From:           jerry@uni-paderborn.de (Gerald Siek)
Newsgroups:     rec.games.abstract
Subject:        Twixt rules
Date:           13 Nov 1992 11:26:26 GMT
Organization:   University of Paderborn, Germany

G.J. McCaughan (gjm11@cus.cam.ac.uk) wrote:
: 
: OK. You haven't stated the rules of Twixt, so I'm going to have to
: guess. 

Rules of Twixt:

The board looks like this:

              BLACK
          . . . . . . . .
         +---------------+
        .|. . . . . . . .|.         .    = holes
        .|. . . . . . . .|.         - |  = borderlines
        .|. . . . . . . .|.
        .|. . . . . . . .|.
 RED    .|. . . . . . . .|.   RED
        .|. . . . . . . .|.
        .|. . . . . . . .|.
        .|. . . . . . . .|.
        .|. . . . . . . .|.
         +---------------+
          . . . . . . . .    <==== note that there are NO holes in the corners
              BLACK

Each player has an arbitrary number of towers (which fit into the holes) and bridges which can connect two towers each. All bridges have the same size.

Red starts , players take their turns alternately. When it's his move, a player MUST place one tower into one hole. Red may NOT use the holes behind black's borderlines and vice versa. After placing a tower, a player may connect ANY number of towers as long as possible. Towers may be connected, if they are a knight's move apart (oh boy - excuse my English) i.e.:

    . o . o .       The center tower (x) may be connected to
    o . . . o       any of the towers marked '*'
    . . X . . 
    o . . . o 
    . o . o . 

The first player who connect two holes behind his left & right (upper & lower) borderlines by bridge wins the game.

Anyone interested in a game of Twixt per e-mail?

Regards,
        Jerry

--
  Gerald Siek  -  jerry@uni-paderborn.de  -  University of Paderborn, Germany

From:           n9110536@henson.cc.wwu.edu (W. Douglas West)
Newsgroups:     rec.games.abstract
Subject:        Re: Let's start off with TWIXT
Date:           13 Nov 92 17:53:44 GMT
Organization:   Western Washington University

In article <1992Nov13.073054.2028@linkoping.trab.se> ath@linkoping.trab.se (Anders Thulin) writes:
>In article <BxK1o5.My6@cs.psu.edu> flee@cs.psu.edu (Felix Lee) writes:
>>Here's a draw, on a small Twixt board.  Neither player can complete
>>their goal.
>>    . . O .
>>    X ./. .
>>    .\O X .
>>    . X O\.
>>    . ./. X
>>    . O . .
>That looks like a draw. I can't find any obvious way to draw on an
>odd board (say 5 x 5), though - is there one?
>-- 
>Anders Thulin       ath@linkoping.trab.se    013-23 55 32
>Telia Research AB, Teknikringen 2B, S-583 30 Linkoping, Sweden

  . . O .    . . O .    . . O .    . . O .
  X ./. .    X ./X .    X ./X\.    X ./X\.
  .\O X . -> .\O/X . -> .\O/X O -> .\O/X\O
  . X O\.    . X O\.    . X O\.    . X O\X
  . ./. X    . ./. X    . ./. X    . ./. X
  . O . .    . O . .    . O . .    . O . .

  O_  .   .   X
    --__     /
  .   X --O / .
     /     /  
  . / O_  X   .
   /    --__  
  X   .   . --O 

Newsgroups:     rec.games.abstract
From:           jonboy@nadia.stgt.sub.org (Jonathan Welton)
Subject:        Twixt - rule correction
Date:           Sun, 15 Nov 1992 22:08:14 GMT
Organization:   Stuttgart Net Systems, FRG

1. Place a peg in any free hole,
2. Remove any of your own bridges,
3. Place bridges between any two of your own pegs which are a knights move apart.

