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        Arimaa >> General Discussion >> Score?
        
(Message started by: qswanger on Sep 23^rd, 2009, 6:36am)

Title: Score?
Post by qswanger on Sep 23^rd, 2009, 6:36am

I apologize if this topic has been broached before, but I (still a newbie) was not able to find any references to it through the forum search feature nor through any other (conspicuous) arimaa.com link:

What's the deal with the game "score"?

Specifically, I noticed that there was some type of score that's listed for both players in at least one of the game clients, but no explanation of how this score is calculated, why it is being calculated, what it is good for, and if I ever need to worry about trying to calculate game scores myself (e.g., in a face-to-face game) in addition to all of the moves and tactics that I must calculate as a matter of course. I saw a reference to a scoring system in one of the downloadable papers off the main page that says it is: "R + P x (C+1)" in the context of "match game requirements" (I had thought at the time to print that particular page off), but score is not mentioned in the match game requirements link in the game room. What's the history behind this? Has this been deprecated? If so, what was the original intent, why is it still in the client, and why was it even necessary in the first place? It seems like setting proper time controls would take care of determining a winner in any game that is taking an excessively long time to complete (at least for one player). I also imagine that this is somewhat controversial (I wouldn't want any of my games to be determined by some arbitrary or contrived score calculation instead of through the usual victory conditions *or* by time). Perhaps it is my ignorance, but I am really confused ... Thank you for any light you can shed on this.

Quinn

Title: Re: Score?
Post by Fritzlein on Sep 23^rd, 2009, 7:58am

The score function is obsolete and has been replaced by piece count. If a game goes beyond a pre-determined length, whoever has more pieces at that point wins.

Deciding a winner by piece count is an extremely controversial policy. Fortunately, it has never happened, ever. Games of Arimaa simply don't drag on forever, so the rule about what happens if they do drag on forever is irrelevant.

The question of what to do if a game of Arimaa were to drag on forever depends very much on the reason why it is happening. Since it has never happened, we don't know why it would happen if it did. You suggest a bad time control as a possible source of the problem, but let's assume that we have reasonable time controls so that what is actually at issue is the number of moves getting too high, say over 120 moves.

A game might not be done after 120 moves because neither player is trying to win. In that case, a tournament requires a result to be imposed so we can get on to the next round. Counting pieces works for me in that situation.

A game might not be done after 120 moves because the player with the advantage needs more moves to finish off a stubborn opponent. If that starts happening, it may be that piece count is inadequate to determine who would have won after further play. It will be a blow to Arimaa, though, if games start taking so long, because it will make Arimaa boring.

A game might not be done after 120 moves because one player is just trying to defend, and not trying to win. Fortunately, so far, everyone who has tried to merely defend has ended up losing in a reasonable number of moves. If pure defense starts to succeed in the future, it will show that Arimaa is flawed, and the piece-count rule isn't going to help at all.

A game might not be done after 120 moves because neither player can make progress. Consider the following position:

+---+---+---+---+---+---+---+---+
8 | e | m | h | h | d | d | c | c |
+---+---+---+---+---+---+---+---+
7 | | | | | | | | |
+---+---+---+---+---+---+---+---+
6 | | | * | | | * | | |
+---+---+---+---+---+---+---+---+
5 | r | r | r | r | r | r | r | r |
+---+---+---+---+---+---+---+---+
4 | R | R | R | R | R | R | R | R |
+---+---+---+---+---+---+---+---+
3 | | | * | | | * | | |
+---+---+---+---+---+---+---+---+
2 | | | | | | | | |
+---+---+---+---+---+---+---+---+
1 | E | M | H | H | D | D | C | C |
+---+---+---+---+---+---+---+---+
a b c d e f g h

Technically, this is a won game for one of the players due to the repetition rule, but repetition wouldn't come into play in our lifetimes. If a position like this happens when at least one player is trying to win, it will be a sad day for Arimaa, because the only reasonable solution in my mind is to call it a draw.

Fortunately, games don't drag on forever (so far) for any reason. I am content to enjoy the current happy state of affairs and ignore the piece-count rule until it comes into play. Why borrow trouble, when trouble isn't even looming on the horizon? If the piece-count rule is ever going to be applied, we will probably have warning signs in many games beforehand, which will give us plenty of time to discuss remedial rule changes then.