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        Arimaa >> General Discussion >> It's all about the E
        
(Message started by: JigglyPuff on Aug 21st, 2009, 10:51pm)
Title: It's all about the E
Post by JigglyPuff on Aug 21st, 2009, 10:51pm
After playing chess for nearly 20 years, I was introduced to Arimaa by a friend because I was complaining that chess had been played out creatively.  I was running into too many people at the club level who memorized openings 20 moves deep... and I wanted something which was new and rewarded creative instincts.  

Arimaa seems to be that.  I'm very happy with a lot of aspects of the game... it has simple concepts, it allows for personal styles and has the potential to be very deep, both strategically and tactically, I think.  

But I've got one big problem, which I'm worried may be a deal-breaker for me, and I need someone to talk me down.  It's the elephant.  

Everything in the game revolves around the elephant.  Basic tactics like the camel hostage are all about where the elephants are.  Trap control is all about which one the elephant's at.  Blockades, again... all about the elephant.  Frames?  Cool until the elephant shows up.  Races?  Yup, the elephant again.  

Coming from a chess background, having the whole game center around one piece is a little uncomfortable.  In that game, I could play my favorite openings, sometimes with very little participation from the queen.  Most often it would be about minor pieces working together to succeed, and the most powerful piece there could be captured by the most lowly piece, given the right circumstances.  There are even openings centered around the sole idea of harassing the queen.  

I understand I'm very new to the game, and some of the deeper strategies elude me.  But while studying the game, I've tried to look through games to see if I'm off-base, and unfortunately even games between top players seem to revolve around the elephant, though to a slightly lessened extent.  

So what am I asking?  I'm really asking to be talked off the ledge.  I'm on the verge of embracing this game, and playing it and studying it as I did chess for so many years, but I can't get around one piece, which cannot be removed (except by gross blunder), which cannot be harassed, so dominating the field.  In chess, all of the pieces seem to work cooperatively, but here, there seems to be very little cooperation between pieces.  Instead, everyone runs in fear of the elephant.  

How does everyone else feel about the power of the big E?  Is it just that tactics and strategy for the game is in its infancy, and won't be discovered until later, like the blockade and pin in chess?  Or will the elephant always dominate the landscape to the point where strategy that doesn't involve the elephant will be pointless?  
Title: Re: It's all about the E
Post by Hirocon on Aug 21st, 2009, 11:29pm

on 08/21/09 at 22:51:10, JigglyPuff wrote:
Coming from a chess background, having the whole game center around one piece is a little uncomfortable.


*coughkingcough*

But seriously, neither elephant can be everywhere at once, and the other pieces are vital.  I'd be interested to see a match where one side has an elephant and eight rabbits, and the other side has everything except the elephant.  Most material evaluators here (http://arimaa.janzert.com/eval.html) seem to predict a huge advantage for the player with everything except the elephant.

Edit: thinking about this more, the side with E+8R would have no chance.  The elephant just wouldn't be able to defend all the traps at once, and the rabbits would get picked off very quickly.

Edit 2: Whether it's "all about the elephant" or not, Arimaa is a fantastic game and you should give it a closer look.
Title: Re: It's all about the E
Post by Adanac on Aug 22nd, 2009, 8:06am
That’s an interesting point that you raise.  Indeed, the opening phase of Arimaa is very Elephant-centric and the smaller pieces don’t usually become actively involved until much later.  But you’ll find that Elephants become relatively less powerful as the board becomes more complicated.  Arimaa is my favourite strategy game of all-time and my appreciation has grown deeper as I learned more subtleties about the game.  However, the one aspect of the game that doesn’t satisfy my personal taste is the opening phase (I much prefer the crazy tactics of the middlegame over the quiet subtleties of the opening).  I find Arimaa openings a bit passive compared to Chess, and they do revolve entirely around the position of the elephants, but at least there’s no memorization required  :)

After the smaller pieces become more active and rabbits start to advance and multiple traps are contested by Horses & Camels then you’ll see where Arimaa really shines.  And if the board gets really depleted and both sides have advanced rabbits then Arimaa becomes wildly tense & exciting.  Unlike Chess Pawns that blockade each other in small clusters in the endgame, Arimaa Rabbits become incredibly dangerous, especially if there are threats on both sides of the board.  By the middlegame, and certainly the endgame, the Elephants become less and less important relative to the other pieces and the advanced rabbits.

This game 71956 (http://arimaa.com/arimaa/games/jsShowGame.cgi?gid=71956&s=w) is one of my favourite - there were lots of tactical mistakes but there were also creative moves and it was unpredictable & exciting throughout.  As always, the elephants dictated the flow of the opening phase but as the game progressed it was the smaller pieces that generated the threats.  And, fittingly, the game was decided in the end by the smaller pieces on the east side while the elephants were isolated on the west side.  The comeback by UltraWeak is also one of the more spectacular that’s ever occurred in Arimaa.  

Incidentally, Blue22 always plays his opening this aggressively.  He’s probably the only player that’s never gotten into one of those passive Elephant-only back-and-forth push-and-pull types of openings that often occur.  Unfortunately, his relentlessly aggressive style often gets him into hot water early, and that’s why most players settle for the more passive Elephant-only focused openings.  But there have been new ideas by the top players in recent years that allow the horses and even the camels to become much more aggressive in the openings without compromising the position.
Title: Re: It's all about the E
Post by JigglyPuff on Aug 22nd, 2009, 9:54am
"This game 71956 is one of my favourite -" Posted by: Adanac

Actually, after watching that game, it kind of goes to my point.  

Even though you used this as an example of wild play with all of the pieces, at a rough guess, without counting, I would say nearly half the moves by the players involved an elephant move at some point.  I'm not sure the same could be said about horses or dogs or cats.

Again... I like the game so far.  I'm not giving up on it.   ;)

But right now it seems to me that every strategy revolves around what the elephant is doing or is about to do, what trap it controls, how far it is from the action, and how quickly you can get your pieces away from it.  And it's not a passive strength, either... elephants seem to be involved in almost every play, from the opening phase, through the middle, and right to the endgame.

One problem I see is that in chess, the pieces as a group are worth more than any other single piece.  For example, my two rooks can cause plenty more damage than a queen, under most circumstances.

Are there any games out there that demonstrate how a camel + horse can school an elephant?  Or two horses can be more powerful than a camel?  

Most of the Arimaa theory I've seen suggests that it's always the strongest free piece that has the advantage, due to the way traps work.  Cooperative piece play isn't nearly as important as having the strongest piece, or so it appears.  
Title: Re: It's all about the E
Post by JigglyPuff on Aug 22nd, 2009, 10:03am
Hmmm....  Just for kicks I was playing with that material evaluator.

I loaded up a gold elephant, two cats and a rabbit against a silver elephant, camel and a rabbit.

Virtually all of the evaluators see gold as being ahead.

Maybe later tonight when I'm free I'll have to experiment a little.  
Title: Re: It's all about the E
Post by omar on Aug 22nd, 2009, 10:41am
Hi JigglyPuff; welcome to Arimaa.