Part 2 is the rule that is most often forgotten. Even in the rule books accompanying some productions of the game it was incorrectly ommitted. It is an important rule, since it often resolves otherwise drawn positions. A good example is the mini situation already posted

>       . . O .    If X is connecting right to      . . O .
>       X ./. .    left, he can play at x,          X ./. .
>       .\O X .    remove his leftmost bridge,      . O X .
>       . X O\.    and make a winning connection.   x X O\.
>       . ./. X                                     . ./. X
>       . O . .                                     . O . .

Twixt was invented by Alex Randolph, a prolific inventor of games (see Sid Sackson's "Gamut of Games"), who introduced it to a group of artist freinds who used to frequent a Vienese cafe. It has been produced by several manufacturers, all of whom are required to credit the inventor (what a good practice).

Twixt is, quite rightly, very highly regarded, and is rated as one of the best modern board games around.

If you think that the concept of non-intersecting knight moves is simple, try programming Twixt. Or try to find a non-intersecting knight tour of 17 moves on a 6x6 board (with no square visited twice). The unique solution can be found in Martin Gardner's "Mathematical Circus".

Alternatively, try the following little game. The first player marks a square on an 8x8 board. The second player draws a line from this square to one a knights move away. The first player then draws a line from this square to another a knights move away and so on, each player extending a knights tour, which must be non-intersecting, and no square may be visited more than once. The last player able to move is the winner. This is an entertaining little game, and one capable of being played with a high degree of skill. I would be interested to hear of anyone who manages to program this one.

-- 
   Jonathan Welton             
   jonboy@nadia.stgt.sub.org  

Newsgroups:     rec.games.abstract
From:           hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Subject:        Re: Twixt - rule correction
Organization:   Naval Research Laboratory, Washington, DC
Date:           Mon, 16 Nov 1992 14:27:12 GMT

jonboy@nadia.stgt.sub.org (Jonathan Welton) writes:

> The descriptions of Twixt posted so far have all been incomplete.
> A move consists of 3 parts -
>  1. Place a peg in any free hole,
>  2. Remove any of your own bridges,
>  3. Place bridges between any two of your own pegs which are a knights
>     move apart.
> In parts 2 and 3 you may remove (add) any number of bridges.

> Part 2 is the rule that is most often forgotten. Even in the rule books
> accompanying some productions of the game it was incorrectly ommitted.

> It is an important rule, since it often resolves otherwise drawn
> positions. A good example is the mini situation already posted

    X   -   - ,,O             X   -   - ,,O         
     \     ,''                       ,''            
    - \ O'' X   -             -   O'',X   -         
       \     \        =>         ,,''  \            
    -   X ,,O \ -             X'' X ,,O \ -         
       ,''     \                 ,''     \          
    O'' -   -   X             O'' -   -   X         

> In fact, with the help of this bridge removal rule, drawn games are
> extremely rare in Twixt.

    - - - - O - O - - - - -
    - - - - - O - O - - - -
    - - - - O - O - - - - -
    - - - - - O - O - - - -
    - X - X O X O X - X - X
    X - X - X O X O X - X -
    - X - X O X O X - X - X
    X - X - X O X O X - X -
    - - - - O - O - - - - -
    - - - - - O - O - - - -
    - - - - O - O - - - - -
    - - - - - O - O - - - -

Flee@cs.psu.edu (Felix Lee) writes:

] How can we make draws illegal in Twixt?  Consider this rule:

] A player is not allowed to make a move that completely blocks off his
] opponent, if the move doesn't win.

I think it would be an extremely difficult rule to put into practice, because after the blockage was established, you would have to spend part of each turn demonstrating that your opponent ``could'' make a connection across the board, as long as you didn't respond to the various double-crosses. Your strategy would then be to form ever more double-crosses, while springing your opponent's. The loser is the one who is forced to start throwing away moves into uncontested parts of the board while the winner paves an enforced right-of-way.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil

Organization:   Carnegie Mellon, Pittsburgh, PA
Newsgroups:     rec.games.abstract
Date:           Tue, 17 Nov 1992 00:24:44 -0500 
From:           "Jonathan R. Ferro" <jf41+@andrew.cmu.edu>
Subject:        Re: Twixt - rule correction

jonboy@nadia.stgt.sub.org (Jonathan Welton) writes:
> The descriptions of Twixt posted so far have all been incomplete.
> A move consists of 3 parts -
>  1. Place a peg in any free hole,
>  2. Remove any of your own bridges,
>  3. Place bridges between any two of your own pegs which are a knights
>     move apart.

