Quantum Tic-Tac-Toe

Widest Point Spread in a Collapse

This month's challenge is quite simple to describe, but answering it will indeed be a challenge. When you get to the end of a QT3 game, the last decision sometimes determines whether X or O wins. How big a point spread can you get? The theoretical maximum is for X to win by two points, or O to win by one point — or could O win by two points?

Be sure to include your name and email address! We want to give credit to the person that sends the best solution.

Stupidest Classical Game

Last month's challenge was to find a really good quantum game that, looked at from the classical point of view, was really stupid. As it turns out, a good quantum game will often turn out to look like a bad classical game. This is simply what we call the Ascertainity Principle: you can tell, by observation, whether a system is quantum or classical, even though your observations are all classical. The less it looks like the system can work, even though it is observed to be working, the more likely it is that the system has a quantum understructure. This goes all the way back to Planck's observation that electrons don't spiral down into the nuclei of atoms, even though they should (it being well known that a moving electric charge emits energy). The inference was that electrons in atoms can emit (and absorb) energy only in discrete amounts.

There are a lot of possibilities; here's just one:

Move   X   O 1   4 - 9   2 - 9 3   1 - 7   5 - 4 5   9 - 8   7 - 8 7   8 - 6   6 - 3 9   3 < 5

Analysis of quantum game X starts with a Knight's move, which is counter-intuitive, but actually a strong opening in Quantum Tic-Tac-Toe. O links to this move, so that if X forces an early cyclic entanglement she gets a real move in open rows. X then makes an intersection threat. If he repeats this move, O cannot win unless she has a defense in the past. O sets up her defense in the past down the middle column. X responds with an attack in the past along the bottom row. O blocks it. X now makes a mistake; his second spooky mark should have been in the center. O sets up a potential win down the 2nd diagonal (squares 3, 5, & 7). X blocks while shooting for a win down the 1st diagonal (squares 1, 5, & 9).

At move 9, O is compelled to collapse the game to this classical game (the other choice gives X the win). When the dust has settled, the classical observer observes that X and O must both be dunces:

Move      X         O    1    4     2  3    1     5  5    9     7  7    8     6  9    3

Analysis of classical game X leads in a side square - bad move. O plays in a side that doesn't block X in any way - bad move. X plays in the corner making a 2-row instead of setting up a fork - bad move. O doesn't block X's 2-row - missed block. X doesn't complete his 2-row nor does he block O's 2-row - missed win & missed block. O doesn't complete her 2-row - missed win. X creates a blocked 2-row. O fails again to complete her 2-row - missed win. X has no choice.

If O does give X the win, the result is still pretty stupid:

Move      X         O    1    9     2  3    1     4  5    8     7  7    6     3  9    5

Analysis of classical game Analysis and evaluation of this alternative will be left as an exercise for the interested gamer.