Most of us learn tic tac toe early in our life. Also, it is easy to find an optimal strategy for playing.
How about Quantum tic tac toe? What is the optimal strategy for playing it?
On a player's turn, instead of placing one large mark in one square, they place two smaller 'quantum' marks in two different squares. Moves are also marked with the number of the turn they occured, so the first player would write
X1 in two different places on the board. The two squares that have any particular move are called 'entangled'. Multiple small marks can be placed in one of the larger squares.
Suppose that the top-left square holds
X5, the center square contains
O4, and the right-hand square contains
X1. This forms a cycle of entangled squares. These cycles can be any length above two.
When there exists a full cycle of entangled pieces, the player who did not complete the cycle (in this case
X5 formed the cycle, so the O player) chooses how to resolve this cycle. Suppose he elects for the top-left square to hold
X5. Then there is only one possibility for the square for
X1, and thus only one for
O4. When a cycle is resolved, write the resolved 'classical' characters in the normal size.
Also, when a cycle is resolved, it may result in hanging chains. Suppose that the centre square from the previous example was actually
O2. When the cycle is resolved, there is now only one possibility for the
O2, so that move can also be resolved.
To win, a player must, just like standard Tic Tac Toe, create a three-in-a-row of classical (not entangled) moves.