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        Arimaa >> General Discussion >> Re: The relative value of pieces in Arimaa
        
(Message started by: 99of9 on Apr 16^th, 2005, 7:22am)

Title: Re: The relative value of pieces in Arimaa
Post by 99of9 on Apr 16^th, 2005, 7:22am

You might be interested in this discussion we had in the bot-writers forum some time ago:

http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=devTalk;action=display;num=1062013358;start=

I still believe those systems we discussed are vaguely right, but I'm sure it deserves to be looked at again after so much time. For example I think I was totally wrong about how much an elephant is worth... I now realise (at the start of the game) it's worth much more than just an M+H.

Title: Re: The relative value of pieces in Arimaa
Post by Fritzlein on Apr 16^th, 2005, 6:12pm

Arimanator, I don't think 99of9 was saying that everything has been thought of on the topic of piece values, or that everything you ever wanted to know about that is in a previous thread. If you read his post, it says "I'm sure it deserves to be looked at again" and "I was totally wrong about [...]". Clearly the topic is still open in his eyes.

Discussion is a give and take. All of us want other people to respond to our ideas. When I post to the forum it is because I hope people will find what I say interesting enough to make comments, and give something back to me. It wouldn't be fair (and I think this is part of your point) for me to say "I can't be bothered to comment on what you say, but you should comment on what I had to say." Maybe this is what it feels like to you to be referred to another thread.

But now try to turn the perspective around. For me and perhaps other members of the forum, you seem to be saying that what we discussed before you were a member is irrelevant to you. You don't care what we said, all that matters to you is the questions you asked. Why are you demanding responses to your thoughts, but refusing to give a response to what others have said?

I am interested in your opinions on this topic. Does Fotland's scheme overvalue the camel? Does the 99of9 scheme undervalue the elephant? I think yes in both cases, but what do you think? Do you have some fixed numbers to propose, or perhaps a floating value for the pieces depending on what exchanges have happened? How would you propose to fix the flaws you see in those outdated schemes?

Would you be so good as to share your thoughts on the previous thread with the rest of us? Good discussion is always a two-way street: the more you respond to other people, the more they will be eager to respond to you.

Title: Re: The relative value of pieces in Arimaa
Post by mouse on Apr 17^th, 2005, 6:18am

I have from time to time posted something in this forum hopeing to get some kind of reply. I have not always goten the reply I hoped for but the response have always been polite.

I have also read the different post some with great interest and some just to keep up to date with the discussion. But in all the post there has usually been a considered tone.

This general friendly atmosphere is one of the things I like about this forum. Hence it was with some sadness I have read this tread. Which I think break with this good tradition of the Arimaa Forum.

And I will ask if comments like this is really nessecary?

on 04/17/05 at 00:03:51, Arimanator wrote:

Now if that's all you've got to me you may keep it to yourself !

Title: 3 Re: The relative value of pieces in Arimaa
Post by mouse on Apr 17^th, 2005, 7:42am

on 04/17/05 at 07:33:07, Arimanator wrote:

Dear mouse, with all due respect, when you take something out of its proper context you can always make it look worse than it actually is. They teach that at school, at least the ones I went to, and when you do it it's not the best way to get high grades.

I was referring to a comment made about one game that I won against clueless. I was proud of that victory but not for long after this comment.

It basically said that I was lucky to have won this one that I just exploited one weakness of this bot and that if it were my commentator instead of the bot I'd be dead in the water. I don't know about you but to boost someone's confidence, there are better ways.

Now you may not like my reaction about this but rudeness is not only a matter of form sometimes it can also be a matter of content, like using someone's words without bothering what motivated them.

By the way I've noticed that your last 5 interventions in that forum were following something I said and I must I am very flattered that you've taken so much interest in my doings :)

Well I did take one quote out of the context yes. But my comment was to the 3 post above it. The quote was just meant as an example.

Futhermore I believe you asked Fritzlein for a comment on the game. So he gave you a comment.

Personally I think the best comment are the ones that tells me what I do wrong in a game. Thats the best way to improve my play.

Title: Re: The relative value of pieces in Arimaa
Post by Fritzlein on Apr 17^th, 2005, 9:49am

on 04/17/05 at 00:03:51, Arimanator wrote:

I didn't particularly appreciate your last comment on my game against clueless and it had for effect to shake my new found confidence that I could play at a higher level, I may have been lucky at this game then again I may not but given your groveling about a game that was about as much risky later it sounded particularly inappropriate in hindsight. Now if that statement makes me irrevocably a pariah here then so be it !

I made a general review of your comments about diverse games of high and low rating and never have I found that level of criticism for someone who WON!

Now if that's all you've got to me you may keep it to yourself !

