Editing TwixT

{{short description|Connection board game in the 3M bookshelf game series}}
{{About|the board game|the horror film|Twixt (film)|other uses|Twixt (disambiguation)}}
{{Use dmy dates|date=October 2020}}
[[File:twixtboard185132.jpg|thumb|right|A computer-generated image of a game of TwixT]]
[[File:Twixt 3M.jpg|thumb|Board and bookshelf of the 3M edition]]

'''TwixT''' is a two-player [[Abstract strategy game|strategy]] [[board game]], an early entrant in the 1960s [[3M bookshelf game series]].  It became one of the most popular and enduring games in the series.  It is a [[connection game]] where players alternate turns placing pegs and links on a pegboard in an attempt to link their opposite sides.  While TwixT itself is simple, the game also requires strategy, so young children can play it, but it also appeals to adults. The game has been discontinued except in Germany and Japan.

== History ==
[[File:Alex Randolph-playing Twixt (cropped).jpg|thumb|upright|Randolph playing ''TwixT'' in 1998]]
TwixT was invented as a paper and pencil game in 1957 by [[Alex Randolph]], a game designer.  When Alex was commissioned along with [[Sid Sackson]] by 3M in 1961 to start a games division, the game was issued as a boardgame, one of the first 3M bookshelf games.  [[Avalon Hill]] took over publication in 1976 when 3M sold its game division. Avalon's parent company was acquired by [[Hasbro]] in 1998, and the game was discontinued. The game is no longer produced in the United States, but a succession of German companies has produced the game since the 1970s under license from Avalon.{{cn|date=July 2021}} TwixT was short-listed for the first [[Spiel des Jahres]] in 1979,<ref name="sdj">[http://www.spiel-des-jahres.com/cms/front_content.php?idcatart=474&id=370 Spiel des Jahres page in German for TwixT]</ref> and was inducted into the [[Origins Award|Academy of Adventure Gaming Arts & Design's Hall of Fame]], along with Randolph, in 2011.<ref name="Origins">[http://www.gama.org/OriginsAwards/tabid/2720/Default.aspx Origins Awards Hall of Fame for TwixT]</ref>

== Rules ==
Twixt is played on a board comprising a 24×24 square grid of holes (minus 4 corner holes). The game has two types of playing pieces, pegs, which fit into the holes, and links, which fit into the top of the peg pieces and are used to connect to peg pieces. In the 3M edition, players are Red and Black; different sets may use different colors. The topmost and bottommost rows of holes belong to the lighter color; the leftmost and rightmost rows to the darker color.

*The players take turns placing pegs of their respective colors on the board, one peg per turn.
*The player with the lighter color makes the first move.
*A player may ''not'' place a peg on their opponent's border rows.
*To counteract first-move advantage, the [[pie rule]] is suggested. After the first peg is placed, the second player has the option to swap sides. This is typically indicated by turning the pieces box end for end, or swapping boxes if they are separate. If the second player chooses not to swap immediately after the first peg is placed, then sides may not be swapped later in that game. (This "one-move equalization" was added by Randolph after 3M published his game. It is present in the [[Schmidt Spiele]] edition and all later editions.)
*After placing a peg, a player may ''link'' one or more pairs of pegs on the board of their colour. The links can only connect two pegs a [[Knight (chess)|knight's move]] away from each other, and cannot cross another link; they block other links, most importantly those of the opponent. As part of the player's move, they may remove their own links (but not those of the opponent) in order to rearrange the sequence of links on the board. A variant for [[Pencil and paper game|pencil and paper]] play allows a connection to cross the player's links but not those of the opponent.
*The object is to make a continuous chain of linked pegs connecting the player's border rows. If neither player can achieve this, the game is a draw.

