Tic Tac Toe

Tic Tac Toe in a schoolyard playground in Duluth, Minnesota

Alternate Names

Noughts and Crosses; Oughts and Crosses; Kit Cat Cannio; Tip Tap Toe; Tripp Trapp Troll (Sweden); Tik Tak Tol (Holland); Hugs & Kisses; Butter, Cheese and Eggs.

No. of Players

Two

Equipment

Most often the game is played as a paper and pencil game or on a chalkboard by school children. Here, I call it a board game sensu lato, in liberal use of the term. As a board game, use one of the two formations above; playing either within the nine squares inscribed by the left diagram or on the intersections and corners of the right diagram. The player going first will need five counters and the other will need four.

History

Surprisingly little is known of the history of this game. A game called Terni Lapilli (translating as Three Little Stones) is widespread in the Roman Empire around the first century BCE. Its grid markings have been found all over the city of Rome and various other places that previously fell within the Roman Empire. It is described here under Three Men's Morris. This game differed, however, in that players were only allotted three stones each that could move after being placed. Tic Tac Toe is possibly derived in degraded complexity from the only slightly more complex game of Nine Holes. Today, it is played mostly by children in America, Britain, and other parts of Europe including Sweden, and Holland.

There are many games worldwide that use a board with nine positions and an objective of forming three counters in a row. The table below outlines their differences.

Objective

An extremely simplistic game, the objective is to achieve three of your counters in an orthogonal or diagonal row.

Play

Alternate turns entail the placement of one of your counters at any of the nine cells (or nodes) on the board. Some English children, when they win, call out:

“Tit tat toe,

Here I go,

Three jolly butcher boys

All in a row!”

Once placed, counters are not moved, removed or captured.

Strategy

Based upon the potential rows of three which may be formed utilizing any position on the board that forms a part, it can be discerned that the center position is the best position and the four middle side positions are the worst.

A careful analysis of the game may be performed using a tree diagram showing all lines of play. Only a few devoted mathematicians or a computer program will have the patience to go through every possible game, however, and thankfully, this has already been done for us. Note that many moves are equivalent by symmetry and thus despite the nine positions there are technically only three opening moves for the first player: placing at the center, a corner, or mid-side.

Despite the advantage of the first player, an expert second player with careful play may always force a tie, if not win.

Variations

Three-dimensional Tic Tac Toe is played on a 3×3×3 board, though the first player has an easy win by playing in the center. Another variant is played on a 4×4×4 board called Qubic. A more complex variant can be played on boards utilizing higher dimensional space, most commonly four dimensions in a 3×3×3×3 board. In such games the aim is to fill up the board and get more rows of three in total than the other player.

In a variation played without materials, players take it in turn to say a number between one and nine. A particular number may not be repeated. Both players aim to say three numbers which add up to fifteen. Plotting these numbers on a 3×3 magic square will reveal the exact correspondence with the game of tic tac toe, given that three numbers will be arranged in a straight line if and only if they add up to fifteen.

Sources