View source for 3D tic-tac-toe

{{short description|Abstract strategy game}}
{{Use mdy dates|date=April 2024}}{{Use American English|date=April 2024}}
{{redirect|Qubic|the cosmology project|Qubic experiment}}
[[File:3D Tic Tac Toe.jpg|thumb|3-D Tic-Tac-Toe played with glass beads]]
'''3D tic-tac-toe''', also known by the trade name '''Qubic''', is an abstract strategy board game, generally for two players. It is similar in concept to traditional [[tic-tac-toe]] but is played in a cubical array of cells, usually 4×4×4. Players take turns placing their markers in blank cells in the array. The first player to achieve four of their own markers in a row wins. The winning row can be horizontal, vertical, or diagonal on a single board as in regular tic-tac-toe, or vertically in a column, or a diagonal line through four boards.

As with traditional tic-tac-toe, several commercial sets of apparatus have been sold for the game, and it may also be played with pencil and paper with a hand-drawn board.

The game has been analyzed mathematically and a [[first-player-win]] strategy was developed and published. However, the strategy is too complicated for most human players to memorize and apply.

== Pencil and paper ==

Like traditional 3×3 [[tic-tac-toe]], the game may be played with pencil and paper. A game board can easily be drawn by hand, with players using the usual "naughts and crosses" to mark their moves.

In the 1970s, 3M Games (a division of [[3M|3M Corporation]]) sold a series of "Paper Games", including "3 Dimensional Tic Tac Toe". Buyers received a pad of 50 sheets with preprinted game boards.<ref>{{cite web|url=http://boardgamegeek.com/boardgame/25257/3-dimensional-tic-tac-toe|title=Gaming Unplugged Since 2000|publisher=BoardGameGeek}}</ref>

== Marker sizes variation ==

Gobblets Gobbler<ref>{{cite journal |last1=McFeetors |first1=P. Janelle |last2=Palfy |first2=Kylie |title=We're in Math Class Playing Games, Not Playing Games in Math Class |journal=Mathematics Teaching in the Middle School |date=1 May 2017 |volume=22 |issue=9 |pages=534–544 |doi=10.5951/mathteacmiddscho.22.9.0534}}</ref> and Otrio,<ref>{{cite book |last1=Kubota |first1=Runa |last2=Troillet |first2=Lucien |last3=Matsuzaki |first3=Kiminori |title=2022 International Conference on Technologies and Applications of Artificial Intelligence (TAAI) |chapter=Three Player Otrio will be Strongly Solved |date=December 2022 |pages=30–35 |doi=10.1109/TAAI57707.2022.00015|isbn=979-8-3503-9950-9 |s2cid=257408458 }}</ref> use marker sizes (small, medium, large) as the replacement of the third element. Players can 'steal' the opponent spot by placing larger marker at the top of the opponent smaller marker or just simply competing with overlapping spot.

== "Qubic" ==

"Qubic" is the brand name of equipment for the 4×4×4 game that was manufactured and marketed by [[Parker Brothers]], starting in 1964.<ref>{{cite web
|url=http://tsdr.uspto.gov/#caseNumber=72461215&caseSearchType=US_APPLICATION&caseType=DEFAULT&searchType=statusSearch
|publisher=United States Patent and Trademark Office
|title=Trademark Status & Document Retrieval (TSDR)}}</ref> It was reissued in 1972 with a more modern design. Both versions described the game as "Parker Brothers 3D Tic Tac Toe Game".

In the original issue, the bottom level board was opaque plastic, and the upper three clear, all of simple square design. The 1972 reissue used four clear plastic boards with rounded corners. Whereas pencil and paper play almost always involves just two players, Parker Brothers' rules said that up to three players could play. The circular playing pieces resembled small poker chips in red, blue, and yellow.

The game is no longer manufactured.

===Reviews===
*''[[The Playboy Winner's Guide to Board Games]]''<ref>{{Cite web|url=http://archive.org/details/playboywinnersgu00free|title=The Playboy winner's guide to board games|first1=Jon|last1=Freeman|first2=John|last2=Jackson|date=6 August 1979|publisher=Chicago : Playboy Press|accessdate=6 August 2023|via=Internet Archive}}</ref>

== Gameplay and analysis ==

=== 3×3×3, two-player ===

The 3×3×3 version of the game cannot end in a draw<ref>[https://math.stackexchange.com/questions/2784654/tic-tac-toe-game-on-the-cube-3%c3%973%c3%973 Tic-tac-toe game on the cube 3×3×3]</ref> and is easily won by the first player unless a rule is adopted that prevents the first player from taking the center cell on his first step. In that case, the game is easily won by the second player. By banning the use of the center cell altogether, the game is easily won by the first player. By including a 3rd player, the perfect game will be played out to a draw. By including [[Stochastic|stochasticity]] in the choosing of the side the player must use, the game becomes fair and winnable by all players but is subject to chance. By making the choice of the player piece (× or ⚬) subject to chance, the game becomes fair and winnable by all players.<ref name="golomb">{{cite book
| first1=Solomon W. | last1=Golomb |first2=Alfred W. |last2=Hales
|editor-last=Nowakowski |editor-first=Richard 
| chapter=Hypercube Tic-Tac-Toe
| title=More Games of No Chance
| series=Mathematical Sciences Research Institute Publications
| volume=42
| date=August 2002
| publisher=Cambridge University Press | isbn=9780521155632}}</ref>