== Computational complexity for general rectangular boards ==
TwixT has been proven to be [[PSPACE-complete#Puzzles and games|PSPACE-complete]] for determining the game value, via a reduction from [[Hex (board game)|Hex]].<ref>{{Cite conference |first1=Édouard |last1=Bonnet |first2=Florian |last2=Jamain |first3=Abdallah |last3=Saffidine |title=Havannah and TwixT are PSPACE-complete |conference=The 8th Intl. Conf. on Computers and Games |location=Keio University, Yokohama, Japan |date=14 August 2013 |arxiv=1403.6518|doi=10.1007/978-3-319-09165-5_15}}</ref> TwixT has also been shown to be [[NP-complete]] regarding whether a single set of vertices can support a connecting path, via a reduction from [[Boolean satisfiability problem#3-satisfiability|3-satisfiability]].<ref>{{Cite web |author1=Dominic Mazzoni |author2=Kevin Watkins |title=Uncrossed knight paths is NP-complete |date=October 1997 |url=http://www.mathematik.uni-bielefeld.de/~sillke/PROBLEMS/Twixt_Proof_Draft}}</ref>
These proofs are indicative of a complex strategy: the game has not been [[Solved game|solved]], no winning strategy has been discovered, nor is the outcome of the game with [[perfect play]] known.
<!--
Number of "legal positions" and resultant "[[game-tree complexity]]"?
 -- see paper cited in "Computer opponents" section

Has it been "solved"? Can it be?  [[Solved game]]

possible "stock" phrase to use:
"Experts have not absolutely resolved what the outcome of a game will be where both sides use [[perfect play]]."

-->

==Related games==
On the 24×24 grid, tactical considerations tend to predominate. The opening phase is over quickly, and the rest of the game is spent attempting to tactically execute the plan.  Hex, which has a very similar game object, may have more predictable tactics, but strategical considerations are much more important. In this sense, Hex is more like Go than TwixT, since a single move is generally less committal, and consequences may take longer to play out.

== Variants ==
[[File:PPrules.png|left|thumb|250px|A contrived position where black to move wins under PP rules, but loses under standard rules.]]

One variant is '''Twixt PP''' ('''P'''aper and '''P'''encil). The rules are almost identical to standard TwixT, except links are never removed and a player's ''own'' links are allowed to cross each other. A winning path might loop across itself but crossed links are not connected to each other at the intersection. The paper and pencil rules may reduce the number of draws (which are already rare). Whether it reduces the complexity of the game or not is highly debatable.

This rules difference has no effect in terms of game outcome most of the time. For those rare situations where it does, most of those cases are where a draw under standard rules is a decisive game under PP rules. The image shows a contrived position where black is to move. Black wins under PP rules but loses under standard rules.

'''Row handicapping''' can be used to equalize the game for players of different strengths. The simplest handicap is to allow the weaker player to move first (i.e. eliminate the pie rule). Beyond that, one dimension of the grid is reduced so the weaker player has a shorter distance to span.

[[File:Diagtwixt.png|right|thumb|250px|A diagonal TwixT board.]]

The game may be played on '''different size grids'''. The 12×12 board shown here leads to a very short game. On the standard board, tactics dominate; larger boards introduce deeper strategic considerations. Since most commercial sets use boards which are made from four "quadrants" which either clip together or are hinged, a 36×36 grid could be assembled from three standard sets of the same size. In Europe, there briefly appeared a TwixT knock-off called "Imuri" which used a 30×30 grid. The board had no holes, and lines were drawn to indicate where the links could be placed. This edition was removed from shelves for copyright infringement.

Mark Thompson's variant '''Diagonal TwixT''' has the same rules as standard TwixT, but the border lines run at a 45-degree angle to the grid.<ref>{{Cite web |url=http://home.flash.net/~markthom/html/twixt.html |archive-url=https://web.archive.org/web/20110509190404/http://home.flash.net/~markthom/html/twixt.html |archive-date=2011-05-09 <!-- most recent copy available --> |title=Mark Thompson's TwixT webpage}}</ref> David Bush's version has the border lines running parallel to link paths. These variants result in different tactical patterns.

