Copyright (c) 2000 Jeff Pickering and Ben van Buskirk
Dao is a simple game played on a 4x4 board with this initial setup:
- MOVE - A player chooses a stone with at least one adjacent empty cell and then moves it orthogonal or diagonal for as many empty cells as possible.
- GOAL - A player wins if he gets one of the following patterns
- All of his stones on an horizontal or vertical line (not diagonal!);
- All of his stones forming a 2x2 square;
- All of his stones on the four corners;
- One stone in a corner, surrounded by three enemy stones.
The last winning goal is to avoid the obvious tactic of trapping a stone to achieve an easy draw.
White has won! He must move c2-d2 and Black cannot stop him to make an vertical four in a row.
According to David desJardins, there are around 110.000 valid DAO positions (each position is, in fact, eight positions under rotation and reflection). I tested the game using Zillions, and after a tree search of over 60 million nodes (this. of course, includes many repetitions) the program does not seem to give any tactical advantage to either player (btw, the best proposed move was 1. b3-a3). This points that DAO is probably a drawish game. Notice that this is not a game death sentence, all two player abstract games end in one of three ways: win for 1st player, win for 2nd player, or draw. What kills a game is to find a specific way to always win or draw! More serious than this, is that after more than 70 turns played almost by random (just avoiding direct winning moves) Zillions was not able to defeat me (and Zillions plays very well on small search spaces like the 4x4 DAO board)...
There is a Java analysis program for Dao on Jan Kristian Haugland's website.