A Möbius strip, Möbius band, or Möbius loop, also spelled Mobius or Moebius, is a surface with only one side (when embedded in three-dimensional Euclidean space) and only one boundary. An example of a Möbius strip can be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip to form a loop.
Tic-tac-toe Collection supports playing on a Möbius strip as a topology option. When playing this way, the play space appears repeated in each direction, but flipped. For example a vertical Möbius strip has each copy of the place space flipped horizontally.
Connect Four (also known as Captain’s Mistress, Four Up, Plot Four, Find Four, Four in a Row, Four in a Line, Drop Four, and Gravitrips (in Soviet Union)) is a two-player connection game in which the players first choose a color and then take turns dropping one colored disc from the top into a seven-column, six-row vertically suspended grid. The pieces fall straight down, occupying the lowest available space within the column. The objective of the game is to be the first to form a horizontal, vertical, or diagonal line of four of one’s own discs. Connect Four is a solved game. The first player can always win by playing the right moves.
The game was first sold under the Connect Four trademark by Milton Bradley in February 1974.
Tic-tac-toe Collection implements a game with the same rules using the name Drop Four. As is standard, the size of the board can be changed and all other game options still exist.
In topology, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined. Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary (for comparison, a sphere is an orientable surface with no boundary).
For the purposes of playing tic-tac-toe, the playing space wraps horizontally and vertically, like a torus. Unlike a torus however, the playing space is flipped in one of the directions.
In this case for example, the playing space wraps normally horizontally, but when going vertically, the space is flipped horizontally.
Support for playing on a Klein bottle, as well as other topological spaces, is coming soon to Tic-tac-toe Collection.
Ultimate tic-tac-toe (also known as super tic-tac-toe, strategic tic-tac-toe, or meta tic-tac-toe) is a board game composed of nine tic-tac-toe boards arranged in a 3-by-3 grid. Players take turns playing in the smaller tic-tac-toe boards until one of them wins in the larger tic-tac-toe board.
Each small 3-by-3 tic-tac-toe board is referred to as a local board, and the larger 3-by-3 board is referred to as the global board.
The game starts with X playing wherever they want in any of the 81 empty spots. This move ‘sends’ their opponent to its relative location. For example, if X played in the top right square of their local board, then O needs to play next in the local board at the top right of the global board. O can then play in any one of the nine available spots in that local board, each move sending X to a different local board.
If a move is played so that it is to win a local board by the rules of normal tic-tac-toe, then the entire local board is marked as a victory for the player in the global board.
Once the outcome of a local board is decided (win or draw), no more moves may be played in that board. If a player is sent to such a board, then that player may play in any other board.
Game play ends when either a player wins the global board or there are no legal moves remaining, in which case the game is a draw.
Ultimate Tic-tac-toe is a planned feature for Tic-tac-toe Collection. As many existing game variations as make sense will be supported, including misère and different board sizes. It may also support different rules for the global an local boards, and possibly different rules for different local boards.
Tic-tac-toe (American English), noughts and crosses (British English), or Xs and Os is a paper-and-pencil game for two players, X and O, who take turns marking the spaces in a 3×3 grid. The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row wins the game.
The game can be generalized to an m,n,k-game in which two players alternate placing stones of their own color on an m×n board, with the goal of getting k of their own color in a row. Tic-tac-toe is the (3,3,3)-game. Harary’s generalized tic-tac-toe is an even broader generalization of tic-tac-toe. It can also be generalized as a nd game. Tic-tac-toe is the game where n equals 3 and d equals 2. If played properly, the game will end in a draw, making tic-tac-toe a futile game.
An m,n,k-game is an abstract board game in which two players take turns in placing a stone of their color on an m×n board, the winner being the player who first gets k stones of their own color in a row, horizontally, vertically, or diagonally. Thus, Tic-tac-toe is the 3,3,3-game and free-style Gomoku is the 15,15,5-game. An m,n,k-game is also called a k-in-a-row game on an m×n board.
The pie rule, sometimes referred to as the swap rule, is a rule used to balance abstract strategy games where a first-move advantage has been demonstrated. After the first move is made in a game that uses the pie rule, the second player must select one of two options:
- Letting the move stand. The second player remains the second player and moves immediately.
- Switching places. The second player becomes the first-moving player, and the “new” second player then makes their “first” move. (I.e., the game proceeds from the opening move already made, with roles reversed.)
This rule acts as a normalization factor in games where there may be a first-move advantage.
In Tic-tac-toe Collection, the pie implemented by allowing the second player to replace the first player’s move (this is equivalent to swapping pieces, but allows players to keep using their own icons).
In games with more than two players, in the first round of moves, any player may replace any other player’s first move.
Gomoku, also called Five in a Row, is an abstract strategy board game. It is traditionally played with Go pieces (black and white stones) on a Go board, using 15×15 of the 19×19 grid intersections. The game is known in several countries under different names.
Players alternate turns placing a stone of their color on an empty intersection. The winner is the first player to form an unbroken chain of five stones horizontally, vertically, or diagonally.
Besides many variations around the world, the Swap2 rule (based on “swap” from Renju) is currently adapted in tournaments among professional players, including Gomoku World Championships.
In Swap2 rule, the first player starts by placing three stones (2 black and 1 white, if black goes first) on the board. The second player then selects one of three options: play black, play white and place one more stone, or place two more stones to and let the first player choose the color. This is essentially a slightly more elaborate pie rule.
Tic-tac-toe Collection does not currently support the Swap2 rule, but it does support the pie rule.
Gomoku is an example of an m,n,k-game: either 15,15,5 or 19,19,5.
A misère game or bettel game is a game that is played according to its conventional rules, except that it is “played to lose”; that is, the winner is the one who loses according to the normal game rules.
Tic-tac-toe Collection supports misère gameplay along with all other game modes.
In multiplayer game modes that also have a target score, reaching the score eliminates the player, other players continue.
In game modes with an unlimited target score, the winner is the player with the lowest score and other players rank in ascending score order.