== Competition ==
The official world championships were held as part of the [[Mind Sports Olympiad]] in 1997, 1998 and 1999.<ref>Mind Sports Olympiad TwixT Results http://www.boardability.com/result.php?id=twixt 10 July 2010</ref> Since 2000 TwixT has had a major international tournament as part of the MSO but there has been no official World Championships. Between 2011 and 2022, the TwixT event at the MSO has again become the World Championships. The list of winners is given below.<ref>MSO main website showing results http://www.msoworld.com/results/ [retrieved 21 May 2016]</ref>

'''List of MSO champions'''

{{columns-list|colwidth=22em|
* 1997: {{flagicon|USA}} [[Alex Randolph]]
* 1998: {{flagicon|GER}} Klaus Hussmanns
* 1999: {{flagicon|GER}} Klaus Hussmanns
* 2000: {{flagicon|GER}} Klaus Hussmanns
* 2001: {{flagicon|GER}} Klaus Hussmanns
* 2002: {{flagicon|GER}} Peter Henke
* 2003: {{flagicon|GER}} Klaus Hussmanns
* 2004: {{flagicon|SWE}} Carl J. Ragnarsson
* 2005: {{flagicon|USA}} David Bush
* 2006: {{flagicon|USA}} David Bush
* 2007: {{flagicon|ENG}} Bharat Thakrar
* 2008: {{flagicon|ENG}} Bharat Thakrar
* 2009: {{flagicon|USA}} David Bush
* 2010: {{flagicon|ENG}} Bharat Thakrar
* 2011: {{flagicon|ENG}} David M. Pearce
* 2012: {{flagicon|FRA}} Florian Jamain
* 2013: {{flagicon|NOR}} [[:no:Jan Kristian Haugland|Jan Kristian Haugland]]
* 2014: {{flagicon|FRA}} Florian Jamain
* 2015: {{flagicon|FRA}} Florian Jamain
* 2016: {{flagicon|FRA}} Florian Jamain
* 2017: {{flagicon|FRA}} Florian Jamain
* 2018: {{flagicon|FRA}} Florian Jamain
* 2019: {{flagicon|ITA}} Cosimo Cardellicchio
* 2020: {{flagicon|USA}} David Bush
* 2021: {{flagicon|FRA}} Florian Jamain
* 2022: {{flagicon|FRA}} Florian Jamain
* 2024: {{flagicon|FRA}} Florian Jamain
}}
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Current status of computer opponents and their difficulty level relative to human champions.

Citations to work off of:

from the abstract -- reduce to important points and reword to avoid plagarism:
"TwixT belongs to the family of connection games and is a two-player zero-sum board game with
perfect information. Challenging characteristics of TwixT include that it has a large branching factor and that the process of estimating a board’s utility value is known to be complex. Human players use strategic and tactical heuristics that work under specific conditions, but it is unclear how these heuristics can be effectively combined and implemented in a TwixT playing program. The state-space (10^140) and game-tree complexity (10^159) make TwixT belong to the highest category in terms of complexity. This means that TwixT is unlikely to be solved in the near future. If the complexity would have been low, then we could have sufficed with a pure search-based approach for computer TwixT. It is evident that an approach to computer
TwixT must add game-specific knowledge."
 -- two kinds of AIs were examined, αβ and Monte-Carlo
 -- pgs. 29–30 examine in detail the mathematical complexity
<ref>{{Cite thesis |type=M.Sc. |institution=[[Maastricht University]] |first=Kevin |last=Moesker |url=http://www.personeel.unimaas.nl/uiterwijk/Theses/MSc/Moesker_thesis.pdf |title=TwixT: Theory, Analysis and Implementation |date=March 2009}}</ref>
 -- master of science of AI thesis

from the abstract -- reduce to important points and reword to avoid plagarism:
TwixT is a perfect-information two-player zero-sum connection game and has a high branching factor, resulting in a high search space. To tackle this problem, we implemented a Monte-Carlo Tree Search (MCTS) player and enhanced it with domain-independent enhancements as well as with knowledge. The result is a player with the strength of a human beginner.<ref>{{Cite thesis |type=M.Sc. |institution=[[Maastricht University]] |first=Janik |last=Steinhauer |url=https://project.dke.maastrichtuniversity.nl/games/files/msc/Steinhauer_thesis.pdf |title=Monte-Carlo TwixT |date=June 2010}}</ref>
 -- master of science of AI thesis

