From: hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Newsgroups: rec.games.abstract
Subject: Re: Twixt - rule correction
Date: 16 Nov 92 14:27:12 GMT
Article-I.D.: aic.9211161027.hoey
 <1dqb3iINNseo@charnel.ecst.csuchico.edu> <BxK1o5.My6@cs.psu.edu>
 <1992Nov13.073054.2028@linkoping.trab.se>
 <1992Nov13.175344.10142@henson.cc.wwu.edu> <BxoC4u.KDM@cs.psu.edu>
Organization: Naval Research Laboratory, Washington, DC

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.

I had thought it was possible to remove bridges, too.  I guess the
problem with the rule books explains why there are ``authorities'' on
both sides of the question.

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

Note that while Jonathan reproduces Felix Lee's flawed mini-situation,
he uses an approach that would be possible with the corrected version.


    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.

But not impossible!  Consider the following situation, in which NO
bridges have been played, nor are any even immeediately playable!

    - - - - 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 - - - -

A knight chain must alternate chessboard colors, and there is no way
to break through either player's monochromatic monopoly.  So neither
player can win, even with the cooperation of her opponent.

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 don't think this rule will have the desired effect, because the
blockage usually happens while some other part of the board is still
technically open, but has a double-cross waiting.  The blockage would
then be playable but the double-cross would thereafter be forbidden!
If both players had double-crosses waiting, everyone could spring them
except the last player, who need not be the player who created the
blockage in the first place.  I think the strategy starts to be
something like Go's Ko wars.

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