The 8 piece endgame databases supplied with Nemesis contain what is known as WDL information (Win-Draw-Loss) for each position possible in the game of Checkers with 8 pieces or less on the board. That means given any such position, Nemesis knows with 100% certainty, the result of a game played out from that position, assuming correct play by both players.

Using this information, Nemesis can ensure that in a drawn position, it will never play a losing move. In a won position, Nemesis will always play a move that will retain the "won" position.

However a problem can sometimes arise when in a winning position, a long sequence of king walk moves by both players are needed before some progress can be achieved. In this case Nemesis could retain the "won" position, but allow the position to repeat by aimlessly moving kings around, as it can't see the critical sequence of king walk moves to lead to progress and ultimate victory.

A good example in Checkers is "Strickland's Position" which requires 26 careful moves by the winning player before progress can be forced. See below for more about Strickland's Position.

This phenomenon is common to all programs that use the WDL endgame databases, including Chinook, WCC, Nexus, Nemesis, Wyllie, Cake, KingsRow. Chinook once failed to win a game against Don Lafferty for this very reason, despite being in a winning position.

Knowing what a tragedy it would be for this to happen to Nemesis at the World Computer Championship, we set about solving this problem. We created MTC databases.

These database are additional to the normal WDL endgame databases and work in conjunction with them. They contain the number of moves it takes each position to reach "Conversion".

A "Conversion" is defined as an irreversible move. In checkers this means either a capture, the Crowning of a man to a king, or a walk move by a man. Conversely, the only reversible move, is a king walk move.

How does this work?

In a winning position, Nemesis can consider all the moves that maintain a winning position (from the WDL database). Nemesis then looks at each position after applying these moves, and plays the move leading to the least moves to conversion (using the MTC database). In this way, progress is always achieved and Nemesis can never get stuck in an endless loop moving kings around the board.

Note that this is true even if the opponent plays with maximum resistance, delaying the winning side from making progress as long as possible.

The MTC databases will not be supplied as standard with Nemesis 2.0. However they can be purchased as an optional extra, but only for Nemesis 2.0 or higher. They will be supplied on CD-ROM.

More information about the MTC databases will be given when Nemesis 2.0 is released.

Here is a remarkable example of what value MTC database can add to Nemesis. Red to play and win, forcing a conversion in 153 moves at the most (when White provides maximum resistance):

4-8 3-7 8-3 7-10 21-17 5-9 32-28 31-26 17-13 9-14 28-24 14-18 13-9 10-15 9-6 15-11 6-10 18-23 1-6 11-7 10-14 7-11 6-2 11-16 24-20 16-19 2-6 19-15 14-10 15-19 6-9 23-27 9-13 27-31 10-14 26-22 14-10 31-27 13-9 27-31 9-14 31-27 20-16 19-24 10-15 24-20 16-11 27-23 14-9 20-24 11-16 23-18 15-11 18-23 16-20 24-27 9-13 23-26 11-15 27-31 20-24 26-23 15-11 23-26 13-9 26-23 3-7 23-27 24-19 31-26 9-14 26-30 7-10 30-25 14-9 25-30 10-15 30-26 9-14 26-30 19-16 27-23 14-9 23-27 16-20 27-23 9-13 30-26 20-16 26-30 15-19 23-27 16-20 30-25 19-24 27-23 11-7 23-18 7-3 25-30 24-19 30-25 20-24 18-14 19-16 25-30 24-27 14-17 27-23 17-21 16-11 30-25 3-7 25-30 7-10 30-25 23-27 25-30 13-9 30-26 9-14 26-30 10-15 30-26 27-31 26-30 15-19 30-25 19-23 22-17 14-9 17-13 9-14 25-22 23-19 21-25 19-15 25-21 15-10 22-25 11-7 25-30 10-15 30-25 31-26 25-29 7-2 29-25 15-10 25-30 26-22 12-8 14-9 13-6 Red wins

Here is another example, well known to all Checkers players. Strickland's Position requires 52 moves in total before progress can be forced. Despite having an extra piece, White has to work very hard and play with great care to force the win.

14-10 16-19 17-14 26-23 10-7 23-26 7-3 22-25 3-8 25-22 8-12 22-25 14-10 25-22 10-7 26-23 13-9 22-25 9-6 25-22 6-2 22-25 7-11 23-26 11-16 26-23 16-20 23-27 12-8 25-22 2-7 22-25 7-10 25-22 10-14 27-32 20-24 19-16 14-10 16-20 24-19 32-27 10-7 22-25 8-11 25-29 19-16 27-23 7-2 29-25 11-7 20-11 White wins