Basic Strategy (with Good Diagrams) Dots and Boxes

4 replies. Last post: 2005-10-27

Reply to this topic Return to forum

Basic Strategy (with Good Diagrams)
  • KnoxB (Computer) at 2005-10-26

    The following is by no means a comprehensive strategy guide. It is instead intended to enable beginners to get up to speed so that they don’t feel completely lost as to what they should be trying to do. And after learning the following, you can now play against your buddies who don’t know the long chain rule and beat them every time. :)

    A Vitally Important Endgame Trick



    Suppose it is your turn in the following position.



    ***
             |
    *  
             |
    *
    **
             |
    **


    Your opponent has just moved at the right end of the bottom
    chain of boxes. All or almost all beginners take the entire chain and then play some move in the remaining chain.



    **
             |
    *  
       |     |
    *
    **
    |X |X |X |
    **


    Your opponent takes all the remaining boxes and hence wins 6 to 3. But there is a better way. You should start by taking the first box as before.



    **
             |
    *  
             |
    *
    **
          |X |
    **


    But now instead of taking the remaining boxes, you make the following double-dealing move.



    **
             |
    *  
             |
    *
    **
    |     |X |
    **


    The point of declining the last two boxes in the chain is that your opponent is forced to open up the 6-chain (chain of 6 boxes) regardless of
    whether your opponent takes the two offered boxes. Your opponent should take the two boxes, otherwise you will take them on your turn. A single move that takes two boxes is called a double-crossed move (these are critical to the mathematical theory of the game). After the double-cross move, your opponent opens up the last chain.



    **
          |  |
    *  
             |
    *
    **
    |O |O |X |
    **


    Now you take the last six boxes. Hence by double-dealing, you changed a 3 to 6 loss into a 7 to 2 win!


    A chain containing three or more boxes is called a long chain. Whoever can force their opponent to be the first one to play in a long chain is said to have control. Now if you have control, you can maintain it by declining the last two boxes of every long chain except the last (you should take all of the last chain). If there are long enough chains around, then you win by getting and maintaining control up to the end.
    For example,



    ****
    |
    ****

    ****

    ****
                   |
    ***  
                   |
    *
    ****


    Your opponent has just opened by upper-most chain. By double-dealing on the first three chains opened up, you give away 6 boxes (two per chain) and you get all the rest for a resounding 19 to 6 victory. If you had instead simply traded chains back and forth like a first time player, then you would have lost 15 to 10.


    This suggests the following strategy. Make sure there are long enough chains around and get control.

    Getting Control — The long chain rule



    If the number of initial dots plus the number of eventual long chains is even, then the player whose moves first has control, otherwise (is odd) the player who moves second has control.


    On littlegolem, the game has 6x6=36 dots. Red goes first and blue goes second. Hence, the above general rule simplifies to the following.


    The red player has control if the number of long chains is even.

    The blue player has control if the number of long chains is odd.


    This rule assumes that there are no early double-cross moves. Each double-cross move switches the desired parity in the remainder of the game (you don’t have to worry about this until you learn about various sacrifice plays).

    Cycles



    Sometimes the ends of a chain meet up forming a closed circle or cycle. For the purposes of the long chain rule, cycles do not count as long chains. Now suppose you have control and your opponent has opened up a cycle instead of chain.



    **
    |  |     |
      *
      
    |        |
    *
    **


    As in a long chain, can you decline some boxes and still maintain control? Yes you can, but with cycles you need to decline four boxes not two. So in the above 6-cycle, you can take two of the boxes (it doesn’t matter which two you decide to take).



    **
    |  |X |X |
      *
    *
    |        |
    **


    The double-dealing move for cycles is to split the last four boxes in half forming two 2-chains.



    **
    |  |X |X |
      *
    *
    |  |     |
    **


    Now your opponent is forced to open the next cycle or long chain.

    Control and Chain/Cycle Length



    Maintaining control costs you 1 box for every 3-chain (you get 1 box and decline 2 boxes), and nets you 0 for every 4-chain. For cycles, maintaining control costs you two more boxes than a long chain of the same length. Of special note is the 4-cycle or quad.



    *
    |     |
        
    |     |
    *
    *


    Maintaining control when your opponent plays in a quad costs you all four boxes of the quad. This is a hefty price when there are only 25 boxes total.


    When you have control, you need to have chains that are long enough to overcome the cost of maintaining control. Hence, the player who is going to get control should try to make the chains as long as possible and try to avoid cycles especially quads. If the cost of maintaining control is more than the number of boxes you are going to get, then at some point it is going to pay to relinguish control by taking all of a chain or cycle (this happens more commonly when the opponent opens a cycle than it does for a chain).


    Conversely, if you are going to lose control, then you should try to keep the chains as short as possible and try to create a cycle particularly a quad. Even when you have lost the fight for control, you can sometimes squeak out a win just by creating a quad.

    Free Boxes: When Greed is Good



    There are a few specific situations where it always pays to be greedy and take boxes. It always pays to take strong>free
    boxes, chains of length 1. Also, it always pays to take chains of length two or three when both ends of the chain are “closed” so that the entire chain is disconnected from the rest of the board.



                   

                  *     **
       |     |              |     |     |        |
         *       **     **-*
    (A)          (B)          ©           (D)



    In A, we have a free box where the capturing move is at the edge of the board. In B, the capturing move is in the middle of the board — since the box neighboring the capturable one has at least three unplayed edges, the capturable box is a free one. In C and D we have chains of length two and three respectively where both ends of the chain are closed. Whenever you encounter one of these four situations, it is always best to take the boxes.

  • KnoxB (Computer) at 2005-10-26

    The second sentence in the paragraph above the last diagram should read as follows.


    It always pays to take free boxes, chains of length 1.


    The string “strong>” is an incomplete html tag which was meant to put the word “free” in boldface.

  • Hjallti ★ at 2005-10-27

    Nice Knox, but the last point you make I don’t get... taking a 3-chain changes control... so it taking entire D or part of D, and double-deal it depends on counting (chains, or even boxes). Or did I miss something... in most games I would double-cross if I know it means keeping control...

  • graff at 2005-10-27

    You can’t double deal with D, because if you take the box from either end you are left wih C.

Return to forum

Reply to this topic




Include game board: [game;id:123456] or [game;id:123456;move:20] or [game;id:123456;move:20;title:some text]