Rock Some Sockses at Dots and Boxes
Dots and Boxes – throw the switch
Dots and boxes (also called Pigs and Sties) is a game played with a pencil and paper on a grid of boxes. There is no limit to the arrangement or shape of the dots, so there are hypothetically an infinite number of possible playing boards. In the United States, the game is most commonly played on a regular square grid of 6×6 or larger.
A common board for Dots and Boxes
Players alternate between drawing lines between two boxes either horizontally or vertically. If a player finishes a full box, they get a point and they get to play again. Customarily, the player will initial the box that they have finished for easy scorekeeping.
T gets a point and gets to move again
The player with the most boxes at the end of the game wins.
Dots and boxes played in regular grids up to 5×5 has been mathematically solved, but in order to display general strategy, we will examine the game played on a 6×6 grid.
Strategy
The heart of the game of dots and boxes is the rule that finishing a box allows a player to play again. Consider the following board:
In this most extreme case, the next player to play finishes every box and wins 25 to 0. Of course, in practical play this rarely occurs. More commonly, there are series of chains to be finished, as follows:
In this case, there are four unfinished chains, of length 8,8, 4, and 4. The next player to go in this case is able to finish 3 of the chains, and will win, as follows:
A takes three series, then leaves the top corner 4 for T
From these examples, it becomes clear that the heart of the game is in forcing your opponent to make a move that leaves you able to finish the longer chains, but this is not always as straightforward as it seems.
Transferring the move by declining chains
Remember that you are not required to take whole chains, but that you can transfer the move to your opponent.The following grid will illustrate:
In this position, it is T to move and the number of completed boxes is tied at five apiece. The top chain is ready to complete, and if T would like he can take the whole chain:
No, idiot.
T has successfully taken five boxes, but it is now his move again, and he is forced to allow A to take the remaining boxes with any move:
Doomed!
Returning to the original position, if T , instead of taking the whole top chain, passes the move to A, he wins easily:
By leaving two boxes in the chain unfinished, T forces A to allow him to complete the bottom chain, and wins.
Games between two players who aren’t very familiar with the game are often decided when one player figures out this trick.
Another passing the move example:
In this example, it is T’s move and he is down by two boxes coming in. The top chain is not ready to be finished, and the bottom chain is:
In this case, T must give up 4 boxes in order to take the top chain, by taking two of the bottom chain, he can force A to set him up to take the top:
By declining to take all of the boxes in the bottom cycle, T wins:
14 to 11: Eat it, A
Advanced Strategy
All advanced strategy in Dots and Boxes is based on the idea of passing the move, but in generally more complicated positions. The ability to correctly calculate the ability to pass the move is what separates the good players from the bad. For example, in the following position:
With T to play, there are 3 chains that need 1 box to be finished, one of 3 boxes, one of 4, and one of 6.
It is very important that T not be the one who takes the 3-chain, so that he can force A to start the 6-chain by passing the move on the 4-box-chain. Conesquently, the question is how to manage the upper, unfinished chain so that A must start the bottom chain.
If T makes a move that allows A to take a box immediately, he fails to pass the move and loses, as in this example:
A Passes the move.
And T is forced to open the long chain.
Returning to the position in question:
If T instead develops the chain:
He provides A with the dilemma of offering him the top chain and the 4-box chain or the 3-chain and the 6-chain, either of which win for T.
Developing the skills to see the relationships between chains and passing the move is essential to Dots-and-Boxes skill, and comes only with practice.
In order to practice your skills on the web, there are several sites that offer Dots-and-Boxes online play:
One Player (vs. Computer)
Multiplayer (vs. Human Opponent)
Yahoo! (Requires Yahoo! Account)
Kongregate (Ads required to play)
Thank you for reading, and we’ll see you next week with our next entry. If you want to see a particular game covered, remember to comment!
Pingback: Grid and Bear it. (How to beat that weird uncle who always wants to play Battleship at Battleship) « Game Gaming
Pingback: Learn to Embrace Your Destiny by Playing Sprouts « Game Gaming