1. Remove any of your own structure that you wish.
2. Place one peg.
3. Link any of your pegs that are a knight's move apart.

> Twixt was invented by Alex Randolph, a prolific inventor of games
> (see Sid Sackson's "Gamut of Games"), who introduced it to a group
> of artist freinds who used to frequent a Vienese cafe. It has been
> produced by several manufacturers, all of whom are required to credit
> the inventor (what a good practice).

The other games you mentioned also sound very interesting. I'll try them out with some friends next weekend.

-- Jon Ferro               Einsprachigkeit ist heilbar

Organization:   Carnegie Mellon, Pittsburgh, PA
Newsgroups:     rec.games.abstract
Date:           Tue, 17 Nov 1992 01:56:28 -0500 
From:           "Jonathan R. Ferro" <jf41+@andrew.cmu.edu>
Subject:        TWIXT rules, and some strategy

Here are the rules as Avalon Hill printed them in the Leisure Time Games version:

----------

HOW TO PLAY TWIXT (for two players)

1. Red plays first.  Players move alternately by placing _one_ peg at a
   time on the board.  Pegs may be placed by a player in any empty peg
   hole except those inhis opponent's border row.

2. When, after he has placed a peg, a player finds that he can _link_
   two or more of his pegs, he may place one or more links between these
   pegs to make a barrier.  Pegs may be linked only when the distance
   between them corresponds to the diagonal of a 6-holed rectangle.

   [ Diagrams "Twix--the basic linking move", "Eight possible linking
     directions from a given peg", "Double-Link (numbers indicate order
     of placement)" not included.  The Double-Link diagram shows how the
     third peg can be bridged to both the first and second pegs. ]

   A barrier cannot be crossed.  No barrier exists where a player could
   have linked but did not--whether the omission was intentional or
   unintentional.

   Before placing a peg, a player may, if he desires, carefully remove
   any pegs and links he has previously placed on the board.  However,
   he should be certain not to remove any pegs and/or links which would
   give the opponent the advantage.

3. To win, a player must connect his borders with an uninterrupted chain
   of linked pegs.  If neither player can complete such a barrier, the
   game is a draw.

HOW TO PLAY DOUBLE TWIXT (for four players)

Double TwixT is TwixT for four players in teams of two.  Rules are the
same as for TwixT, with the following qualifications:

1. Partners sit opposite one another.  Play alternates counterclockwise
   around the board.

2. No partner is limited to any one sector of the TwixT board: partners
   may play the two ends of a common barrier, or they may build
   independent sectors on any part of the board.  Partners may not
   communicate strategies to one another by any form of signalling.

3. Once, and only once in each game, on partner of either team may call
   out, "Privilege!" after making his own move.  On claim of Privilege,
   the opponent who would ordinarily move next must yield his turn to
   the other member of the "Privileged" team, giving the Privileged team
   two successive plays.

   The player to move next will be the partner of the opponent who
   yielded his turn.  If the opponents have not been defeated by the
   Privilege move, they may take their own Privilege at that point or
   later in the game.

   Privilege is invoked primarily for defensive reasons.  If this option
   is carefully planned by well-matched teams, it can make Double TwixT
   a fast, challenging game.

----------

Note 1. These rules ALLOW the removal of some of your structure at the beginning of your move. The ramifications of this have already been discussed in another thread on this newsgroup.

Note 2. The rules make no mention of play in the corners, despite their existence in the AH board. A cutthroat variation is to allow play in the opponent's border row, with a corner being a legal border connection for either player.

