## May 12 Square's Strategy

Square's is a game played between two people on a grid of dots. The players take turns to draw one line and then pass the turn to the other player. The aim is to be the person to draw the final line to make a square which results in you claiming the square (by writing your initial in it) and gives you another go to try to claim more squares. If you went to highschool then you probably know this game.

Play typically starts with both players playing conservatively so that they never complete the third side of a square (which would let their opponent nab it). This results in a grid full of snaking chains of various sizes such as the one below:

At this point the player who's turn it is can no longer lay a line without gifting their opponent a square. As soon as they have one square in the chain they can keep going until they have them all. At which point they will have to place a line in the next chain to let the first person claim that one. This continues until each chain has been claimed with ownership rights alternating between each one. This means that it makes sense for the first player to give the second the shortest chain possible. In the example above, let's say that they draw a line like this:

That means the second player will claim all 4 of the left hand squares and then draw a line in one of the 5 on the right, which gives first player all of them and thus player 1 wins 5:4.

But we can do better. The trick to beat amateurs at squares is to realise that it isn't always worth claiming an entire chain. Let's go back to the situation from earlier:

Player 2 can claim some squares on the left, but let's try only claiming 2 and then placing their last line (which previously would have opened up the other 5 squares for player 1)  at the bottom of the chain to waste it.

This gives player 1 two squares on the left, but it is now their turn to open up the 5 squares on the right:

So player 2 wins 7:2. This strategy of sacrificing the ends of chains to keep the tempo is the trick. Between two players that know this trick, the strategy is to sacrifice squares so that you won't be the first one to open up the chains.