TacTix is a two-player
strategy game
A strategy game or strategic game is a game (e.g. a board game) in which the players' uncoerced, and often autonomous, decision-making skills have a high significance in determining the outcome. Almost all strategy games require internal decisio ...
invented by
Piet Hein, a poet well known for dabbling in math and science, best known for his game
Hex.
TacTix is essentially a two-dimension version of
Nim
Nim is a mathematical two player game.
Nim or NIM may also refer to:
* Nim (programming language)
* Nim Chimpsky, a signing chimpanzee Acronyms
* Network Installation Manager, an IBM framework
* Nuclear Instrumentation Module
* Negative index met ...
; players alternate moves, removing one or more tokens in a single row or column until the last one is removed. At the time of its founding, TacTix was played on a 6x6 board, but is now usually played on a 4x4 board.
The game can be played in its misere and non-misere forms. The strategies listed here render the non-misere gameplay trivial. The game is often used as a
programming exercise, and many versions are available on the web as
Java
Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's List ...
applet
In computing, an applet is any small application that performs one specific task that runs within the scope of a dedicated widget engine or a larger program, often as a plug-in. The term is frequently used to refer to a Java applet, a program w ...
s.
Game play
TacTix is played on a NxN grid of squares, where N was initially 6, but has more commonly been played as 4.
Players alternate removing pieces a selected row or column, as many contiguous pieces as desired. For instance, in a 6x6 game, a player might remove pieces one through four on the first row. They cannot remove only the first and third pieces, these are not contiguous.
Players alternate doing this until the last piece is removed. The player who takes the last piece ''loses'' in the
misère Misère ( French for "destitution"), misere, bettel, betl, or (German for "beggar"; equivalent terms in other languages include , , ) is a bid in various card games, and the player who bids misère undertakes to win no tricks or as few as possi ...
play convention, or wins in the non-misère version.
Strategy
First Player If N Is Odd (non-misere): The player takes the center piece and symmetrically imitates every one of the opponent's moves.
Second Player If N Is Even (non-misere): Player copies opponent's moves symmetrically. You will eventually take the last piece and win.
Variations
The hexagonal variation of the game, played on a six by six by six board, is called TacTex. TacTix can also be played on any size NxN board. A Non Misere version of TacTix, where the player who makes the last move is the winner, is also playable.
Analysis
On the 4×4 grid originally proposed by Hein, the second player will always win with correct play (
HAKMEM
HAKMEM, alternatively known as AI Memo 239, is a February 1972 "memo" (technical report) of the MIT AI Lab containing a wide variety of hacks, including useful and clever algorithms for mathematical computation, some number theory and schematic ...
item #74).
If the game is instead played with the normal play convention (player who takes the last piece wins), the second player can always win by symmetrically mirroring the first player's moves. (Or on an ''odd'' × ''odd'' size grid, the first player can win by choosing the center piece and subsequently mirroring.)
Tac Tix has 65,536 reachable positions. Out of the reachable positions, 57,156 are winning, and 8,380 are losing
References
External links
TacTix appletfrom thinks.net
at Four.com
TacTix iPhonean
jPhone game available at the
App Store
An App Store (or app marketplace) is a type of digital distribution platform for computer software called applications, often in a mobile context. Apps provide a specific set of functions which, by definition, do not include the running of the co ...
*
* {{bgg, 27612, TacTex
JavaScript TacTix Mathematical games