Here is the basic strategy session from the AH rules:

----------

BASIC SETUPS

A setup is a planned pattern of pegging which permits the player to
double-link in either of two directions during the third move.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . *2. . . . . . . . . . . . . . . . . . . . . .2x . . . . . . . .
. . . ./.\. . . . . . _-*2. . . . . _-*2. . . . . . _-*-_ . . . . . . .
. . . o3. o3. . . .3o-./. . . . .3o-. .\. . . . .3o-_ . _-o3. . . . . .
. . . .\./x . . . x/_-o3. . . . . x\. _-o3. . . . . .-*-. . . . . . . .
. . . x *1. . . .1*-. x . . . . . .1*-x . . . . . . . x1. . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

      Beam         Tilt            Coign            Mesh
    (3 holes,    (2 holes,       (diagonal        (1 hole,
    straight)    diagonal)       of 8-holed       straight)
                                 rectangle)

Pegs are numbered in order of placement.  In the third move (o) of any
setup, a player can both peg and double-link.

Generally, it is easier to concentrate on the placement of the second
peg, rather than the whole pattern.  If the second peg is placed the
correct distance from the first, the alternate locations for the third
peg will be obvious.

The most important part of the strategy of a setup is to avoid wasting a
move.  Do not place the third peg until your opponent moves to bar one
of your linking alternatives.  Instead, concentrate on building another
section of your barrier.

A setup can be foiled if the other player moves to block it immediately
after the first peg of the setup is placed.  Such foils are extensive;
some possibilities are indicated by x on the diagrams.  A well-placed
linking move is the simplest foil for a setup.

----------

Despite the game clearly not being as complex as GO, much of the terminology of GO applies well to its strategy. The section above covers the introduction to "connecting" and "making shape". Other terms which have broad application across many abstract games, such as "sente", also work here.

The Beam and the Tilt are the best setups for moving quickly across the board, but can be attacked easily by the x moves shown, among others. The Coign is much more solid, the only direct block being a connection across the points marked x in that diagram. The Mesh and the unmentioned "Anti-Tilt" (consider the o moves in the Tilt diagram to be 1 and 2, followed by either of the * moves as the double-link) are to be remembered as methods to connect pegs that were originally placed as defensive or blocking moves.

Whereas the first three (which I call "long") are usually attacked by building a barrier between pegs 1 and 2, the last two ("short") can be attacked effectively by blocking their possible connections to the double-link spots _without_ actually separating them with a barrier (this is the intention of the x moves on the "mesh" diagram; a "beam" connection between the x's would smother a possible connection on that side). In tight situations this attack could be used against the long setups also.

The primary weakness of long setups is the inability to link them end-to-end. In the situations below the moves x will quickly lead to tight fighting and should be given consideration regardless of the relation of x to the rest of your pegs, due to the devastation they will cause in the opponent's barrier.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . * . . . * . . . * . . . . . . . . . . . . . . . * . . . * . . . . .
. . . x . . x . . x x . . . . . . . . . . . . . . . . x . . x . . * . .
. . . . . . . . . . . . . . . . . . . . . . . . x . . . . . . . . . . .
. . . . . . . . . . . . . * . . . . . * . . x . . * . . . . . . . . . .
. . * . . . . . . . . . x . . . . . . x . . * . . . . . . . . . . . . .
. . . . . . . . . . . . . . . x x x . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . * . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  Beam Beam   Beam   Tilt  Tilt  Tilt  Coign Coign Coign Beam Coign

The one exception to this rule is the linear Coign-Coign link, which does not appear to have a single devastating countermove. I have not completed this analysis, but it seems that a similar result can be shown for short setups and for combinations, but is complicated by the possibility of smothering attacks as well as cuts.