I would not have commented on your game against Clueless if you had not asked me to. I don't go around looking for ways to criticize people and make them feel bad. But since you specifically asked me to comment, I felt it would make you feel bad if I ignored your request. Indeed you had told me before in chat how it had hurt your feelings when no one responded to a particular post of yours in the forum, so I made sure to honor your request for commentary.

Now I see you did not want my commentary, you wanted my agreement. You said you didn't use any "tricks" to beat Clueless. If I did not agree with that, I should have kept my comment to myself.

I am sorry it dashed your confidence that I believe it is indeed a species of trick to force a goal on one side of the board by letting a bot get caught up in capturing a bunch of pieces on the other side. I wouldn't have commented in those terms, except that you seemed to be asking precisely that question. Also I am sorry you found it an unuseful comment that there probably was a defense for your attack by bringing the elephant home. Perhaps you might someday play a opponent who doesn't get as distracted with material gain, and who defends his goal better, but perhaps this information will indeed never have any use to you. Or maybe the problem was that I should have been more specific and given a precise alternative move for Clueless rather than outlining a strategy; if that was the prbolem, I can remedy it even now with a specific suggestion for an alternative move.

I did not mean to undermine your confidence with my comments, because I truly believe the way you won is a technique which requires some cleverness and insight. By winning as you did you were demonstrating your superiority of strategic judgement over Clueless, and I should have emphasized this more. Furthermore, I am sure that you discovered this winning technique on your own, and not by seeing how others had done the same thing in the past, which makes it a greater achievement. You have reason to be proud of your progress in Arimaa, and the individuality of your effort makes it all the more significant.

I responded to your rebuttal to 99of9 and not your original post to this thread, because I found your rebuttal to him unfair, and was not eager to join a conversation where I might get the same treatment. You had always treated me with courtesy to that point, and I had hoped I could persuade you to extend that same courtesy to 99of9. Now I see that you would rather take offense at me too than make some room for seeing his perspective.

I have found the Arimaa community to be very friendly, so I doubt any of your comments have made you "irrevocably a pariah". There have been disagreements before, and people have worked through them, and tried to see from each other's point of view, so I don't think any of the bad feelings have been permanent. But maybe the interactions which we think are friendly don't suit you, and you would prefer to be ignored than get the kind of responses you have gotten so far. If this is your choice, I will respect it, and not trouble you again.

Title: Re: The relative value of pieces in Arimaa
Post by mouse on Apr 17^th, 2005, 11:28am

on 04/17/05 at 11:20:03, Arimanator wrote:

By initiating this topic I just meant to contribute to the advancement of the game and nothing else. If it did sound like a nuisance I am sorry and if you want to remove it, I won't mind.

I think the topic is both interesting and relevant. But only the first two post. So I would hapilly remove my contributions so the debate could start over from scratch.

Title: Re: The relative value of pieces in Arimaa
Post by Fritzlein on Apr 17^th, 2005, 12:10pm

Arimanator, that is a very moving apology. I can tell that you speak from the heart always. I admire and respect that.

Your questions and comments about Arimaa haven't been a nuisance, they have been a contribution to the community. Maybe the main trouble is just that you fear that other people think your contributions are worthless. You are creative and insightful, so on that score you have nothing to fear but fear itself.

I know what it is to have personal failures affect me negatively. Since you have shared so openly, let me share this about myself: Arimaa is for me an attempt to escape from failure in other areas of my life. I play so that I can win and forget that I am a loser in other ways. But even though I have won the Arimaa World Championship and have the highest rating, I am still afraid that I am really a loser. I play against the bots because I am afraid the other humans will beat me. I can't handle losing, so I try to avoid situations where I might lose.

I can see that you are sincere, and not mean-spirited. I never meant to hurt your feelings, and I am sorry that I did, and I will try not to do so again. If you can forget what I said before, we can go forward in harmony from here.

I will give your initial post in this thread some thought, and try to respond intelligently in my next post.

Title: Re: The relative value of pieces in Arimaa
Post by PMertens on Apr 18^th, 2005, 1:10am

he is not the first one ;-)

Title: Re: The relative value of pieces in Arimaa
Post by Fritzlein on Apr 18^th, 2005, 9:37am

I have been thinking more about why, in the opening, I consider a camel superior to a horse and a rabbit, and probably also a horse and a cat, but in the ending I consider a camel inferior to a horse and a cat and probably also a horse and a rabbit. The best answer I have is that it depends on whether goal threats are an important theme are not.

In the opening, no attack, no matter how reckless, can create a realistic goal threat. The struggle is all about winning material. But winning material is not so easy either, because the two elephants can stalemate each other, the two camels can stalemate each other, horses can stalemate each other, and so on down the line. Equal forces are more likely to cancel each other out than to have one side or the other gain an advantage.