You are right that elephants appear quite invincible in Arimaa; especially since they cannot be captured, but in actual play you find that they are not so dominant as to overshadow the importance of other pieces and groups of pieces working together. A strategy based solely on an attacking elephant can be trumpeted by strategies that develop the other pieces and launch a multi-piece attack.

There have been games where my big E felt quite helpless and overwhelmed against a group of weaker pieces working together. In this postal game I thought I was doing pretty well, until blue22 launched a multi-piece attack and overwhelmed my elephant with just a dog and some advanced rabbits:
   http://arimaa.com/arimaa/games/jsShowGame.cgi?gid=51146&s=b

This game also shows another interesting feature of Arimaa. Because the object is to get just one rabbit to goal, the game does not become overly one sided as soon as one player gains a material advantage. This can lead to some very dramatic and suspenseful games which swing back and forth before being decided. For me it makes watching Arimaa games as much fun as playing them :-)
Title: Re: It's all about the E
Post by lightvector on Aug 22nd, 2009, 11:31am
Sure the elephant is strong, and more generally, the strongest free piece tends to dominate in Arimaa a lot more consistently than in chess.

I actually think that this stability of piece strength is a benefit to Arimaa. The fact that weaker pieces cannot force the capture of stronger piece, and that equal pieces tend to cancel each other out makes the game somewhat less tactical and more about fighting for long-term positional advantage. This opens up a great deal of strategic depth, and increases the importance of judging a position in more than just material and short term threats, which I find quite is one of Arimaa's greatest strengths.

You might also appreciate this alternate perspective on the game: it is not the case that Arimaa leaves no room for coordinating weaker pieces to overcome stronger ones. Rather, Arimaa is *all about* doing this. By tying down the opponent's stronger pieces with weaker pieces, as with frames, blockades, advanced rabbits, hostages held by pieces other than the elephant, you gain the upper hand on the balance of strength over the rest of the board. The fact that the "stronger pieces" tend to be the elephant doesn't change this fact.
Title: Re: It's all about the E
Post by mistre on Aug 22nd, 2009, 7:48pm
Jigglypuff,

Welcome to Arimaa!  I am sure that your concern over the Elephant will fade with time.  Yes, the E is moved more often than any other piece (it actually would be interested to have a % - but I don't think I have seen that calculated anywhere), but it is far from invincible.  I guess you haven't seen a game that incorporated an E-blockade (when an E can't move) as a strategy.  It actually can be easy to fall into that trap when you are first learning the game.  Against weaker opponents, you can easily win without an E (check out some of the handicap games on the wiki for example).

In the end game, the % of times that you can even move your E will go down because it will either be holding an enemy camel or horse hostage or the board will be so thin that you are forced to move other pieces to block rabbit threats or create some of your own.  The key point is that the E can't be everywhere at once.  Generally it can help at 1 or 2 traps, but the other side of the board will be wide open for Camel, Horses, and even Dogs to dominate in the later stages of the game.  I say give it 50 games and you will be convinced of the nearly unlimited depth of this game.  I have played 1200+ games of Arimaa and am still discovering new strategies and techniques just about every game.
Title: Re: It's all about the E
Post by jdb on Aug 22nd, 2009, 7:51pm

Quote:
Are there any games out there that demonstrate how a camel + horse can school an elephant?  Or two horses can be more powerful than a camel?  


Here is a position where a single rabbit is stronger than the elephant.

http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1164380026;start=7#7
Title: Re: It's all about the E
Post by aaaa on Aug 23rd, 2009, 5:08am
There is compelling evidence that a large number of Arimaa players start out overvaluing the quality of pieces relative to their quantity. Perhaps in light of that, it may require a slight leap of faith on the part of the potential neophyte skeptical of the strategic depth of the game due to a hierarchical preconception of it.
Title: Re: It's all about the E
Post by Arimabuff on Aug 23rd, 2009, 8:14am

on 08/23/09 at 05:08:26, aaaa wrote:
There is compelling evidence that a large number of Arimaa players start out overvaluing the quality of pieces relative to their quantity. Perhaps in light of that, it may require a slight leap of faith on the part of the potential neophyte skeptical of the strategic depth of the game due to a hierarchical preconception of it.

Correct me if I am wrong but a "potential neophyte" is someone who's never heard of the game yet, unless you're talking about someone about to embrace the Catholic religion and that would explain the "leap of faith" part.  :P ;) ;D
Title: Re: It's all about the E
Post by Fritzlein on Aug 25th, 2009, 8:49am
[SATIRE]

on 08/21/09 at 22:51:10, JigglyPuff wrote:
But I've got one big problem, which I'm worried may be a deal-breaker for me, and I need someone to talk me down.  It's the elephant.  Everything in the game revolves around the elephant.

I have a major problem with chess, and before I give up chess entirely, I need someone to talk me off the ledge.  You see, chess is all about the king.  If you don't take care of king safety, boom, you get checkmated, and the game is over.


Quote:
Coming from a chess background, having the whole game center around one piece is a little uncomfortable.

Coming from an Arimaa background, it's a little uncomfortable that I can lose a game of chess just by losing one piece.  Sure, in Arimaa I rely heavily on my elephant, but at least I can sacrifice my elephant to force a win if need be, and there are dozens of examples of that happening in the game database.


Quote:
Most of the Arimaa theory I've seen suggests that it's always the strongest free piece that has the advantage, due to the way traps work.  Cooperative piece play isn't nearly as important as having the strongest piece, or so it appears.

Most of the chess games I have seen show that whichever player's king gets surrounded by enemy pieces just loses, no matter what the rest of their pieces are doing.  This just makes chess too simple.  Queening a pawn or winning the other guy's rook isn't nearly as important as protecting your own king.


Quote:
Are there any games out there that demonstrate how a camel + horse can school an elephant?

I have watched hundreds of chess games, and I haven't seen even one example of where a player can sacrifice his king to win the game.  Heck, in one game I played the other guy let me take his queen and a rook for my king, and I still lost!  Can anyone show how chess isn't horrendously flawed in this way? ;)
[/SATIRE]

JigglyPuff, I'm glad you are interested in exploring Arimaa as a game that isn't creatively played out.  I appreciate your concern about the strength of the elephant, but I think you have miscast the problem.  It is very important to Arimaa strategy to understand that the elephant is dominant, but that isn't all you need to know.  Arimaa would indeed be broken if you jumped to be a 2000-level player the instant you had the elephant-dominance insight, but that doesn't happen.  It isn't enough.  You have realized something crucial, yet an infinite learning curve still awaits you.

You implicitly expressed exactly why chess is a great game:


Quote:
After playing chess for nearly 20 years [...]

Chess is awesome because you can play and play and play and it doesn't get old.  You have the insight that your king must be kept safe at all costs, but you aren't done learning.  You realize that you shouldn't put pieces where they can be taken in one turn, but you aren't done learning.  You discover forks, pins, skewers, and discovered checks, but you aren't done learning.  You appreciate the importance of mobilizing your pieces and controlling the center, but you aren't done learning, and so on and so forth.  You are never done learning about chess, which is why we will still play it centuries after its invention.