The GO proverb "Do not touch what you are attacking" also applies to Twixt, although in a different sense that is difficult to define. If your opponent has a free end heading straight towards her border it is already too late to try to set up just one barrier to block her. You should skip at least 3 holes away ahead of her to start setting up a more extensive wall. (This is the area that I am very fuzzy in and will expect to see the most advances in, similar to the development of chess openings or GO joseki.) Conversely, an opponent who plays too closely to your free end is giving you a gift by letting you either (a) choose which way to go around it with a single-link move or (b) make move 2 of a setup on the other side of her peg, forcing her to make the decision of which double-link connection to block.

-- Jon Ferro               Einsprachigkeit ist heilbar

From:           dbush@csugrad.cs.vt.edu (David Bush)
Newsgroups:     rec.games.abstract
Subject:        A small TwixT game
Summary:        An annotated game on a 12x12 board, and some generalities.
Keywords:       twixt
Date:           19 Nov 92 02:24:07 GMT
Organization:   Virginia Tech Computer Science Dept, Blacksburg, VA

                       RED

        A   B   C   D   E   F   G   H   I   J   K   L
    1       .   .   .   .   .   .   .   .   .   .

    2   .   R8  .   .   .   .   .   .   .   .   .   .
             \
    3   .   . \ B7  .   .   .   .   .   .   .   .   .
               \ ~~---__
    4   .   .   R3  .   B6  .   B2  .   .   .   .   .
B                \               \                          B
L   5   .   .   . \ .   .   .   . \ .   .   .   .   .       L
A                  \               \                        A
C   6   .   .   .   R7  .   .   R1  B5  .   .   .   .       C
K                  /     __---~/   /                        K
    7   .   .   . / .   R4  . / . / .   .   .   .   .
                 /_---~~     /   /
    8   .   B3  R2  .   .   R6  B1  .   .   .   .   .
             ~~---__         \
    9   .   .   .   B4  .   . \ .   .   .   .   .   .
                               \
   10   .   .   .   .   .   .   R5  .   .   .   .   .

   11   .   .   .   .   .   .   .   .   .   .   .   .

   12       .   .   .   .   .   .   .   .   .   .

                       RED

  RED  BLACK
1. G6             A solid opening move. By playing midway between the red
               borders, red is making black's task as difficult as possible.
1.      G8      On a larger board, this might be too close to the red peg,
               but black's game is already desperate. Black might have tried
               G10 instead, after which 2.E9,G4;3.E5(linking G6),D9;
               4.C8(linking E9),E11(G10,D9);5.B10(C8),D3;6.D2 (red wins) is
               one possible continuation.
2. C8            Red gets in black's face. Playing 4 holes away from your
               opponent's peg like this is frequently a good blocking move
               to make, particularly when the move is supported by a nearby
               peg as it is here.
2.      G4       Black follows the opening maxim: "Don't start a fistfight
                too soon." Simply playing E7 loses to 3.D6(C8),D5(E7);
                4.C4(D6) and red will win the race to the wall. Note that
                in this variation, red's G6 peg is not part of the final
                bridge. It's perfectly okay to abandon pegs this way.
                 Black might have played F4, after which one continuation is
               3.E5(G6),D5(F4);4.C6(E5) and red is unstoppable.
3.C4             The C4-C8 pegs form what is called a "setup," which means
               they threaten to link together in one move in two different
               ways. C4-G6 also threatens to link in one move, but they can
                only link via E5, so this is not a setup.
3.      B8     Black tries to make two threats at once. Now we're in the
              middle game (things move along quickly on a quarter board.)
4.E7          (linking G6,C8): the best move. Red covers both threats at
              once. If for example red had played D6(C4,C8) then
              4. ... D9(B8);5.G10,E7(G8,D9);6.H8(G6,G10),F6(G4,G8) and black
              has a win. Or if 4.E9(C8),D7(B8);5.E7(C8,G6),F6(G4,D7).
4.      D9    (linking B8): the only move, not that it matters.
5.G10         Now it's red's turn to make two threats at once.
5.      H6    (link G4,G8)  Black is just going through the motions.
6.F8          (link G10,G6) E9 was also possible.
6.     E4
7.D6(C4,C8),C3(E4);
8.B2(C4)             Black resigns.

