User:Itandy/The Dot Game

= Advanced Tactics in The Dot Game =

To win the game, it is necessary to control the game play from as early as possible.

For a summary of variations of the game and basic tactics, refer to Dots and Boxes.

Definitions
Non-chain: A non-chain is any single or double box. A non-chain counts as "0".

Chain: A chain is any string of 3 or more boxes that begins in one place and ends in another. A chain counts as "1".

Loop: A loop is any string of 4 or more boxes that begins and ends in the same place. A loop counts as "2".

Y-Chain: See below for the value of a Y-Chain.

The Chain Rule
In any board size found in the Dot Game (3x3, 5x5, 7x7)

Player 1 should aim to have an even number chain count

Player 2 should aim to have an odd number chain count (for games with an even number of boxes, like 4x4, this rule would be reversed)

Exception to this rule - in 3x3, a "0" chain count benefits Player 2

Taking Every Chain
In order to capitalize on the chain counting principles, you must be able to take every chain that is made. When your opponent gives you the first chain, take every box EXCEPT THE LAST TWO. Sacrifice these two by placing your line at the end of the two boxes, leaving space for a line in between one box and the other. This is known as the Double Cross.

If your opponent plays within a loop, leave FOUR boxes and play so that there is a space between two boxes on either side of your last line. By sacrificing the last 2 boxes of a chain or the last 4 boxes of a loop, you are guaranteed to obtain every single chain in the game.

Advanced #1: Exceptions
In 3x3, there are 9 boxes - you need 5 to win

In 5x5, there are 25 boxes - you need 13 to win

In 7x7, there are 49 boxes - you need 25 to win

Because you must sacrifice boxes to obtain all the chains in the game, it is sometimes possible for your opponent to make a bunch of boxes.

Be careful not to allow the amount of boxes you sacrifice get too high as you might sacrifice too many and lose the game. Since you are sacrificing all except the last chain you know that you will be giving your opponent 2 boxes for every "1" in the chain count (except for the last chain)

So mathematically: 2 * (chain count - 1) = number of boxes sacrificed

Advanced #2: Non-Chains
Let's call the person who is going to get all the chains the 'leader' and the other person the 'follower'. Since the leader is going to get the chains, the follower will get the last non-chain. In some cases, the follower also gets the first non-chain.

When you are the leader, you wish to avoid having non-chains as this may contribute to your opponent's score and allow them to win. When you are the follower, create as many as these as possible to allow for a closer game.

Advanced #3: Altering the Count
Since loops are "2" and chains are "1", turning a chain into a loop or a loop into a chain causes the count to change by "1".

This makes an even number odd, or an odd number even. If you are the follower, try to alter the count by converting a loop into a chain or a chain into a loop. If you are the leader, try to prevent the follower from doing this to you.

Advanced #4: Mistakes
Everyone makes mistakes, sometimes you can use this to your advantage. If you are the follower, you can sometimes take the opportunity to give a chain away early.

If your opponent forgets to sacrifice the two boxes at the end, the count will drop by 1 which can sometimes result in victory if your sacrifce did not give away too many boxes. To avoid excessive sacrifices, pick the smallest chains to sacrifice.