ArticleslgStudy

mathematics

Notakto

Notakto is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Notakto rather than just read about it. In short: Notakto is a tic-tac-toe variant, also known as neutral or impartial tic-tac-toe. The game is a combination of the games tic-tac-toe and Nim, played across one or several boards with both of the players playing the same piece (an "X" or cross).

Notakto — main illustration
Notakto — illustration

Key takeaways

  • Notakto belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Notakto to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Notakto from memory before moving on to harder problems.

Reference excerpt

Notakto is a tic-tac-toe variant, also known as neutral or impartial tic-tac-toe. The game is a combination of the games tic-tac-toe and Nim, played across one or several boards with both of the players playing the same piece (an "X" or cross). The game ends when all the boards contain a three-in-a-row of Xs, at which point the player to have made the last move loses the game. However, in this game, unlike tic-tac-toe, there will always be a player who wins any game of Notakto. Notakto is an impartial game, where the allowable moves depend only on the state of the game and not on which player is taking their turn. When played across multiple boards it is a disjunctive game. The game is attributed to professor and backgammon player Bob Koca, who is said to have invented the game in 2010, when his five-year-old nephew suggested playing a game of tic-tac-toe with both players as "X".

Play Notakto is played on a finite number of empty three-by-three boards. Then, each player takes turns placing an X on the board(s) in a vacant space (a space not occupied by an X already on the board). If a board has a three-in-a-row, the board is dead and it cannot be played on any more. When one player makes a three-in-a-row and there are no more boards to play on, that player loses.

Optimal strategy

The optimal strategy for a single-board game of Notakto allows the first player to force a win. It is for the first player to play the center and then play a knight's move (two squares vertically and one square horizontally, or vice versa) away from the opponent's play. This strategy works because it makes a boot-like structure, which is called the boot trap. From the boot trap position the first player will be able to force a win. With two boards, the second player should on their first move play in the center square of the empty board (the one with no Xs in it). Then, the second player sacrifices one of the boards (by making a three-in-a-row) if it is possible. Now, the game is a 1-board game of Notakto so the second player uses the knight's move or boot trap strategies to win. From these two strategies, any game with more than two boards can always be won by the first player (on an odd number of boards) or by the second player (on an even number of boards).

See also Misère

References

Illustrations

Notakto illustration
Notakto: The "finger trap", in which the first player (who started by playing the center "X") is guaranteed a win
The "finger trap", in which the first player (who started by playing the center "X") is guaranteed a win

Worked examples

Example 1 — a first encounter with Notakto

Start with the simplest possible case. Write down what Notakto claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Notakto before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Notakto ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Notakto

In research
Notakto appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Notakto in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Notakto is common in secondary-school and first-year university syllabi. It links to neighbouring topics Combinatorial game theory, Mathematical games, Paper-and-pencil games, so understanding it makes those chapters shorter.
In everyday life
Look for Notakto outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Notakto” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Notakto in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Notakto means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Notakto out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Notakto in simple terms?

Notakto is a tic-tac-toe variant, also known as neutral or impartial tic-tac-toe. The game is a combination of the games tic-tac-toe and Nim, played across one or several boards with both of the players playing the same piece (an "X" or cross).

Why does Notakto matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Notakto?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Notakto.

Tags

  • Combinatorial game theory
  • Mathematical games
  • Paper-and-pencil games
  • Tic-tac-toe
  • Tic-tac-toe variants

Keep exploring