• Sometimes the best offense is a good defense. See red's move #2 above. By falling back to block, red tries to have a "net" built by the time black gets there.
• In the opening, keep the whole board in mind. Don't get drawn into a local battle if a distant move would help your position more. Remember just because you put some pegs down doesn't mean they have to be part of your final bridge.
• Develop an eye for the "diagonals"- for example in the game above, the line B2-C4-D6... was very important for red. In a "race" such as in the analysis to black's 2nd move, being at least on such a crucial diagonal means you will win the race to the wall.

As the above game demonstrates, red has a powerful initiative. Between strong players of equal strength, this may mean that red will win more often than not. Here's a ritual the players can go through that is intended to equalize the game- make it more balanced. On an otherwise empty board, one player puts down two red pegs (which might be linked) and one black peg, producing a position with black to move. The other player then decides which side to play. Play then proceeds from this position. The red pegs should be placed less than ideally (although not abysmally), whereas black's peg is well placed, producing a position that is as close to even as the "placer" can make it.

On the other hand, it is more likely that there will be a considerable disparity between the players. In order to compensate, here's a possible way to handicap the game: reduce the width of the playing field, so that black (the weaker player) has less distance to bridge than red. With an actual game set, this might be accomplished with a black rubber band of the right size. A "half board" game (12x24) is a pretty severe handicap. Reducing black's distance from 24 to 23, on the other hand, just might serve to balance out red's first-move initiative! I have no idea if this is true. If it is, that would render my proposed "placer-chooser" ritual unnecessary.

David Bush        Virginia Tech, Blacksburg, VA    dbush@csugrad.cs.vt.edu

Newsgroups:     rec.games.abstract
From:           sillke@math25.mathematik.uni-bielefeld.de (Torsten Sillke)
Subject:        TWiXT for experts
Date:           Sat, 21 Nov 1992 13:30:25 GMT
Organization:   Math MadHouse Bielefeld, Germany
Keywords:       twixt, Twixt, tournament, books, addesses

1. Andreas Kleinhans
   TWiXT (Ein Klassiker von Alex Randolph)
   Kleines Twixt-Expertenheft (a small booklet for the experts of twixt)
   pp 35, Mai 1990, KLEE-SPIELE GmbH
   (you can get it for nothing)
2. Vierzig Twixt-Aufgaben (40 Twixt problems)
   Fuer Spieler, die ihre Taktik auf schnelle Weise verbessern wollen
   pp 83, KLEE-SPIELE GmbH, (T. Nr. 165999)
   (yuo can try to get it for nothing, it comes with the game, which is distributed by KLEE.)

KLEE-SPIELE GmbH
Postfach 1961
W 8510 Fuerth/Bayern
Germany
Telefax: +49-911-746607
Telefon: +49-911-747881
Telex:    623365 klee

The strongest Twixt players come from Germany. Every year they play a Twixt tournament by mail. They plan to write a book about Twixt. The 'Kleines Twixt Expertenheft' is a preliminary version. Every year (Oct. or Nov.) there is a Twixt tournament sponsored by KLEE at the fair 'SPIEL' in Essen (Germany). There you can meet the strongest Twixt players. If you are interested in Twixt by mail contact: Klaus Hussmanns.

Addresses you can contact: (from 'Kleines Twixt Expertenheft')

 Christoph Brueggenthies
 Hoehenweg 26
 W 4200 Oberhausen 11

 Klaus-Dieter Hoffmann
 Maistr. 4
 W 8000 Muenchen 2

 Klaus Hussmanns
 Hirschgasse 7
 W 4120 Krefeld
 +49-2151-22217

 Andreas Kleinhans
 Reinbeckstr. 25
 W 7000 Stuttgart 80
 +49-711-747576

 Hartmut Thordsen
 Im Werth 41              (I think he moved)
 W 4270 Dorsten 1
 +49-2362-22785

Someone told me, that it is NP-Complete to decide, if one can lay the bridges to connect your two sides for Twixt played on the n*n board. (searching for not selfintersecting paths is difficult.) Who can give a proof?

