Tue Sep 10 2019

Dots and Boxes

Dots and Boxes

Dots and Boxes Made Complicated

The most basic strategy of dots and boxes is to avoid drawing the third line of a box until you have to. Of course, you can draw the third line of a negative box because your and you opponent would normally want to avoid completing a box with negative points.

The next step in the strategy is that near the end of the game when your opponent draws a line in a long chain (3 squares or longer), instead of snatching all the boxes up, do not take the last 2 boxes. Instead, draw a line on the other end of the 2 boxes to enclose them. That way, you will not have to draw a line into the next long chain and your opponent instead will be forced to even when he/she draws a line to take the two squares.

Now you’ll want to know how to force the opponent to make the first move into a long chain. Here are the rules for doing that. Now keep in mind that the following applies because this game is a 5x5 square. It can change for even-by-even squares and other dimensions!

Basically, the 1st player wants an even number of long chains to form while the 2nd player wants an odd number of chains to form. In other words, at the end of the game if there is an even number of chains, the 1st player will force the other player to start playing into the long chains and vice versa.

However, the game is not so simple. A special thing that only Gambit seems to have is the dangerous negative point boxes. This leads to the creation of “dominoes” that are not made in a normal dots and boxes game. A “domino” is two or three adjacent squares with only their outlines drawn in. That’s why it’s called a domino. The funny thing with dominoes is that every time one of them is made, the number of chains each player wants switches! To put it simply,

    Without dominoes:
  • 1st player: even chains
  • 2nd player: odd chains
    But when a domino is made:
  • 1st player: odd chains
  • 2nd player: even chains
    When a second domino is made:
  • 1st player: even chains
  • 2nd player: odd chain

There is more. At this point, I’ve only talked about chains. Loops are basically chains without any ends. If you think of a chain as a path, a loop would be a path with no entrance or exit! The shortest possible chain would be a 2-by-2 square with only its outline drawn in. Loops themselves do not count as a chain.

Branches are like chains (using a path analogy) that has 1 or more forks in the path. It’s a little more complicated than loops. If there is only 1 fork, that is, there are three or four single branches that meet up to one square, you want to count the number of branches that have 3 or more squares (called “long branches”) ignoring the center square. Here’s how to count them as chains:

  • 0 long branches (unlikely): 1 chain
  • 1 long branch: 1 chain
  • 2 long branches: 1 chain
  • 3 long branches: 2 chains
  • 4 long branches: 2 chains

The final phase is the endgame when all possible moves without making a box can be made. Take turns first sacrificing “short chains” (with only 1 or 2 squares). Warning! When drawing a line to give up a 2-square chain, draw the line separating the 2 squares. If you draw a line on one end of a 2-square chain, the opponent can choose to make another domino if they want to switch the number of chains for them to win! Of course, if the number of chains are wrong for you, it wouldn’t hurt to try and draw on one end of a 2-square chain and see if your opponent accidentally makes another domino in your favor.

With long chains, as mentioned above, you want to take all the squares, except for the last 2, then draw a line on the other end of the 2 remaining squares, forming a domino. These dominoes do not change the number of chains you want, because it was part of a chain itself. Remember that a domino can be 2 or 3 squares, so you can also leave three squares as a domino if some or all of them are negative squares.

Now to deal with loops during the endgame, you can take all but 4 squares in the loop, then draw a final line splitting the 4 squares into a couple dominoes. Remember that dominoes are 2 or 3 squares, so you can also make a couple of dominoes in a loop by splitting 5 or 6 squares. But it’s only a good idea to do that if most squares are negative.

To deal with branches (with only 1 fork) during the endgame, give up the short branches as if they were short chains being careful as described above. You can then treat the long branches as long chains and always give up 2 or three squares as a domino. Now it’s not explained what to do with more than 1 fork.

But generally, you can alter the number of chains depending on where you place the line. Try avoiding multiple forks or use it to confuse your opponent…just don’t confuse yourself!

Finally, will all said and done. You should be able to win against players who do not know this strategy! Get out there and win!

Here are some side notes for those who want to step up their game even more: To control the number of chains, try splitting up the board evenly if you want multiple chains, but… Avoid making long chains with only 3 squares and/or with bonus points (+2, +3, etc.) at the ends. This starts to give opponents more points than you because you will give up at least 2 squares. For example, if you have a 3-square long chain with 2 bonus squares, one on the end and one in the middle, the opponent can draw a side of the non-bonus square. You will then be forced to take only one square for one point and give up the two bonus squares as a domino!

When a chain with bonus points at one end has already started forming, try to make that chain longer and also try ending the chain with bonus points on both ends to even out the net increase in points! Also, try avoiding making loops as you end up giving up 2 dominoes. Though, try making loops around negative squares so that you can give away most of them to your opponent. Though, be very careful when trying to do this, as your opponent can try to make some of those pesky dominoes before the endgame.

Another worrisome thing is when an opponent draws into a long chain before the endgame. Try see if you should treat it as a long chain now, or see if you can take all the squares and still make another chain to replace it.

An even higher strategy would be to look at the board right when the game starts and deciding whether it’s easier to force an even or an odd number of chains. Try making the domino you need with negative squares at the start before your opponent realizes which number of chains is easier to make. When both players becomes good at estimating the number of chains that can be made good luck! It becomes a battle for dominoes. At this stage, you can consider taking negative squares to avoid making any dominoes at all. Or start early and form a short long chain (3 squares) to save room for a couple long chains. Just be sure to have long enough chains made later on to make up for the losses!

It will require careful planning and seeing ahead when trying to control the number of chains and whether you should make a sacrifice or not. Now be aware that even all this information is just the tip of the iceberg. There are players that are good at playing “defense”. They will purposely lose the battle of making the number of long chains and concentrating on forming loops and short chains with bonus squares at the ends. They will literally try and do what I just advised you to avoid! Sometimes, playing this defensive strategy will beat players who are not used to this version of play. Try playing this way against players who are really good at controlling the number of chains!

There are extra tips on how to force chains to be made and to not be made, but that won’t be covered at the moment. Perhaps in a future update! Have fun and be square!