-->

==Reception==
''[[Games (magazine)|Games]]'' magazine included ''TwixT'' in their "Top 100 Games of 1980", describing it as "much more subtle and interesting than the old Bridg-It, with which it should not be confused".<ref>{{cite magazine | date=November–December 1980 |title=Top 100 Games of 1980  | magazine=[[Games (magazine)|Games]] | issue=20 | pages=57 }}</ref>

''[[Games (magazine)|Games]]'' magazine included ''TwixT'' in their "Top 100 Games of 1981", noting that "The best offense, oddly enough, is a good defense."<ref>{{cite magazine | date=November–December 1981 |title=Top 100 Games of 1981  | magazine=[[Games (magazine)|Games]] | issue=26 | pages=56 }}</ref>

''[[Games (magazine)|Games]]'' magazine included ''TwixT'' in their "Top 100 Games of 1982", noting that "Subtlety and finesse will win every time against straightforward aggression in this game of great depth and varied tactics."<ref>{{cite magazine|editor-last=  Schmittberger|editor-first= R. Wayne | date=November 1982 |title=The Top 100 Games 1982|magazine=[[Games (magazine)|Games]]| issue=33|pages=43}}</ref>

==Reviews==
*''[[:fr:Jeux et Stratégie|Jeux & Stratégie]]'' #6<ref>{{cite web | url=https://archive.org/details/jeux-et-strategie-06/page/46/mode/2up | title=Jeux & stratégie 06 | date=December 1980 }}</ref>
*''[[Games & Puzzles]]'' #18<ref>{{cite web | url=https://archive.org/details/sim_games-and-puzzles_1973-10_18/page/n3/mode | title=Games and Puzzles 1973-10: Iss 18 | date=October 1973 | publisher=A H C Publications }}</ref>
*''[[The Playboy Winner's Guide to Board Games]]''<ref>{{cite web | url=https://archive.org/details/playboywinnersgu00free/page/124/mode/2up | title=The Playboy winner's guide to board games | date=1979 }}</ref>
*''Family Games: The 100 Best''<ref>{{cite book | url=https://archive.org/details/familygames100be0000unse/page/338/mode/2up | isbn=978-1-934547-21-2 | title=Family games : The 100 best | date=2010 | last1=Lowder | first1=James | publisher=Green Ronin }}</ref>
*''The Guide to simulations/games for education and training''<ref>{{cite book | url=https://archive.org/details/guidetosimulatio04edunse/page/476/mode/2up | isbn=978-0-8039-1375-2 | title=The Guide to simulations/Games for education and training | date=1980 }}</ref>

==See also==
*[[Connection game#List of connection games|List of connection games]]
*[[Shannon switching game#Gale|Gale]], also called Bridg-It

==References==
{{reflist}}

==External links==
*[https://icga.org/icga/games/twixt/ Introduction to TwixT] on the International Computer Games Association website. Introduction, rules, computer-TwixT related links
*{{bgg|949}}
*[http://senseis.xmp.net/?Twixt Sensei's Library: Twixt] More info about TwixT
*[http://www.johannes-schwagereit.de/twixt/programs.html Current Twixt-playing programs]
*[https://drericsilverman.com/tag/twixt/ Connection Games Part VI: Twixt] from Dr. Eric Silverman's blog on abstract games

{{3M bookshelf games}}
{{Avalon Hill}}

[[Category:3M bookshelf game series]]
[[Category:Abstract strategy games]]
[[Category:Alex Randolph games]]
[[Category:Avalon Hill games]]
[[Category:Board games introduced in 1962]]
[[Category:Connection games]]
[[Category:Kosmos (publisher) games]]
[[Category:Paper-and-pencil games]]