Torsten Sillke

Date:           Fri, 10 Apr 1998 20:05:06 -0400
From:           "George B. Bush" <gbbush@rockbridge.net>
To:             eppstein@ics.uci.edu
Subject:        Twixt theory

My name is David Bush. I'm a fanatic about Twixt. The search engine 'Web Crawler' led me to your web site. I was pleased to see past postings about Twixt given a (more or less) lasting home for the curious to peruse. One of the postings (the annotated quarter-board game) was mine, in fact.

However, despite the plethora of inputs regarding the correct rules, there is one more rule that was left out: the "swap rule," Which Alex Randolph (the game's inventor) calls the "pie rule." Jonathan Ferro's verbatim posting of the rules from an Avalon Hill set were surely accurate; unfortunately, AH didn't quite get it right either, ignoring the "pie rule." I have been in direct correspondence with Mr. Randolph, and I assure you, the following rules are correct:

The board is a 24x24 square grid of holes, MINUS THE CORNER HOLES. (If the AH set has corner holes, then AH got that wrong as well.) The rows along the edges are referred to as "border rows." The 'top' and 'bottom' rows are Red's border rows. The 'left' and 'right' rows are Black's border rows. (European sets may use different colors.) The board is empty at the start. Red moves first. Each move in Twixt consists of three stages:

1. Place one peg of your color in any vacant hole EXCEPT in either of your opponent's border rows.
2. Remove as many of your OWN links (which were placed on previous moves) as you wish to remove.
3. Place as many legal links between pegs of your color as you wish. A link may be placed ONLY between pegs which are at opposite corners of a six-hole rectangle (like a knight's move in chess). Your links may not cross any other link, not even one of your own.

After Red places the first peg on the board, the second player has the option of either responding normally as Black, or swapping sides. If sides are swapped, the player who moved first as Red is now Black, and makes the next move. Sides may be swapped only once per game. If the second player does not swap immediately after the Red places the first peg, sides may not be swapped at all that game. (This is Alex Randolph's "pie rule," so named because it is like "I cut the pie, you choose the slice." It is also called one-move equalization, and can be adapted to balance many two-player games.)

The object is to connect your border rows with an UNINTERRUPTED chain of linked pegs. If neither side can complete such a chain, the game is a draw.

The 3M and AH sets include rules for "double Twixt," as Mr. Ferro described, but as far as I know, this is not Alex Randolph's idea. It could be; I didn't ask him.

I also refer you to the website at www.gamerz.net/pbmserv/#twixt for more info, including some cool puzzles written by Randolph!

Now we're almost ready to talk about Twixt theory, but first, I want to describe a notation system for making moves. The "European" coordinate system is what I will use here.

The rows are lettered A to X, and the columns are numbered 1 to 24. Red has border rows at A and X. That is, the holes A2 ... A23 and X2 ... X23 are the Red border rows. Black's border rows are 1 and 24. That is, the holes B1 ... W1 and B24 ... W24 are the Black border rows. Red's moves are numbered 1, 3, 5, ... Black's moves are numbered 2, 4, 6, ...

Normally, a move is described by the coordinates where the peg is placed. An asterisk is placed after these coordinates for each link which is made to that peg. There should be precisely as many asterisks as there are possible links to the peg just placed, without removing any previous links. Since you always have the option of removing your links later, most moves automatically involve making all possible links to the peg just played.

Once in a rare while, however, you may have to remove some of your links in order to avoid a draw (or even to avoid a loss.) Some of the puzzle problems illustrate this theme. Here is a syntax for describing all types of moves:

NOTE:  the bar | means "or."
       brackets [] mean "what is enclosed is optional."