Arimaa is excellent for the same reason that chess is excellent.  You can't bust it with a single insight.  In spite of a large and growing communal knowledge about Arimaa, we don't all play the same way.  There remains a rich variety of styles and strategies to keep the experience interesting and necessitate further learning.

I hope you interested enough in Arimaa to start exploring those strategies.  If you do explore Arimaa, I am confident that the power of the elephant won't make you bored with the game.

Oh, and one minor point to wrap up:


Quote:
For example, my two rooks can cause plenty more damage than a queen, under most circumstances. [...] Can two horses can be more powerful than a camel?

As the first trade of the game, two horses are more powerful than a camel by somewhat more than two rooks are more powerful than a queen, although positional considerations can tip the balance in Arimaa as well as chess.
Title: Re: It's all about the E
Post by JigglyPuff on Aug 25th, 2009, 8:27pm
I appreciate everyone's input over the past couple of days.  I see that there are players who are passionate about the game and are willing to take the time to talk me down off the ledge.

I think that's cool and I wanted to thank everyone for their kind replies.

I downloaded a little Arimaa game so I could play on my laptop while at work, and I've read up a little and plan on ordering the Begining Arimaa book to see what else I can learn.

I'm also happy to see that folks that have been playing a long while find that the pieces work synergistically together, but, without trying to argue, I still have the same feeling I had initially.

Everything seems to revolve around the elephant.   ;)

I appreciate omar's link to his game, and I watched it in full... and it was indeed a good game.  But then I went back and counted the number of times the elephant participated in a move.  

Out of roughly a hundred moves between the two sides, the elephant moved at least once in 47 of them.  Nearly half of all moves involved the elephant.  

Now, I didn't keep track of how many squares an elephant moved during each of the four-segment turns, but I would guess that this number would be very high, as well.  And toward the endgame, it tailed off a little, but was still involved.

And that's where I'm a little uncertain about the game.  Any strategy game that has one piece on the board shuffling to and fro in 47 out of 100 moves may be a little out of balance.  

Fritzlein presents his reasoning about the importance of the king in chess, but any player who finds their king is participating in anywhere near as many moves is going to be in lots of trouble.  The same goes for the queen.  I think what has made chess such a durable game is that synergism between the pieces... big or small, they all play their part.  No piece needs to be touched nearly as much as the elephant does.

Now, not for a moment am I saying this makes Arimaa a bad game.  I find it fascinating, and I'm kind of hooked on it now.  And I'm certainly not trying to argue and convince anyone I'm right.  

But right now I'm at that stage where I would like to make Arimaa my chess substitute for the next 20 years... only I'm reluctant to grab that elephant every other move.   :(
Title: Re: It's all about the E
Post by The_Jeh on Aug 25th, 2009, 8:33pm

on 08/25/09 at 20:27:13, JigglyPuff wrote:
But right now I'm at that stage where I would like to make Arimaa my chess substitute for the next 20 years... only I'm reluctant to grab that elephant every other move.   :(


The elephant is like that little ball in a can of spray paint. It keeps the game fluid. But you don't have to take my or anyone's word for it, nor do I think it is best that you do. Play the game for a few months - you won't lose anything by doing so. Then make your own judgment as to whether the game feels right. We who have played hundreds and hundreds of times do not fear what you will decide.
Title: Re: It's all about the E
Post by JigglyPuff on Aug 25th, 2009, 8:36pm
Oh, and I should probably add quickly that even though I'm using chess as a comparison in my posts, I don't expect Arimaa to BE chess.

I love chess for what it is, but as I mentioned in my original post, it's got it's problems.  

What I think it does right, though, is piece cooperation, that that's the main reason I continue to use the comparison.  I like a lot of things about Arimaa:  it's simple but deep, it's fresh, it's open to creativity and experimentation.

But my one concern, for me at least, is a biggie.  

47 moves out of a hundred is a lot.  I'm having a hard time getting around that.   :)
Title: Re: It's all about the E
Post by JigglyPuff on Aug 25th, 2009, 8:43pm

on 08/25/09 at 20:33:57, The_Jeh wrote:
But you don't have to take my or anyone's word for it, nor do I think it is best that you do.


I don't intend to.  

I wondered originally if others had the same concern I did, especially veteran players who had a better grasp of strategy than I did.  

I'm very relieved to see that's not the case.  Had there been a lot of posts here saying, "Yeah, I've played the game for three years now, and there's not much else going on but that d**n elephant" I would probably pack my bags and head on out.

I'm really happy to see that after playing for a long while, others feel a deeper sense of unity between the pieces.  I'm going to keep playing and hope I get to the same point.

Time will tell.  It's a good sign when everyone rallies around the game, though.   ;D
Title: Re: It's all about the E
Post by Arimabuff on Aug 26th, 2009, 8:01am

on 08/25/09 at 20:43:11, JigglyPuff wrote:
I don't intend to.  

I wondered originally if others had the same concern I did, especially veteran players who had a better grasp of strategy than I did.  

I'm very relieved to see that's not the case.  Had there been a lot of posts here saying, "Yeah, I've played the game for three years now, and there's not much else going on but that d**n elephant" I would probably pack my bags and head on out.

I'm really happy to see that after playing for a long while, others feel a deeper sense of unity between the pieces.  I'm going to keep playing and hope I get to the same point.

Time will tell.  It's a good sign when everyone rallies around the game, though.   ;D

To tell you the truth I never thought of counting the number of elephant moves in a game before. To me it would be like counting the number of brush strokes in a painting  by Van Gogh or the use of the letter "a" in Victor Hugo’s literature , kinda pointless and missing the big picture... by light years.

I've never heard of a piano player who would say I don't like that piece from Chopin because I have to hit that key far too many times for my taste…
Title: Re: It's all about the E
Post by Fritzlein on Aug 26th, 2009, 9:42am

on 08/25/09 at 20:27:13, JigglyPuff wrote:
 Any strategy game that has one piece on the board shuffling to and fro in 47 out of 100 moves may be a little out of balance.
 
The preponderance of elephant moves is a superficial characteristic that one could suspect is related to more fundamental characteristics such as strategic depth, scope for creativity, etc.  But supposing that it isn't related to deeper problems, I don't see how the dominance of the elephant is in itself a flaw, or why a good game would need to have all pieces be moved equally often.

