Y-Chain: See below for the value of a Y-Chain.
Player 1 should aim to have an even number chain count Player 2 should aim to have an odd number chain count Play this on any odd (or non-square odd-by-even) board size (such as those found in the Dot Game (3x3, 5x5, 7x7). For games with an even number of boxes on each side, like 4x4, this rule is reversed). Exception to this rule - in 3x3, a “0” chain count benefits Player 2
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.
So mathematically: 2 * (chain count - 1) = number of boxes sacrificed
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.
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.
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 sacrifice did not give away too many boxes. To avoid excessive sacrifices, pick the smallest chains to sacrifice.
Most Y-Chain will count as “2” since there will be one base and branch with one additional branch. It is very important you only consider chains within a Y-Chain. non-Chains can sometimes branch off of a chain but this is not a Y-Chain. Y-Chains are when a long chain has a small chain branching off of it. Sometimes more than one. Sometimes if there is more than one branch, consider the possibility that the Y-Chain can be broken in the middle making only 2 regular chains. Without considering this possibility you might think the Y-Chain is worth “3” since it has 2 branches. But if it is broken in the middle, leaving only 2 chains, then it is worth “2”.
When you encounter a Y-Loop, the loop is always the base and branch which counts as “2” followed by the count of the chains that branch off of it. Similar to the Y-Chain, if there are 2 or more chains branching off of it, there is a possibility of cutting the Y-Loop by sacrificing 1 or 2 boxes within the loop and creating one large chain. This would reduce a Y-Loop with a value of “4” to a chain with a value of “1” which can drastically change the final score.
