## Sunday, February 06, 2005

### Dvonn and Game Patterns

Following my several games of Go, I decided to play several games of Dvonn.

There is something about playing several games of a quick abstract that one game can't give you. Within the core of any game are the "patterns".

The patterns in Chess have practically all been named: the Schwarkplof-Flarkstein opening, the Baggins-Balrog defense (I'm making this up, but you get the idea).

In Go, you have the atari, ko, komi, etc... whose very definitions explain the patterns in the game.

These patterns exist in most games, I assume, from Candyland to Puerto Rico to Monopoly.

Dvonn seemed like a fairly random game when I first started, after playing a single game on several occasions. Sitting down to play several games at once, I begin to see some of the patterns emerge.

Dvonn is a game with an elongated hexagon of circles, as follows:

..o.o.o.o.o.o.o.o.o..
.o.o.o.o.o.o.o.o.o.o.
o.o.o.o.o.o.o.o.o.o.o
.o.o.o.o.o.o.o.o.o.o.
..o.o.o.o.o.o.o.o.o..

Each player takes 23 disks, either white or black. The white player also takes 2 red disks, and the black player 1 red disk. Players alternate placing disks on the board one at a time, starting with the red disks (phase 1). Then (phase 2) players alternate moving any stack of disks (stack being one or more disks on top of each other). You can only move stacks that have your color on top. Each stack moves exactly the number of spaces as it has pieces in the stack. Each move must land on another stack. You cannot move pieces surrounded on all six sides by other pieces. Any stack that cannot trace a path to a red disk is removed from the game - typically this means that a whole lot of pieces are removed from the game as soon as the sole connecting piece is moved.

In the end, after no legal moves are possible, the player's remaining stacks are combined, and the higher total wins.

Playing several games, the patterns in the second half of the game start to emerge. The capture and recapture of large stacks by single pieces. The isolation and destruction of half the board by removing the connecting piece. The capture and movement of the red pieces. Most importantly, that the game is not going to continue until all pieces have been moved, but is likely to end quickly after several pieces are removed from play. The object seems to be to to wipe out all possible moves once you have an advantageous position.

The patterns for placing disks in the first half of the game still seem elusive. Of course, you want plenty of disks near the red ones and plenty near the outside so as to have more possible choices, and so that you can ensure that your pieces are not wiped out before you are ready. But it still seems highly chaotic.

The only thing that helps me is to place one of the red stones right next to one of the others. By reducing the playing area to two places, instead of three, I can contain the possible moves somewhat more in my head.

There is a game which I am working on that starts with 37 pieces distributed randomly on a hexagonal grid. Afterwards, each player alternate to combine any two pieces with various results. I tried this out on my friend and his immediate remark is that it felt that the opening moves were too random. I wonder if playing several games would take away that feeling after the patterns emerge.

Yehuda