Sure, it could be that having the elephant involved in many moves makes it easy to find the right move.  It could be that the dominance of the elephant means that the position of the other pieces hardly matters.  It could be that the answer to every question is "move your elephant."  But it doesn't, it doesn't, and it isn't.  I'm glad that you expect such issues to be decided by practice rather than by argument, and that you are willing to give Arimaa a try.  :)

In short, I am not trying to talk you out of a misconception about the Arimaa elephant.  I am trying to talk you out of fixating on a superficial feature of Arimaa play as a fundamental measure of Arimaa's quality as a game.
Title: Re: It's all about the E
Post by jdb on Aug 26th, 2009, 10:43am

on 08/26/09 at 09:42:50, Fritzlein wrote:
Sure, it could be that having the elephant involved in many moves makes it easy to find the right move.  It could be that the dominance of the elephant means that the position of the other pieces hardly matters.  It could be that the answer to every question is "move your elephant."  But it doesn't, it doesn't, and it isn't.  I'm glad that you expect such issues to be decided by practice rather than by argument, and that you are willing to give Arimaa a try.  :)


Jigglypuff does have a point. It is a reasonable rule of thumb to check elephant moves first.
Title: Re: It's all about the E
Post by Fritzlein on Aug 26th, 2009, 11:45am

on 08/26/09 at 10:43:08, jdb wrote:
Jigglypuff does have a point. It is a reasonable rule of thumb to check elephant moves first.

I'm not sure how we are disagreeing.  Going back to my earlier post, I concede that elephant dominance is an important insight, but claim that there is still an inexhaustible learning curve after having realized that.  We wouldn't want to create a game where there are no rules of thumb, and no insights to be had.  We merely require that no simple insight "busts" the game, and makes it uninteresting for people who have had that insight.
Title: Re: It's all about the E
Post by mistre on Aug 28th, 2009, 8:01am
One area that is pretty much unexplored in Arimaa to date is to take too equally rated players and have one play without his E and the other without some combination of pieces that are of general strength of the E by itself.  In this way we could see how such a game would develop and in particular how the player without the E would approach the game.  

Also, as far as how often the Elephant moves, I guess I never gave it much thought and did not see it as an issue.  A good player needs to figure out HOW and WHERE to move the Elephant.  A beginning player may read the rules, see that the E is the strongest piece and move his E all over the place only to realize that he is wasting moves as his E will either be out of position, blocked, or arrive too late to protect a trap.  Arimaa is about positioning of pieces just as much if not more than it is about strength of pieces. That is what makes it so fascinating.  
Title: Re: It's all about the E
Post by Arimabuff on Aug 28th, 2009, 3:18pm

on 08/28/09 at 08:01:22, mistre wrote:
One area that is pretty much unexplored in Arimaa to date is to take too equally rated players and have one play without his E and the other without some combination of pieces that are of general strength of the E by itself...

Well, given that in the bait and tackle approach, you sacrifice one piece and then commit at least 7 pieces to the sole action of blockading the elephant and still win the game then my guess would be that at least 8 and maybe even 9 pieces of various strength would be necessary to even the chances, between two players of equal strength that is. You can also notice that in the case of the blockade you are constantly threatened by a breaking of the blockade by the opponent, which you would be spared in a case of an initial sacrifice. So I am afraid that the privileged of having the strongest piece on the board is worth a lot and would reinforce the "It's all about the E" theory.
Title: Re: It's all about the E
Post by Simon on Aug 28th, 2009, 7:07pm

Quote:
Well, given that in the bait and tackle approach, you sacrifice one piece and then commit at least 7 pieces to the sole action of blockading the elephant and still win the game then my guess would be that at least 8 and maybe even 9 pieces of various strength would be necessary to even the chances


It's a mistake to think of the pieces in a blockade as doing nothing beyond holding in the elephant. In the early game, only a few pieces tend to be activated, the others sit around blocking the opponent from taking over the player's traps (and from sending a rabbit to goal, which would be a big danger with 8 or 9 pieces gone). Those stay-at-home small pieces can do their jobs almost as well as part of a blockade.
Title: Re: It's all about the E
Post by lightvector on Aug 28th, 2009, 7:37pm
I think it would be cool to see an experimental game with an initial sacrifice of E for MHH. All the material evaluators prefer the side with the MHH, and it would seem intuitively hard for the E to make any substantial threats when the MHH dominate every other piece besides the E. I expect that between evenly matched players, the E would get overloaded very fast.

If this is a bit too unbalanced, E versus MHD seems interesting too. The various evaluators at http://arimaa.janzert.com/eval.html are somewhat less in agreement on which side has the advantage. The extra horse would probably make a huge difference for the E side, since it can't be pushed by the opposing horses.
Title: Re: It's all about the E
Post by ocmiente on Jan 13th, 2010, 2:02pm
Adanac,

I was in the process of moving my response to another topic, but you beat me to it!  

The topic of playing with a rat or a mouse seems different enough from the original post, that I figured it would be better to start a different thread.  That thread is here:
http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1263419748

Your reply makes a lot of sense.  Generally, I think that adding a rat would change the game so significantly that the strategies would have to be reworked completely - but I'm not sure - since I haven't tried it.  So, the new thread is there in case someone is around who can shed some light on the topic.
Title: Re: It's all about the E
Post by Adanac on Jan 13th, 2010, 2:19pm

on 01/13/10 at 14:02:02, ocmiente wrote:
Adanac,

I was in the process of moving my response to another topic, but you beat me to it!  

The topic of playing with a rat or a mouse seems different enough from the original post, that I figured it would be better to start a different thread.  That thread is here:
http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1263419748

Your reply makes a lot of sense.  Generally, I think that adding a rat would change the game so significantly that the strategies would have to be reworked completely - but I'm not sure - since I haven't tried it.  So, the new thread is there in case someone is around who can shed some light on the topic.


OK, I've moved my post over to the new thread.
Title: Re: It's all about the E
Post by JoeHead on Feb 16th, 2010, 7:18am
Interesting analogy with Chopin.

I am extreme fan of Chopin and have all his work on my computer.
So hitting one key a lot of times may be bad? Like moving an E many times means boring?
Chopin wrote a piece, one of the best piano pieces ever written. It is called Prelude no. 15 d flat major, sostenuto.
In this piece you play one key almost from begining to the end and yet that it what gives the beauty to music. The underlying "rain drops" (although chopin himself didnt like the name) gives fluid. Other notes add to the melody and dynamics, but you still now where are you. Playing forte parts , piano parts you know that all music is linked. It is not torn, no, it is one compact beautiful piece of music - ARIMAA!!!!

:-)))
PS: if you want to actually listen the piece, you have to find the best available interpretation, because musician make often the song sad, BUT it is not at all. It must be played with fluid. From many, many versions I know, only one is absolutely the best, the most correct, the most correctly expressing the true nature of the song.
http://www.extropygroup.com/vanity%20audio/piano_recordings.htm
and then find prelude no 15 d flat major "raindrop"
Title: Re: It's all about the E
Post by Fritzlein on Feb 16th, 2010, 8:17am
I am blessed to have a pianist for a wife.  She is familiar with that Chopin prelude you mention, JoeHead, and she is playing it for me now thanks to your post.  Yes, that A-flat does get played about a jillion times, and it's a gorgeous piece.  Thanks for the fine analogy, Arimabuff!
Title: Re: It's all about the E
Post by Victorwss on Feb 21st, 2010, 8:59pm
The thread is somewhat old, but I think that JigglyPuff's observation is valid.

Chess has its deficiencies, but this does not imply that arimaa does not have some deficiencies too.

The fact that half of the times you are moving the elephant and that most tatics envolves around the elephant is a deficiency in arimaa.