=== 4×4×4, two-player ===

On the 4×4×4 board, there are 76 winning lines. On each of the four 4×4 boards, or horizontal planes, there are four columns, four rows, and two diagonals, accounting for 40 lines. There are 16 vertical lines, each ascending from a cell on the bottom board through the corresponding cells on the other boards. There are eight vertically-oriented planes parallel to the sides of the boards, each of these adding two more diagonals (the horizontal and vertical lines of these planes have already been counted). Finally, there are two vertically-oriented planes that include the diagonal lines of the 4x4 boards, and each of these contributes two more diagonal lines—each of these including two corners and two internal cells.

The 16 cells lying on these latter four lines (that is, the eight corner cells and eight internal cells) are each included in seven different winning lines; the other 48 cells (24 face cells and 24 edge cells) are each included in four winning lines.

The corner cells and the internal cells are actually equivalent via an [[automorphism]]; likewise for face and edge cells. The group of automorphisms of the game contains 192 automorphisms. It is made up of combinations of the usual rotations and reflections that reorient or reflect the cube, plus two that scramble the order of cells on each line. If a line comprises cells A, B, C and D in that order, one of these exchanges inner cells for outer ones (such as B, A, D, C) for all lines of the cube, and the other exchanges cells of either the inner or the outer cells (A, C, B, D or equivalently D, B, C, A) for all lines of the cube. Combinations of these basic automorphisms generate the entire group of 192 as shown by R. Silver in 1967.<ref>{{cite journal
| author=R. Silver
| title=The group of automorphisms of the game of 3-dimensional ticktacktoe
| periodical=Amer. Math. Monthly
| volume=74
| number = 3
| pages=247–254
| date=March 1967
| publisher=Mathematical Association of America
| doi=10.2307/2316015| jstor=2316015
}}</ref>

3D tic-tac-toe was [[solved board games|weakly solved]], meaning that the existence of a winning strategy was proven but without actually presenting such a strategy, by Eugene Mahalko in 1976.<ref>{{cite thesis
|author=Eugene D. Mahalko
|title=A Possible Win Strategy for the Game of Qubic
|publisher=Brigham Young University 
|date=1976
|degree=M.Sc.
}}</ref> He proved that in two-person play, the first player will win if there are two optimal players.

A more complete analysis, including the announcement of a complete first-player-win strategy, was published by [[Oren Patashnik]] in 1980.<ref>{{cite journal
| title=Qubic: 4 x 4 x 4 Tic-Tac-Toe
| author=Oren Patashnik
| periodical=Mathematics Magazine 
| issue=4
| volume=53
| pages=202–216
| jstor=2689613
| date=September 1980}}</ref> Patashnik used a [[computer-assisted proof]] that consumed 1500 hours of computer time. The strategy comprised move choices for 2929 difficult "strategic" positions, plus assurances that all other positions that could arise could be easily won with a sequence entirely made up of forcing moves. It was further asserted that the strategy had been independently verified. As computer storage became cheaper and the internet made it possible, these positions and moves were made available online.<ref>{{Cite web|url=https://drive.google.com/file/d/0B6pbHEZND52eMzlzWWRCWFdrTm8/edit?pref=2&pli=1&usp=embed_facebook&usp=embed_facebook|title=qubic.dictionary|website=Google Docs|accessdate=6 August 2023}}</ref>

The game was solved again by [[Victor Allis]] using [[proof-number search]].<ref>{{cite book
| chapter=Qubic solved again
| pages=192–204
| author=L .V. Allis
| author2=P. N. A. Schoo
| name-list-style=amp
| date=1992
| title=Heuristic Programming in Artificial Intelligence 3: The Third Computer Olympiad
| publisher=Ellis Horwood, Chichester, UK
| editor=H. J. van den Herik
| editor2=L. V. Allis
}}</ref>

== Computer implementations ==
{{Infobox video game
| title = 3-D Tic-Tac-Toe
| italic title = no
| image = 3dtictactoe.png
| developer = [[Atari, Inc.]]
| publisher = Atari Inc.
| programmer = [[Carol Shaw]]
| released = 1978
| genre = 
| modes = 
| platforms = [[Atari 2600]], [[Atari 8-bit]]
}}

Several computer programs that play the game against a human opponent have been written. The earliest of these used console lights and [[Sense switch|switches]], text terminals, or similar interaction: the human player would enter moves numerically (for example, using "4 2 3" for fourth level, second row, third column) and the program would respond similarly, as graphics displays were uncommon. 

