The History of Notakto: From a Five-Year-Old to a Solved Game

Most classic games are decades or centuries old. Notakto is young: it began in 2010 with a child’s offhand suggestion, picked up a name and a research question, and was fully solved on the 3×3 board within a few years. It is a short history, but an unusually well-documented one for a game this simple.

For the rules, see what is Notakto.

A Child’s Idea, 2010

Notakto started at a kitchen-table level of profundity. According to the usual account, the professor and backgammon player Bob Koca was playing tic-tac-toe with his five-year-old nephew, who suggested that both players should be X. Koca recognised that the throwaway idea changed the game entirely: with no O, and the natural twist that completing a line loses rather than wins, ordinary tic-tac-toe’s tired draw becomes something with real structure. That is the seed of Notakto. The name came later, from Thane Plambeck and Greg Whitehead’s iPad app, as a play on “tic-tac-toe”. The game is also known as neutral or impartial tic-tac-toe, since both players share the mark.

From Curiosity to Research Question

A neat variant is one thing; a solvable problem is another. The game reached the wider mathematical community when Timothy Y. Chow posed it as a research question on MathOverflow, the question-and-answer site where professional mathematicians trade hard problems. That turned a family curiosity into something people with the right tools wanted to crack.

Solved, 2013

They cracked it. Thane E. Plambeck and Greg Whitehead published “The Secrets of Notakto: Winning at X-only Tic-Tac-Toe” (arXiv:1301.1672) in 2013, giving the 3×3 board its complete misère theory. The headline result is that the single board’s misère quotient has order 18, a small enough structure that any number of 3×3 boards can be analysed exactly, which is what makes perfect multi-board play possible. They also left a door open: whether the 4×4 board has a finite misère quotient at all is still unknown. The full picture is in is Notakto solved?

The solution leans on the same idea that gives the game its best story: that the boards are Nim heaps in disguise.

A Wider Audience, 2015

A solved game in an arXiv paper reaches a few hundred people. Numberphile reached rather more. In 2015 the channel ran two videos featuring Plambeck (“Tic-Tac-Toe (with Xs only)” and “Secrets of 3-Board Tic-Tac-Toe”) which introduced Notakto, and its hidden Nim structure, to a popular audience. The second is about three-board tic-tac-toe, the version this site plays by default.

Why a Tiny Game Got This Much Attention

Notakto rewards attention out of all proportion to its size. It is trivial to explain, impossible to draw, fully solved on the board we play, and carries an honest open problem one step up, all from three rules changed in a game every child knows. That ratio of depth to rules is exactly what makes minimal games worth studying, a theme its sibling game Triad explores in elegance in game design.

Play Notakto now: the game a five-year-old started.