Maybe if the elephant (or even the camel) had some sort of handicap and could be pulled and pushed some way, the game could me more interessing. Lets suppose some variants:

1. Lets suppose an arimaa variant where one move of the elephant is equivalent to two steps, I think that arimaa would be much more interesting.

2. Lets suppose another variant where the elephant could be pulled or pushed when adjacent to two opposite horses or horse+camel, this would be very interesting too.

3. Lets suppose still yet another variant where a piece may push or pull an enemy piece of equal strenght, but only if this is the only action did in the turn. This could be interessing because even rabbits could push/pull opposite rabbits.

In all that variants, the camel and the horses would became more important, equilibrating better the power of the elephant.

So, though "move the elephant" is not the answer to everything in arimaa, it is always one of the first things to think about and is the most frequent answer. So, in my opinion, surely this is a deficiency in arimaa.

Finally, I observe that arimaa has another deficiency too (in my opinion): cats and dogs has little to do in the game.

However, besides its deficiencies, arimaa is still a great game.
Title: Re: It's all about the E
Post by Fritzlein on Feb 22nd, 2010, 7:31am

on 02/21/10 at 20:59:09, Victorwss wrote:
So, though "move the elephant" is not the answer to everything in arimaa, it is always one of the first things to think about and is the most frequent answer. So, in my opinion, surely this is a deficiency in arimaa.

Victorwss, we all agree that the elephant is very important in Arimaa and that it gets moved often.  We don't all agree that that is a problem.  Can you explain a little bit more why you think it is a problem?  Is it just too easy for you to find the right move?  Do you win every time that you move your elephant a lot?  Or is the "deficiency" simply a matter of taste, about which there is nothing to say?

Consider this argument: Although Chopin's Raindrop Prelude has many notes besides A-flat, it is the most frequently played note and it is being played most of the time.  Some notes don't even get played at all!  So, in my opinion, this is a deficiency in Chopin's Raindrop Prelude.  Maybe we can experiment with a variation where we only play half of the A-flats that Chopin put in.

To me my argument seems to jump from true facts straight to an unrelated conclusion without anything in the middle to connect the logic.


Quote:
However, besides its deficiencies, arimaa is still a great game.

I'm glad you like it!  My guess is that learning more and more about Arimaa makes the game seem less and less boring.  This is not true for every game; some games seem interesting at first and only become boring once you know how to play them well.  But Arimaa seems fairly boring on the surface and then gets more and more interesting as you understand its depth.  That is my opinion, of course, but I think it is the experience of other players as well.  We have seldom had a player quit Arimaa because they thought there was "nothing left" to it.
Title: Re: It's all about the E
Post by RonWeasley on Feb 22nd, 2010, 9:42am
Quidditch usually seems to be all about the golden snitch if you've read Harry's books.  If you play keeper or chaser, the game is much more about the quaffle. which the spectators can follow more easily.  If you play on a team without talented beaters, the bludgers can be the most important thing.

Like arimaa, quidditch at a high level is all about the coordination of your efforts.  And once you have reached a certain age, you realize most of the coordination is centered around the beer.
Title: Re: It's all about the E
Post by Victorwss on Feb 24th, 2010, 5:27pm

on 02/22/10 at 07:31:28, Fritzlein wrote:
Victorwss, we all agree that the elephant is very important in Arimaa and that it gets moved often.  We don't all agree that that is a problem.  Can you explain a little bit more why you think it is a problem?  Is it just too easy for you to find the right move?  Do you win every time that you move your elephant a lot?  Or is the "deficiency" simply a matter of taste, about which there is nothing to say?

Consider this argument: Although Chopin's Raindrop Prelude has many notes besides A-flat, it is the most frequently played note and it is being played most of the time.  Some notes don't even get played at all!  So, in my opinion, this is a deficiency in Chopin's Raindrop Prelude.  Maybe we can experiment with a variation where we only play half of the A-flats that Chopin put in.

To me my argument seems to jump from true facts straight to an unrelated conclusion without anything in the middle to connect the logic.

I'm glad you like it!  My guess is that learning more and more about Arimaa makes the game seem less and less boring.  This is not true for every game; some games seem interesting at first and only become boring once you know how to play them well.  But Arimaa seems fairly boring on the surface and then gets more and more interesting as you understand its depth.  That is my opinion, of course, but I think it is the experience of other players as well.  We have seldom had a player quit Arimaa because they thought there was "nothing left" to it.


Comparing arimaa to Chopin's Raindrop Prelude is non-sense. They are things completely different in nature. Is something like to comparing an orange with a cell phone.

What is one of deficiency in chess? Lets say, the opening follows some few memorizable patterns that can be compiled in an opening book. Why is this a problem? Instead of learn how to play with talent, people and computer just recognize the patterns and use the pre-built solutions.

Other chess deficiency: Due to the rule that white always start, white normally gets a significant advantage over black and is more likely to win than black.

In arimaa the elephant moves frequently. This can be considered a deficiency because suggests to people and computers to think about the elephant first. So, a computer using some sort of alpha-beta search could consider the elephant moves first to get a better pruning in the search tree. This leads to a bit of mechanical playing in opposition of intelligent life playing.

The additional observed pattern that cats and dogs rarely moves because they have few to do in the game leads people and computer to further machanical thinking. A computer may consider dogs and cats moves last, because they are more likely to be pruned in the search. Humans frequently don't care too much in thinking about cats and dogs because they know that will use they in the game just a few.

Arimaa is a very good and intelligent game, but this does not mean that it could be even better with just minor changes in the rules. If the game was not so centered around the elephant and if cats and dogs had more to do, I bet that arimaa would be much better and computers much weaker.

However these deficiencies (or whatever you prefer to call them) are small enough to not lead to significant problems that we see in chess, checkers or tic-tac-toe. However small or not, they are still there.

Another thing I was thinking about is the initial positing of the pieces. Although the distribution may be very random, we see that people and computers follows some patterns that significantly reduces the number of likely-to-see opening positions and so there are just a few that are likely to occur with just some minor variations. For example, if we see both elephants in the same column, gold may start moving his elephant four steps forward blocking silver's elephant. We very frequently see the elephant and the camel in the central rows, the horses in the sides and 6 to 8 rabbits in the first row, specially for gold which does not know how silver will plot his pieces. In the other hand, Silver normally has few non-stupid options to choose how to plot their pieces in response to the way that gold plotted. This sort of commons opening patterns may lead to the development of an arimaa opening book someday.
Title: Re: It's all about the E
Post by Fritzlein on Feb 24th, 2010, 6:25pm

on 02/24/10 at 17:27:42, Victorwss wrote:
In arimaa the elephant moves frequently. This can be considered a deficiency because suggests to people and computers to think about the elephant first. So, a computer using some sort of alpha-beta search could consider the elephant moves first to get a better pruning in the search tree. This leads to a bit of mechanical playing in opposition of intelligent life playing.

Thanks for the further explanation.  The power of the elephant might lead players to automatic moves and therefore might take the thinking and creativity out of the game.  I can see the concern.  I would agree that this was a real problem if there was an absolute rule, i.e. if players always knew that moving the elephant was a good idea.