A program written for the [[IBM 650]] used front panel switches and lights for the user interface.{{citation needed|date=March 2017}}

William Daly Jr. wrote and described a Qubic-playing program as part of his Master's program at the Massachusetts Institute of Technology. The program was written in assembler language for the [[TX-0]] computer. It included lookahead to 12 moves and kept a history of previous games with each opponent, modifying its strategy according to their past behavior.<ref>{{cite thesis
|url=http://www.mirrorservice.org/sites/www.bitsavers.org/pdf/mit/tx-0/Daly_Thesis_Feb61_Cubic/mastersthesis.pdf
|type=M.Sc.
|title=Computer Strategies for the Game of Qubic
|publisher=Massachusetts Institute of Technology
|author=William George Daly Jr.
|date=February 1961}}</ref>

An implementation in [[Fortran]] was written by Robert K. Louden and presented, with an extensive description of its design, in his book ''Programming the IBM 1130 and 1800''. Its strategy involved looking for combinations of one or two free cells shared among two or three rows with particular contents.<ref>{{cite book
|title=Programming the IBM 1130 and 1800
|author=Robert K. Louden
|publisher=Prentice-Hall
|chapter=Integer manipulation in FORTRAN
|pages=179–204
|year=1967
|asin=B0006BRBTQ}}</ref>

A Qubic program in a DEC dialect of BASIC appeared in ''101 BASIC Computer Games'' by [[David H. Ahl]].<ref>{{cite book
| title=101 BASIC Computer Games
| date=1975
| author=David H. Ahl
| url=http://bitsavers.trailing-edge.com/pdf/dec/_Books/101_BASIC_Computer_Games_Mar75.pdf
| publisher=Digital Equipment Corporation
| pages=175–177}}</ref> Ahl said the program "showed up", author unknown, on a G.E. timesharing system in 1968.

[[Image:3-D Tic-Tac-Toe-2600.png|thumb|Gameplay of ''3-D Tic-Tac-Toe''|left]]

[[Atari, Inc.|Atari]] released a 4x4x4 graphical version of the game for the [[Atari 2600]] console and [[Atari 8-bit computers]] in 1978.<ref>{{Cite web |title=Atari 2600 VCS 3-D Tic-Tac-Toe |url=http://www.atarimania.com/game-atari-2600-vcs-3-d-tic-tac-toe_18106.html |accessdate=6 August 2023 |website=Atari Mania}}</ref><ref>{{Cite web|url=http://www.gamefaqs.com/atari2600/584536-3-d-tic-tac-toe/data|title = 3-D Tic-Tac-Toe Release Information for Atari 2600 - GameFAQs}}</ref> The program was written by [[Carol Shaw]], who went on to greater fame as the creator of [[Activision]]'s ''[[River Raid]]''.<ref>{{cite web|url=http://www.atariage.com/programmer_page.html?ProgrammerID=80|title=AtariAge - Programmers - Carol Shaw|access-date=2016-02-08|archive-url=https://web.archive.org/web/20161130002402/http://www.atariage.com/programmer_page.html?ProgrammerID=80|archive-date=2016-11-30|url-status=dead}}</ref> It uses the standard joystick controller. It can be played by two players against each other, or one player can play against the program on one of eight different difficulty settings.<ref>{{cite web | url=https://www.mobygames.com/game/3-d-tic-tac-toe | title=3-D Tic-Tac-Toe at MobyGames}}</ref> The product code for the Atari game was CX-2618.<ref name="ad1">{{cite web | url=https://www.newspapers.com/image/#63379754 | title=(Atari Ad) | publisher=The San Bernardino County Sun (San Bernardino, California) | date=5 August 1981 | access-date=6 August 2014|via = [[Newspapers.com]]}} {{Open access}}</ref>

Three-dimensional tic-tac-toe on a 4x4x4 board (optionally 3x3x3) was included in the [[Microsoft]] [[Microsoft Entertainment Pack|Windows Entertainment Pack]] in the 1990s under the name ''TicTactics''. In 2010, Microsoft made the game available on its ''[[Game Room]]'' service for its [[Xbox 360]] console.

A program library named Qubist, and front-end for the [[GTK+|GTK 2]] window library are a project on SourceForge.<ref>{{cite web|url=http://sourceforge.net/projects/qubic/|title=Qubist source code |date=12 December 2018 |publisher=SourceForge}}</ref>

{{Anchor|Anchor 3D}}

== See also ==
* [[Score four]]
* [[Quarto (board game)]]

== References ==
{{Reflist}}

== External links ==
* [http://www.boardgamegeek.com/game/13714 Qubic] at [[BoardGameGeek]]

{{Tic-Tac-Toe}}

[[Category:Abstract strategy games]]
[[Category:Tic-tac-toe]]
[[Category:Parker Brothers games]]
[[Category:Three-dimensional board games]]
[[Category:Paper-and-pencil games]]
[[Category:Tic-tac-toe variants]]
[[Category:Solved games]]