to the left edge,

abcd12345

so if Blue just defends the ziggurat, then Red can't do any better here

abcd12345

than Red getting the outside of the ziggurat and C3 connecting left.

Red C2 captures C1 and D1, turning the corner into

abcd123451

a region where whoever moves connects.

Giving Red A2 and B2 does not change that,

abcd123451

so Red's 1 is a peep at Blue's ziggurat.

By star decomposition domination, red C2 is at least as good for Red as red B2.

Also, red B2 captures D1 and C2, so

red B2 is at least as good for Red as red C2.

Thus red B2 is equivalent to red C2, so

abcd1234511

Red playing B2 instead of C2 is also a peep at Blue's ziggurat.

Crucial Peep

Playing peeps can be very useful. In certain situations, playing a peep can make the difference between winning and losing. Consider the following example:

abcdefghi123456789

The only winning move for Red is the peep at d6. If Red misses it, the game proceeds as follows and Blue wins:

abcdefghi123456789132546

If Red starts by playing d6 instead, Red wins.

abcdefghi123456789231

Bad Peeps

There are at least several ways a peep can be bad:

  • Due to circumstances outside of the region, the apparent cutting threat does not actually work, in which case the peep is close to a wasted move.
  • While the apparent threat does work, it's not big-enough for the opponent to respond by defending against that threat.


  • The opponent can minimax, rather than answering more-locally.
abcdefgh12345678

Here, Blue wins fairly easily with G1 or F3.

abcdefgh1234567811

If Blue plays the bridge peep, then * would give the win back to Blue

abcdefgh1234567821

, but Red wins by instead minimaxing with 2.


  • The opponent benefits by resisting the peep.

Resisting a Peep

Rather than responding in the obvious way, the opponent can play a move that mitigates against the peep's threat, while also getting something else. The most common example of this is foiling.

For example, Blue can play 2 instead of *.

12

Red could've gotten a height-2 ladder towards the right, but after 1 and 2, a red ladder towards the right would be height-3.

Note that this does not necessarily mean the peep was bad.

For example, Red could be fine with the ladder being height-3, and Red can now get

abcdef1234535142

C2 before pushing the ladder, whereas if Red had started with C2

abcdef12345146325

, then Blue would presumably just defend the bridges.


The consequences of resisting a peep can also be much harder to assess.

12

Here, Blue chose to resist with 2, rather than just play *.