However, although I can see how theoretically a very powerful piece could make the play of the game mechanical, I don't see that it actually does affect Arimaa that way.  For example, look at move 30g in the ongoing postal game TheMob vs. Fritzlein.  If the Mob had mechanically thought that they must do something with their elephant, they would have missed the fact that their elephant was already on an excellent square at e5, even though it wasn't directly attacking or defending any trap.  Moving the gold elephant in any direction on 30g would have put it on a weaker square.  So you can't just think that because the elephant is strong you must always be moving it around.  It isn't that easy.

You are quite right that humans and computer alike should pay great attention to the elephant.  But fortunately, that doesn't tell us what to do with the elephant.  Should I move it here or there or just leave it still?  There is no simple rule for it.  Therefore, there is still room for truly intelligent play.


Quote:
The additional observed pattern that cats and dogs rarely moves because they have few to do in the game leads people and computer to further machanical thinking. A computer may consider dogs and cats moves last, because they are more likely to be pruned in the search. Humans frequently don't care too much in thinking about cats and dogs because they know that will use they in the game just a few.

Certainly cats and dogs are less important than the elephant, but it is not true that they can be ignored, or that it doesn't matter whether it is a cat or a dog on a given square.  For example, look at this game (http://arimaa.com/arimaa/games/jsShowGame.cgi?gid=135491&s=w) that I just played against chessandgo in the World Championship.  I purposely set up a dog on the c7 square, not a cat or a rabbit.  Chessandgo commented after the game how important this decision was.  Look at the position before Gold's move 7g.  If I had a cat defending the c6-trap, the Gold dog from c4 could just push it away and I would be completely losing the game.  But since I have a dog there, the Gold camel has to come from the opposite side of the board to make a threat, which means I am winning.

Once again, if it did not matter at all what the cats and dogs do, I would have to agree with you that Arimaa is less interesting and requires less thoughtful play.  But, just like with the elephant, there is no simple rule to let you avoid thinking what to do with cats and dogs.


Quote:
Arimaa is a very good and intelligent game, but this does not mean that it could be even better with just minor changes in the rules.

I agree that we should not assume that Arimaa is perfect just because it is good.


Quote:
If the game was not so centered around the elephant and if cats and dogs had more to do, I bet that arimaa would be much better and computers much weaker.

I quite disagree that the changes you propose would make Arimaa better and make computers weaker relative to humans.  The fact that an elephant can't be pushed or pulled in any circumstance is a fact that benefits human strategy more than it benefits computer calculation.  In order to win, computers need sharp changes to the position, and they need humans to say, "Oh, I didn't see that!"  The fact that there are ways for humans to understand Arimaa strategically is what allows them to play Arimaa better than computers.

For example, the backbone of Arimaa strategy is the camel hostage.  If a horse and camel together could push an elephant, the camel hostage position would not be stable.  When there are no stable positional features, it is hard for a human to see further ahead than a computer can see ahead.

However, even though I think the changes you propose would not make Arimaa a better game or harder for computers, I have to admit that I can't really tell without playing a lot of games.  The rules themselves don't make it obvious what strategies will be "in there" at a high level of play.  Your proposal would destroy the camel hostage strategy, but maybe it would create a new strategy that is even deeper.  It is impossible to tell from the rules alone.

So when I disagree with your rule changes, it is half in ignorance.  I know that the Arimaa rules work, but I don't know whether your rules work or not.  I don't think there is any problem caused by the powerful Arimaa elephant, but that doesn't mean I think Arimaa is perfect, and I admit the possibility that your suggested rules could have marvelous benefits that I simply can't see without trying them.


Quote:
For example, if we see both elephants in the same column, gold may start moving his elephant four steps forward blocking silver's elephant. This sort of commons opening patterns may lead to the development of an arimaa opening book someday.

Yes, standard Arimaa openings may happen some day, and I am curious to see whether they will or not.  They haven't happened yet, though.  For example, the opening setup I just used against chessandgo in the game I linked above was one I had never used before.  Probably the position after chessandgo set up his pieces and I set up mine was a position that had never occurred between any two players ever in 135,490 previous games on the Arimaa server.  Such a thing could not happen in chess where after each player makes a move only 400 positions are even possible.  So if you don't like memorized openings from chess, I believe that Arimaa will provide you some relief.
Title: Re: It's all about the E
Post by omar on Feb 25th, 2010, 9:30pm
Victorwss, your variations do sound interesting and I never thought to try those while play testing Arimaa. The closest I came to reducing the power of the elephant was allowing the rabbits to push/pull/freeze the elephant. That version didn't seem to work. See my posting of Jan 15, 2010:
http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1263419748

Replacing one rabbit with a mouse has been suggested before and even played tested by IdahoEv and ocmiente. However, I would not have even considered that when I was play testing Arimaa since it would not have fit one of my original goals for Arimaa being that it should be playable with a standard chess set.

You are most likely correct that within the space of games possible with the Arimaa mechanics and using only a standard chess set the variant I picked is probably not the optimal in terms of being the most difficult for computers. But when you have multiple criteria it is difficult to optimize all of them and there will have to be some trade-offs. In addition to being playable with a standard chess set and being difficult for computers I was also trying to make it easy to learn and fun and interesting to play. The easy to learn criteria always made me not want to add any more rules than what was absolutely necessary. And of course the fun and interesting criteria is very subjective. Although one somewhat objective aspect of it is that a game should not take too long to finish. I strongly suspect that variants which are more difficult for computers would also take longer to finish. So the particular version of Arimaa we play does an amazingly good job of trying to achieve these four goals in a well balanced way.

When I released Arimaa I think I was more confident of how well it met my goals than I should have been. Only later did I come to realize how lucky I got. There was no way my play testing could tell me if the game was deeply flawed. I could only look for obvious flaws. Only after the game has been played many, many times at very strong levels of play can we begin to say that it is not deeply flawed. It could have turned out that a camel hostage gave the hostaging player such an advantage that they always win and if say the first player could alway take a camel hostage then the game would be seriously flawed. It is only after intense playing that we come to know about the deeper characteristics of the game.

I've come to think of the rules of a game to be analogous to the genes of a specimen. You can't tell by looking at the genes what the final organism is going to be like. Those genes have to be expressed in the slow and meticulous genotype to phenotype mapping process. Only then will you know it's characteristics and whether or not it is a mutant and can't survive. Likewise it is hard to tell the nature of the game and whether it is flawed or not by looking at the rules. We have to play out the rules, create a collection of games and analyse them to begin expressing it. Only then can we begin to see if it might be deeply flawed. I guess in this analogy that makes us players the ribosomes :-)

With the current Arimaa rules we are beginning to build some confidence that it is not deeply flawed after having played thousands of games. However even slight changes to the rules can completely alter the game and we have to start over. So even being the creator of the game I don't think I can easily alter the game anymore. The genie is out of the bottle and the only thing that can stop this variant of Arimaa from continuing to build it's dominance is if we find that it is flawed.
Title: Re: It's all about the E
Post by Victorwss on Feb 26th, 2010, 1:07am

Quote:
Thanks for the further explanation.  The power of the elephant might lead players to automatic moves and therefore might take the thinking and creativity out of the game.  I can see the concern.  I would agree that this was a real problem if there was an absolute rule, i.e. if players always knew that moving the elephant was a good idea.

