Re: Mancala solved!

[RGSnatzke@aol.com]

> > > I did notice a few things about their method that were confusing -
> > > mainly it appears that the "value" of the game for their analysis
> > > depends only on the remaining position, not the current score
> > Couldn't that lead to situations in which were 'drawn' because neither
> > player could guarantee positive expectation from the current situation,
> > but weren't drawn in practice because one player is ahead enough that they
> > can sacrifice a lot for the few more stones needed to win?
> 
> I think this is true. I am looking at the http://awari.cs.vu.nl/statistics.html page to see if
> that makes any sense, they seem to have assigned each position a score (expectation?). 

In a finite game this cannot happen. The score really doesn't influence best play from any given board position. The game tree will be identical regardless of the score, only at the leaves of the tree the values will be shifted by a constant. Retrograde analysis (max - min) therefore works, and works the same way no matter the score. 

In the rules section of awari.cs.vu.nl you can find the following sentence, which guarantees finiteness:

"Finally, a position that is repeated for the third time results in a even division of the remaining stones, including a possible half stone."

Therefore a sacrifice to stop a game that would be drawn otherwise is not necessary.

BTW, I had the honor to attend a talk at the Computers and Games Conference 02 where the team from Holland gave a talk about their brute-force solving of Awari. They've really done a great engineering job and used the available modern hardware to the utmost extent to get the work done. Very impressive!

And no - don't get mad because a game is "solved". If you get into this mood you will unnecessarily lose the fun of many more games, as one after the other will finally fall to one sort of analysis or the other. Some games are ripe in the next few years (e.g. 8x8-checkers), others will probably stand out for centuries to come (e.g. Go), but who knows. Let's have fun!

Georg