<move>       = <simplemove> | <messymove>

<simplemove> = <coordinates> <asterisks>

<messymove>  = <coordinates> [ - <unlink list> ] + [ <link list> ]

<coordinates>= <letter A to X> <number 1 to 24>

<asterisks>  = * [ <asterisks> ]

  <coordinates> <coordinates> [ <coordinates> ... ][ , <list> ]

If you choose to make no links on your move, even though you could link to the peg just played, this is indicated by the + symbol with nothing after it.

Here is an example of a messy move. The diagrams need to be viewed with a non-proportional font such as Courier.

Before move:

   3  4  5  6  7  8  9
 G .  O  .  # _O  O  .
       \  _---     \
 H .  .| O  .  O_ .| #    Only part of the board is shown here.
        \        ---\ 
 I .  .  O  . _#_ O  O    O to move.
        / _---   ---_ 
 J .  . |#  .  .  . _#
       /        _---  
 K .  O  .  .  #  .  .

   3  4  5  6  7  8  9
 G .  O  .  # _O  O  .
          _---     \
 H .  . _O  . _O_ .| #
    _---  _---   ---\ 
 I O  .  O  . _#_ O  O
    \   / _---   ---_ 
 J .| . |#  .  .  . _#
     \ /        _---  
 K .  O  .  .  #  .  .

>BASIC SETUPS
>
>A setup is a planned pattern of pegging which permits the player to
>double-link in either of two directions during the third move.
>
>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
>. . . . *2. . . . . . . . . . . . . . . . . . . . . .2x . . . . . . .
>. . . ./.\. . . . . . _-*2. . . . . _-*2. . . . . . _-*-_ . . . . . .
>. . . o3. o3. . . .3o-./. . . . .3o-. .\. . . . .3o-_ . _-o3. . . . .
>. . . .\./x . . . x/_-o3. . . . . x\. _-o3. . . . . .-*-. . . . . . .
>. . . x *1. . . .1*-. x . . . . . .1*-x . . . . . . . x1. . . . . . .
>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
>
>      Beam         Tilt            Coign            Mesh
>    (3 holes,    (2 holes,       (diagonal        (1 hole,
>    straight)    diagonal)       of 8-holed       straight)
>                                 rectangle)
>
>Pegs are numbered in order of placement.  In the third move (o) of any
>setup, a player can both peg and double-link.

Talking about setups is a good way to begin to get a handle on tactics, especially for understanding the concept of NOT WASTING MOVES. Setups are usually unassailable, unless the opponent can find a way to threaten the setup AND ANOTHER PART OF YOUR POTENTIAL BRIDGE at the SAME TIME. Making two threats at once, or defending two threats at once, is what you should strive to do on every move. So, if your opponent is not threatening your setup, you usually should not waste precious time linking it up!

The Beam setup is generally the one you should try for, if your opponent allows you to make it. I have played many games against newbies who allowed me to march right across the board this way. In fact, the Beam is so strong, frequently the only way to block a peg is to play in the same hole that your opponent would play in to make a Beam.

There is a drawback to thinking strictly in terms of setups, however. Setups are just a part of the arsenal of weapons availble to you. From the very first move, you must PLAY THE WHOLE BOARD. Here is an example of a possible opening between two experienced players:

1.F7 (not swapped) 2.O10
3.M16              4.P16
5.R9               6.I16
7.I21              8.F19

As far as writing a Twixt-playing program is concerned, I absolutely agree with the general consensus that this is not an easy task. I have been trying to incorporate some of John Conway's ideas in his book "Winning Ways," specifically his discussion of temperature and cooling. I haven't been making much headway. I suspect a good Twixt engine would have to have access to a very large database of local positions before it would be able to "merge the analysis" of several local positions into an overall board strategy.

Torsten Sillke mentions an interesting problem, which I interpret to be: is a given input position a draw, or is it still possible for one side to complete a bridge? This might actually be a feature you would like a Twixt server to have, so that the machine can tell you if the position is a draw or not. In practice, however, if two players are strong enough to achieve a draw, they would recognize the game was drawn long before all possible paths are actually blocked.

Well, enough blathering. Thanks for your time and patience!

David Bush
gbbush@rockbridge.net