However, although I can see how theoretically a very powerful piece could make the play of the game mechanical, I don't see that it actually does affect Arimaa that way.  For example, look at move 30g in the ongoing postal game TheMob vs. Fritzlein.  If the Mob had mechanically thought that they must do something with their elephant, they would have missed the fact that their elephant was already on an excellent square at e5, even though it wasn't directly attacking or defending any trap.  Moving the gold elephant in any direction on 30g would have put it on a weaker square.  So you can't just think that because the elephant is strong you must always be moving it around.  It isn't that easy.

You are quite right that humans and computer alike should pay great attention to the elephant.  But fortunately, that doesn't tell us what to do with the elephant.  Should I move it here or there or just leave it still?  There is no simple rule for it.  Therefore, there is still room for truly intelligent play.


Well, I said that it made the thinking a bit more mechanical. Players (both humans and computers) first consider moving the elephant because it is likely that it should be moved, but this does not means that they always should move the elephant nor to where. So, yes there is still a very large room for intelligent play.


Quote:
Certainly cats and dogs are less important than the elephant, but it is not true that they can be ignored, or that it doesn't matter whether it is a cat or a dog on a given square


I did not said that they can be ignored. If you just ignore they you will probably lose miserably. I said that they have few to do. I did not said that they have nothing to do. Normally, cats and dogs are very shy in the game and they function tends to be to obstruct the way of enemies pieces, protect traps and unfreeze allies pieces. Frequently their moves are just to keep they alive and protected from stronger enemies pieces or to support stronger allies pieces. It is very unlikely to see they hunting or directly attacking and it is very common to see they staying quiet in their places for numerous turns.


Quote:
Yes, standard Arimaa openings may happen some day, and I am curious to see whether they will or not.  They haven't happened yet, though.  For example, the opening setup I just used against chessandgo in the game I linked above was one I had never used before.  Probably the position after chessandgo set up his pieces and I set up mine was a position that had never occurred between any two players ever in 135,490 previous games on the Arimaa server.  Such a thing could not happen in chess where after each player makes a move only 400 positions are even possible.  So if you don't like memorized openings from chess, I believe that Arimaa will provide you some relief.


Yes, an opening book in arimaa whould be much more larger and shallow than a chess opening book. But it is still possible to have some standardized well-known frequently used openings. The start positions does not need to be identical, just similar. Get some frequently used start position, switch a dog with a cat or a cat with a rabbit and probably few things would be different in the opening. It is true that that diffence may be anywhere between decisive and irrelevant in the middle game, but in the opening it is much more likely irrelevant, and so, the same opening tatics would be applicable.


Quote:
Replacing one rabbit with a mouse has been suggested before and even played tested by IdahoEv and ocmiente. However, I would not have even considered that when I was play testing Arimaa since it would not have fit one of my original goals for Arimaa being that it should be playable with a standard chess set.


Their tests sounds very interessing. There seems to be some stone-scissors-paper pattern which casts the game strategies very complex. And I think that this is something harder for computers, because this jams and twists the calculation of the relative value of the pieces, except when the elephant or the mouse dies.


Quote:
With the current Arimaa rules we are beginning to build some confidence that it is not deeply flawed after having played thousands of games. However even slight changes to the rules can completely alter the game and we have to start over. So even being the creator of the game I don't think I can easily alter the game anymore. The genie is out of the bottle and the only thing that can stop this variant of Arimaa from continuing to build it's dominance is if we find that it is flawed.


I don't think that Arimaa is flawed and I don't see any evidence of this. It is much more solid than chess and checkers. Chess has a lot of defficiencies and has some evidences that it is possibly flawed, however it is still a great game. Arimaa has much fewer defficiencies than chess, and so is a very good game.

These variants I suggested earlier where thought when I was posting just to give an example of how minor changes to the rule could change the game to something better or worse. I did not tested that rules nor thought about them deeply, was just the three firsts variations that went out of my mind. However, if you think that would be interessing to test them, it would be nice. :)

Arimaa is great the way it is, does not needs to be fixed. However, Arimaa's defficiencies must be studied and that was the objective of my posts: to point out and analyze some of such defficiencies. I am not asking for changes in the rules!
Title: Re: It's all about the E
Post by novacat on Feb 26th, 2010, 5:56am

on 02/26/10 at 01:07:46, Victorwss wrote:
Normally, cats and dogs are very shy in the game and they function tends to be to obstruct the way of enemies pieces, protect traps and unfreeze allies pieces. Frequently their moves are just to keep they alive and protected from stronger enemies pieces or to support stronger allies pieces. It is very unlikely to see they hunting or directly attacking and it is very common to see they staying quiet in their places for numerous turns.


All pieces in Arimaa obstruct the way of enemy pieces (includes framing), protect traps (including taking control of enemy traps), unfreeze allied pieces, and attack weaker enemy pieces (except rabbits).  All pieces except the elephant support stronger allied pieces.  

Dogs and cats often support by defending the home traps when other allied pieces are attacking, thus they often do not move much but have an important function. They can be used as bait as well to offer a kill while gaining momentum in a race elsewhere on the board.  They can also attack, but most people don't use the dogs or cats extensively for this because it takes understanding and foresight that the people haven't developed.  If you look at http://arimaa.com/arimaa/games/jsShowGame.cgi?gid=135050&s=w you will see chessandgo uses his dogs very effectively.

There are more uses for dogs and cats, but the main thing I see is that people don't use them for active positions because they are easier to use for jobs that require little movement.  If cats and dogs were replaced with horses, most games would likely have a few horses that rarely moved.
Title: Re: It's all about the E
Post by Fritzlein on Feb 26th, 2010, 7:29am
J. Mark Thompson has an excellent essay (http://www.thegamesjournal.com/articles/DefiningtheAbstract.shtml) about what qualities an abstract strategy game should have.  He points out that there is a kind of contradiction between the need for depth and the need for clarity.


Quote:
Depth means that human beings are capable of playing at many different levels of expertise. For most board positions, until the last stages of the endgame, the puzzle of finding the best move should not be completely solvable.
[...]
But in addition to depth a good game must have clarity. Clarity means that an ordinary human being, without devoting his career to it, can form a judgment about what is the best move in a given situation.  [...]  In a game that lacks clarity, the player simply has no instincts.
[...]
if a usable algorithm is known which will always reveal the best move in any situation of a game, then the game's clarity is perfect, but it has lost all its depth.

To enjoy a game, we need it to be deep.  We need to have levels of thought.  There needs to be a ladder to climb.  If we had Elo ratings and everyone was about the same rating, outside observers would wonder what kind of game doesn't have any experts.

