The perfect Dvonn move:

1. Covers an opponent's stone that could have caused significant damage.

2. “Unleashes” one or more of your own stones.

3. Does not unleash any of your opponent's stones.

4. Leaves one or more of your opponent's stones less valuable – so they no longer have the chance to cover any of your stones (but only their own color), for instance.

5. “Cuts” so you are able to “orphan” some of your opponent's stones, or increases the chance you'll be able to do so.

6. Forces your opponent to react to your move to avoid more damage, rather than launch an attack of his own (similar to keeping sente in go).

What else have I missed?

For those of you (like Jan) who write computer programs, is this how you go about programming them?

Rex

(Feel free to use the word “ring” instead of “stone” above.) ;-)

My program's main concern is maximizing mobility, hence, covering most of your guidelines towards the perfect move. For my program also the average connected-distance to a dvonn-stack is taken into consideration. Least important, but still taken into account is number of stacks owned.

I should add thaat I never tought my program these guidelines. It is able to learn from (self)played games and adapt it's strategy. So far mobility seems to be by far most important. In the endgame (22 stacks or less) it's pure counting…

Thanks for the response, Jan.

–By “maximizing mobility,” do you mean trying to keep your stacks as short as possible?

–Could you please explain what “average connected distance” is?

–I'm a bit surprised that your program doesn't place a higher priority on staying ahead in the “stack race.” It seems that having more stacks than your opponent in the end game is always a big advantage.

–Finally, when you say “pure counting,” what kind of counting do you mean?

It's funny that I would have these simple questions, but sometimes the terminology for newer games is vague.

Thanks,

Rex

It's funny that I would have these simple questions, but sometimes the terminology for newer games is vague.

Probably my terminologie is somewhat borrowed from either Othello or madeup by myself…

By “maximizing mobility,” do you mean trying to keep your stacks as short as possible?

Having good mobility means being able to choose from many (reasonable) moves. Thus with 'maximizing mobility' I mean, maximizing the number of playable stacks. More precise would be to say:

- maximizing the total number of different moves

- minimizing the number of moves for your opponent

- giving somewhat better value for moves targeting opponent rings

> Could you please explain what “average connected distance” is?

Assume a fully filled board, b2 is a dvonn piece. Then c5 would have a connection-distance of 3, while f5's connecting distance is 4. This distance to the nearest dvonnstack is computed for every stack, both colors. I brought this factor into the evaluation to lessen the risk of gettng cut-off.

> I'm a bit surprised that your program doesn't place a higher priority on staying ahead in the “stack race.” It seems that having more stacks than your opponent in the end game is always a big advantage.

It does, but it is the smallest factor built-in explicitly since it is largely covered by the mobility factor.

> Finally, when you say “pure counting,” what kind of counting do you mean?

Solving the endgame for perfect score by computing through all possible positions in a smart way. This is generally done from when 20-22 stacks are left on the board.

I totally agree with Jan that getting ahead in the “stack race” is a low priority for the middle game… except when you can guarantee that a stack is difficult or impossible to retake.

As for “maximizing mobility” my intuition is that the correct formulation should emphasize singleton's more than Jan's program might do. This is because it is not only maximum mobility now, but also maximum mobility after a jump that counts. Example: If a mobile singleton and a mobile 2-stack both have four possible moves… it is likely that the stack created after moving the mobile singleton will be more mobile.

It is interesting that “the perfect DVONN move” has a lot of things in common with a good Othello move, while those are two completely different games.

Yes, many people like to compare Othello to Go, but Dvonn is definitely a closer relative to Othello.