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As players get more advanced especially when playing on a physical board , they start to see and block these checkmates before they are set up. This is when wins get increasingly complicated.

Very skilled players win by using forcing sequences. Forces are moves in which one player gets 3 moves in a line, forcing their opponent to move in the last open spot in that line.

Even if the other player could make their own forcing move, they are required to respond to the current force, since they would otherwise lose on the very next move.

Since the opponent's move is predetermined, this allows a skilled player to maintain control of the board for many moves. These forcing sequences can often include forcing moves and sometimes many more , requiring the player to hold future moves in their head.

These wins can be very tricky to see coming and block effectively. One in-plane example looking at just a single plane of a board is shown in the gif to the right.

This is a fairly standard forcing sequence that I call a 3-move-force, since it takes 3 moves in a plane to set it up.

Not any 3 moves in a plane allow for this style of win, but many combinations do! Watching for this setup in all planes including diagonal and vertical planes on every move can be very difficult.

Once players are good enough at planning out forcing sequences, they are theoretically unbeatable from the first move.

The next section explains how computers have been able to reach this level of play, but no human ever has—maybe you could be the first!

Tic tac toe has been the subject of a surprising amount of research. Mathematicians have analyzed its game theory and explored its many symmetries, computer scientists have used it to prove out game playing algorithms, and XNO is working to optimize these algorithms for working on 4Play's processor.

Mathematicians have looked at many different tic tac toe games, with different sizes in different numbers of dimensions.

This makes any 3 or more dimensional 3-wide game of tic tac toe is a first player win game. These symmetries are typically called automorphisms: ways of resorting the squares of the board without changing the state of the board.

While 3x3 has 8 automorphisms, from rotations and reflections, 4x4x4 has This goes beyond rotations and reflections, and includes switching out the inner and outer parts of the board and switching the order of rows and columns.

This paper details the mathematics behind these automorphisms. One important result of these automorphisms is that there are only two possible first moves—read the papers or work on your own to figure out what they are!

These results open the door for interesting computational work. In , Oren Patashnik, an MIT researcher, used hours of computer time late at night on a then state-of-the-art machine to create the world's first winning dictionary for 4x4x4.

This is a full dictionary of moves to take before reaching force-able boards; it's assumed that the computer is able to complete all potential forcing sequences perfectly.

While there are nearly a billion different potential games before either player can start forcing a win, the dictionary consists of only moves.

This efficiency is achieved by clever move selection and not repeating automorphic boards. However, as Patashnik explains in his paper , while he produced a winning dictionary, it's not the optimal winning dictionary p.

Another winning program was built in for the third Computer Olympiad, and detailed in this book. Their algorithm used a much longer move dictionary, but a much faster forcing algorithm.

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