Quantum Noughts and Crosses
I’m a sucker for a good noughts and crosses variant – I’ve previously written about Ultimate Noughts and Crosses, for example – so imagine my excitement when I came across Quantum Noughts and Crosses in Ben Orlin’s book Math Games with Bad Drawings.
A bit about the book
This is a terrific book, by the way – I highly recommend it. I have many, many books full of traditional games including loads of pencil and paper games, so I was already familiar with some of the ones in the book. But because Ben is sharing games primarily devised by mathematicians and many of them more recent, there were lots that were new to me.
If maths isn’t your thing, don’t be scared off. The book is extremely approachable. The instructions for each game are accompanied by ‘Tasting Notes’, which dig into the strategies a bit; a ‘Where It Comes From’ section, talking about the creation of the game; a ‘Why It Matters’ section, which explains why the maths is relevant to every day life; ‘Variations and Related Games’, which is self explanatory and the obligatory bad drawings, which are delightful and brilliantly instructive.
Other than Quantum Noughts and Crosses (well it’s actually called Quantum Tic-Tac-Toe in the book), my favourites are Prophecies (a grid-filling prediction game) and LAP (a grid-filling deduction game).
The quantum bit
I’m not going to explain quantum mechanics. I’m not qualified … and anyway, my understanding is very very limited. The important thing is the idea that very tiny particles can seemingly exist simultaneously in multiple different places. However, when you try to observe this, quantum behaviour changes. As soon as you try to take a measurement, each particle fixes in a single location.
You’ve probably heard of Schröedinger’s Cat. This thought experiment illustrates quantum principles. A cat is in a box with a device containing a radioactive atom that might kill the cat. Until the box is opened, the cat could be alive or dead. In fact, until the box is opened, the cat is both alive and dead. It is only the act of opening the box that fixes the outcome one way or the other.
The game
So let’s look at how to play Quantum Noughts and Crosses, which was invented in 2002 by Allan Goff, a software engineer.
To set up, draw a 3×3 grid, though you might want to make it slightly bigger than for regular Noughts and Crosses. One player plays Noughts, the other Crosses. Crosses takes the first move.
On your turn, place your mark (X or O) in any two adjacent boxes, but keep these marks small, you don’t want to fill up the whole box. The boxes can be orthogonally or diagonally adjacent. Now join the two marks with a line. You’ve created a pair of entangled particles! The final position of that mark will be in one of the two boxes, but you just don’t know which one yet.
Now the other player does the same. You can have multiple small marks in a single box, but this is a work in progress, eventually each square will just have one large mark in it.
Keep playing, alternating between players, until some of the entanglements have formed a loop. This loop could be as small as two connected squares, or could potentially involve all 9 squares. When a loop is created all the particles involved in the loop collapse – taking their fixed and final positions.
If you are the player who created the loop, the other player collapses it. Each loop can be collapsed in two ways. To collapse the loop, choose which of the two locations the final particle placed settles in. The way it goes will force all the other particles in the loop to resolve to their final positions.
When a collapse occurs and particles fix to a final location, draw a big, heavy mark over the top of the smaller marks in each box. (You can redraw the grid if it gets too messy).
Some particles might be only partially in the loop. These particles will be forced out and into their other locations.
The win conditions are the same as regular Noughts and Crosses – three of your large marks in a line will win you the game. However, it is possible for both players to win simultaneously.
Other quantum-style games
If playing Quantum Noughts and Crosses gives you a taste for quantum games, here are a couple of others you can try.
Quantum Hangman
This game is also from Orlin’s Math Games with Bad Drawings.
Play like regular Hangman, but instead of choosing one word, which other players have to guess, you choose two words of the same length (e.g. 5 letters). When letters that appear in the word are guessed, you write them in the blank spaces. However, at some point, two different letters will appear in the same space (because you’re giving the answers for both words). At this point, the guessers must perform a collapse and decide which letter to keep in the space. At this moment, the single word that the players are guessing is defined. Scrub out any letters that relate to the other word. But crucially, the hangman doesn’t regress. You still have the same number of guesses overall, so when you’re collapsing the word, try not to lose too much progress!
Cat in the Box
This is a published game from Pegasus Spiele.
Cat in the Box is a trick taking game. Cards can be one of four different colour suits, but all the cards are actually colourless. While the cards are in your hand, they can each belong to any suit. But as soon as you play a card, you put a token on the board to indicate which suit it belongs to – e.g. a blue 5. This also stops another blue 5 being played later in the round. You must always follow the lead suit if you can, but at any time, you can declare you have no more cards in that suit left in your hand, removing the token for that suit on your own little player mat as a reminder.
There are five cards of each rank in the game, but only four suits, so there will be more cards in play than can possibly be played. Keep playing until one player cannot play because to do so would create a paradox. The round ends and players score according to how many tricks they predicted they would take and how well they’ve connected their tokens on the board.
Do you know of any other quantum style games? I’m developing a bit of a passion for them, so please do share in the comments!
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