Also we need clarity.  If you can't write a strategy guide with rules of thumb like "rabbits are more valuable in the endgame", then the game feels inhumane.  People would get frustrated at the lack of guiding principles, and think you have to be an alien to understand how to play.

But there is a tension between depth and clarity.  Whenever something can be clearly expressed about a game, one should fear that it will make the depth of the game dry up.  For example, when I wrote that a key strategy of Arimaa was to overload the enemy elephant, i.e. tie the enemy elephant down to defense of one threat and then create a second threat elsewhere, IdahoEv said that sounded like it made Arimaa "too easy".

Superficially, the criticism is valid.  The more I can say about Arimaa strategy, the more it gives the appearance that we are near to figuring it out, or the appearance that Arimaa strategy can be put into an algorithm.  But in practice it turns out that as long as the strategies are still fuzzy enough, the clarity doesn't take away from the depth.

In terms of abstract game design, it would be a shame to think poorly of a game as soon as a strategy guide is published.  If reading any principle (e.g. "use strong pieces to make a frame, then rotate them out for weak pieces") spurs the thought that the game is too simple and therefore the rules need to be changed to make the strategy unreliable, then we could slip into strategy prevention mode.  Look, there is a player trying to execute Strategy X in every game, and it is helping him win.  Quick, we must changes the rules to make Strategy X no longer effective!  The ultimate goal of a game designer: stop a strategy guide from being written.  :P

But in reality we don't need to prevent a game from having clarity as long as the depth is still there.  The key thing to observe is whether everyone has to start playing Strategy X in order to compete, and if so, whether it makes the resulting games boring when everyone has caught on.  If the play is still varied, unsettled, and intense after everyone knows about Strategy X, i.e. if there are ways to counter it or variety within it, then all is well.

To bring it back to the forum topic, we all know the elephant is vastly powerful, and we're not bored yet!  :)  Arimaa seems to be one of the few games that can have a lot of clarity and a lot of depth at the same time.
Title: Re: It's all about the E
Post by JoeHead on Feb 26th, 2010, 8:35am
Quick look at amount of elephant steps
JoeHead

Introduction

There is a live discussion wheather moving elephant too often is bad for arimaa as a game. How much does the elephant move? The claimes were made without any statistical methodology. So I performed simple yet very effective statistical analysis. Now everybody will have starting point.

Method

World Championship 2010 games were used as a starting population. There were 48 games played up to this moment. From these 5 games were chosen randomly using excel function "randbetween( 1, 48 )". Number of plies of each chosen game was calculated. Final ply is: rabbit reaching the goal, resignation, time. Number of steps was calculated. Piece removal from the board was not recognised as a step. One ply can consist of 1 to 4 steps. Number of elephant steps during the game was counted. Then the ratio "Elephant Steps/Total steps in game". Next average of ratios in 5 games was calculated and finally 95% confidence intervals about the average using t-distribution with 4 degrees of freedom.

Results

Average number of plies in a sample: 66,2

95% confidence interval for number plies: 38,1 - 94,2

Average ratio of E steps: 0,249

95% confidence interval for ratio of E steps: 0,18 - 0,31

Discussion

Wide spread is caused by small sample size. Nevertheless it is still best possible estimate for true value to be captured 95% of times.
The game length is little lower then experience tells us because one randomly chosen game lasted only 27 plies.
From the data we can see that almost every fourth step is made by elephant. Also one should realise that majority of steps is done during opening. The shortest game in a sample had ratio 0,34. Other games had ratio around 0,22. As the game gets longer non-elephant pieces start their significant contribution.
These are data. How much enjoyment comes from the arimaa playing is subjective. This is answer to how much elephant actualy moves in the game.
Title: Re: It's all about the E
Post by lightvector on Feb 27th, 2010, 1:53am

on 02/24/10 at 17:27:42, Victorwss wrote:
In arimaa the elephant moves frequently. This can be considered a deficiency because suggests to people and computers to think about the elephant first. So, a computer using some sort of alpha-beta search could consider the elephant moves first to get a better pruning in the search tree. This leads to a bit of mechanical playing in opposition of intelligent life playing.

The additional observed pattern that cats and dogs rarely moves because they have few to do in the game leads people and computer to further machanical thinking. A computer may consider dogs and cats moves last, because they are more likely to be pruned in the search. Humans frequently don't care too much in thinking about cats and dogs because they know that will use they in the game just a few.

Arimaa is a very good and intelligent game, but this does not mean that it could be even better with just minor changes in the rules. If the game was not so centered around the elephant and if cats and dogs had more to do, I bet that arimaa would be much better and computers much weaker.


In regards to the computer vs. human strength, actually, my experience in coding for Arimaa and working on my bot seems to indicate that the opposite is true. One of the major advantages for Arimaa strategy, in regards to human strength against bots, is exactly the domination of the elephant. This allows for more stable positions, such as hostages, frames, elephant deadlocks, etc. Getting a bot to play with more than most primitive understanding of these features is a enormous obstacle, precisely because their value and their implications depend very precisely on complex and subtle variations in the position, and yet their stability makes them persist for potentially many moves, many orders of magnitude beyond resolving by standard search methods. The fact that the elephant can't be displaced by weaker pieces seems to be one of the key reasons that such long-term positional features can occur.

Anyways, I also don't believe that human vs. computer strength for a game necessarily has anything to do with how interesting the game is for people to play. But in the particular case of Arimaa, I actually do feel the same way here as well. It's extremely hard to tell how a game would play with alternate rules, as Fritzlein mentioned. But at least my own intuition says that if the elephant could be too easily threatened or overwhelmed by weaker pieces, and if weaker pieces could play more significant roles than they already do in attacking, then sure, more possibilities would now be allowed, but the human-understandable depth may not increase, or could even decrease, because one might have fewer stable positional patterns, and more tactical positions where strategic insight is less important than exhaustively reading out all the combinatorial possibilities.

I would agree with many others that have posted here that the quality of a game like Arimaa should not be judged just on a statistic showing that moving one piece is best several times more often than another. It should be on judged on whether a great deal of dynamics and possibilities for deep strategy remain and develop from such an observation, or whether such an insight threatens to make the game uninteresting or stagnant. For Arimaa, nothing could be further from the case right now, so in my opinion, there's no urgent need to fix anything.
Title: Re: It's all about the E
Post by jdb on Feb 27th, 2010, 7:03am

on 02/27/10 at 01:53:06, lightvector wrote:
In regards to the computer vs. human strength, actually, my experience in coding for Arimaa and working on my bot seems to indicate that the opposite is true. One of the major advantages for Arimaa strategy, in regards to human strength against bots, is exactly the domination of the elephant. This allows for more stable positions, such as hostages, frames, elephant deadlocks, etc. Getting a bot to play with more than most primitive understanding of these features is a enormous obstacle, precisely because their value and their implications depend very precisely on complex and subtle variations in the position, and yet their stability makes them persist for potentially many moves, many orders of magnitude beyond resolving by standard search methods. The fact that the elephant can't be displaced by weaker pieces seems to be one of the key reasons that such long-term positional features can occur.


I agree with this 100%. Well said.


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