Arimanator mentioned this cancellation in the initial post, and this is the key point. If I have a camel and my opponent does not, I will angle for a position in which our elephants are locked in a struggle so that my camel can operate elsewhere as the strongest piece. Having the strongest piece in some area is what leads to material gain.

In the endgame, however, I care much less about being able to capture pieces, because goal threats matter so much more. In the endgame, there is often not time to make captures even when one has the power to do so. Then the number of pieces matters more than their strength.

Just for the interest of the bot programmers, I would like to come up with a formula for material advantage based on all the remaining pieces, which values quality over quantity on a crowded board and quantity over quality on an empty board. This is worth some more thought.

Title: Re: The relative value of pieces in Arimaa
Post by omar on Apr 27^th, 2005, 2:45pm

Don Dailey and I once discussed this while he was working on bot Occam. We came to the conclusion that the value of a piece is highly determined by what other enemy pieces are around it (basically within 4 steps of it). If a dog is in one corner of the board with nothing stronger than another dog in proximity, then it is basically the elephant in that area. But for a program to actually value pieces that way could be disastrous. It might leave want to exchange its horse which is close to stronger enemy pieces for the opponents dog that is not close to stronger enemy pieces. So at one point we thought of having local and global values for the pieces. The local value being determined by the proximity of other opponent pieces and the global value fixed based on the overall rank of the piece. But still there were so many quirks that Don never actually tried implementing it.

Title: Re: The relative value of pieces in Arimaa
Post by Fritzlein on Apr 28^th, 2005, 5:34pm

Omar, I think your point (and Arimaanator's) is getting to the heart of the matter. What matters is the strongest piece locally, but unless the strongest local piece is an elephant, the opposing elephant can swing by and make the formerly strongest piece impotent. Non-elephant pieces need to consider the mobility of every stronger opposing piece before going on the attack, but if all the stronger pieces seem to be tied up in one way or another, the remaining pieces are effectively promoted in strength.

When it is phrased that way, I can see how to use it as a tool in evaluating the position in a couple of ways. Each strong piece needs to be assigned a mobility number which expresses how much it will hurt the controlling player to move that piece away from the trap it is currently near.

Also one can consider the value of trades in mobility as well as the value of trades in pieces. Do I want my elephant to be tied up strongly with the opposing elephant, or do I want both of us to have the option to break away? There are things that one can do to cement an elephant stalemate as being even more impossible for either side to leave, and whether or not one want to do that depends on the rest of the board.

In our postal game, Omar, since the opening when I got a camel for a horse and a cat, I have wanted our elephants to be tied up around the same trap so that my camel would be dominant on the rest of the board. Perhaps I will finally get my wish on move 47 if you don't want to abandon your rabbit on c6. On the other hand, if you can force that c6 rabbit to goal, my material threats are irrelevant, too little, and too late.

And that brings up my previous point about the value of material depending greatly on whether or not there are goal threats on either side. For as long as rabbits are threating to get to goal, I stand by my hunch that quantity is better than quality.

So what do you think of our game where I have taken MDR for HCRR? Do I have a material advantage? If so, is it relevant?

Title: Re: The relative value of pieces in Arimaa
Post by Fritzlein on Apr 29^th, 2005, 10:24am

Hehe, I guess I am jumping the gun to do the post-mortem while the corpse is still kicking. But sometimes analysis is all too easy after the fact. Once we know who has won the game, it is trivial to say "Omar's goal threat made Fritz's material advantage irrelevant" or "Fritz's material advantage eventually snowballed into a victory". We can fool ourselves into thinking we understand more than we do about the relative value of the camel vis-a-vis little pieces by just looking at past results. Only when we try to do a "pre-mortem" do we realize how little we know.

Title: Re: The relative value of pieces in Arimaa
Post by omar on May 5^th, 2005, 11:46am

on 04/28/05 at 17:34:56, Fritzlein wrote:

So what do you think of our game where I have taken MDR for HCRR? Do I have a material advantage? If so, is it relevant?

Well Karl, you are definitely building a bit of a material advantage, and it may become very relavent towards the end. I will have to try to keep up the rabbit preasure to have any chance.

But it is really too hard to evaluate with much certianty. I think I play a lot of my moves just by feel and can't really explain why I did it; and never really know for sure if it was the right move in the long run. I use logic only to the point of avoiding blunders and tactics. Beyond that strategy and planning kicks in and I just have to go on judgment (based on past experience) and intuition (a sense of knowing without knowing how one knows).

In chess I was never really able to get past the level of avoiding blunders and tactics to get into this zone of strategy and planning. With Arimaa I was able to avoid blunders and tactics after a hundred games or so. Actually Im not totaly cleared of that; I still make blunders and tactical mistakes especially in fast games, but the frequency has gone down quite a bit that I can begin to focus on strategy.