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Subject: Arimaa is well on its way to becoming a classic. rss

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Fritz Juhnke
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J. Mark Thompson defines four axes on which to evaluate an abstract strategy game: depth, clarity, drama, and decisiveness. Arimaa scores well in all four, so well that it appears destined to take a place among the classics.

Player ratings on arimaa.com provide strong evidence for Arimaa's depth. Although Arimaa is less than four years old and the number of active players is under one hundred, player ratings span a wide range from 1100 to 2300.[*] The range widens every year as new strategies are unearthed. Established players who don't stay abreast of developments in Arimaa theory may easily fall back 100 or 200 points from their peak rating.

Further proof of the depth of Arimaa comes in game post-mortems when the loser may ask, "Where did I go wrong?" Often the winner can say specifically what strategic theme guided him, and the loser says not, "I didn't see that move," but rather, "I didn't realize the importance of that idea." It is not usually the case that both players are trying to do exactly the same thing, and the winner is merely the one who executes better. On the contrary, often the players disagree about what is most important in a given position, and the eventual winner is the one who has the better judgement.

It may seem, if players so frequently disagree about positions, that Arimaa lacks clarity, but this is an illusion. It isn't that players have no handles by which to grab the position, it is that there are different aspects of the position which must be balanced. Ideas such as material advantage, hostages, pins, blockades, trap control, goal threats, elephant mobility, and so on are individually easy to grasp with minimal study, but difficult to synthesize properly. It doesn't take an expert understanding to have a rough idea what is going on; players can take pleasure in observing games several classes above their own playing level.

The drama of Arimaa can be seen in many come-from-behind victories available for replaying on arimaa.com. Dramatic turnarounds are not mere flukes, they are a product of the escalating layers of aggression in this order:

Pull a rabbit with your elephant
Pull a piece with your elephant
Attack opposing trap with elephant and horse
Attack opposing trap with elephant, camel, and rabbits
Attempt to directly force a goal

The top strategy is mostly likely to succeed, the bottom least likely to succeed. However, each strategy is more forcing than the previous, because the benefits of success are greater. If the opponent outplays you at one level, you have the option of escalating to the next, knowing that the odds are against you, but also knowing that if you can pull it off it will obviate all your previous errors. Many games end in a desperation goal attack by one side when all else is lost. This keeps games exciting long after it is clear who has the advantage.

At the same time, Arimaa is decisive. Escalating to a higher level of aggression gives a chance of a comeback, but in any case makes it even more clear who is winning. Only at the very beginning of the game does a player have a chance to hunker down and try to protect everything. Present experience is demonstrating that it is not quite possible to keep everything safe. If nothing else, since rabbits can't retreat, one can graudally draw rabbits out into the open. Rather than accept a slow, torturous loss, even the most defensive of players must attempt to generate some offense.

And in another way Arimaa is extremely decisive: less than one game in five thousand ends in a draw. It does not seem to be the case with Arimaa, as it is with chess, that equally matched grandmasters will grind the position down until no play is left. On the contrary, Arimaa tends to become more sharp and unbalanced as the game progresses until it is inevitable that one player or the other will break through.

The worst thing that can happen to an abstract strategy game is for it to be "busted" by a simple idea, a simple strategy that dominates all the rest. At best the dominant strategy forces everyone to play the same way, which is boring, and at worst the dominant strategy solves the game as either a forced win or a forced draw. Yet Arimaa has held up through more than thirty thousand games on arimaa.com without any easy answers emerging. No one believes that experts fundamentally understand Arimaa in a way can be refined but not shaken. On the contrary, deep strategic questions remain unanswered, and the theory of how to play well, judging by its rapid growth, is still in its infancy.

For every passing year that the Arimaa community doesn't bump against some upper bound of fundamental strategic knowledge, beyond which there is only refinement of technique, Arimaa takes a step closer to joining chess, go, and other immortal games of abstract strategy.

[*] Edit: Arimaa is now almost seven years old, the pool of players has grown, we have played over 100,000 games, and the ratings now span the range 1000-2600. The upper end of the rating scale is still nowhere in sight, and many people are predicting the emergence of a 3000-level player by 2015.
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Michael Howe
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Very thoughtful and insightful discussion of a game that I already knew was outstanding. Now I'm even more convinced. For those who are interested, it's a nice feature of Arimaa that it can be played with a standard chess set.
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I've played this game a few times ... and it is intriguing. Although reaching a draw in chess does not really bother me as a player, I still agree that the lack of draws in Arimaa (a fact which is also true of Shogi to a lesser degree) is an advantage. I hope interest in this game continues to grow.
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Jim Getzen
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Here is a question which has probably been answered numerous times, but I'll pose it anyway:

Why play Arimaa instead of chess, go, shogi, chinese chess, one of the many chess variants like Fischer Random, etc.? Is it just a matter of personal preference, which is a perfectly valid reason, or is Arimaa simply better than those games in some way? Is it a sense of adventure in exploring the depths of this relatively new game?

I noticed that Arimaa remains very difficult for computers to play well. To me, that is actually a downside. I love the fact that I can play the computer in, say, chess and pick a skill level that suits me, or one that can blow me out of the water.

Don't get me wrong -- I went through the Arimaa tutorial some time ago, and I kind of liked the game, but it didn't grab me. It seemed odd or, to use a harsher word that probably isn't deserved, convoluted. That said, I am sure I need more exposure to fairly evaluate it, but I am wondering what Arimaa devotees see as the biggest attraction. Sell me on it, if you will, in comparison to the alternatives.

(Interesting and well-written opening essay, by the way.)
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Fritz Juhnke
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Getzen wrote:
Why play Arimaa instead of chess, go, shogi, chinese chess, one of the many chess variants like Fischer Random, etc.? Is it just a matter of personal preference, which is a perfectly valid reason, or is Arimaa simply better than those games in some way? Is it a sense of adventure in exploring the depths of this relatively new game?


On the basis of my limited knowledge of Go, I don't know of any shortcomings it has which Arimaa could claim to remedy. I expect Go deserves its BGG ranking as the #1 abstract strategy game of all time.

I'm more familiar with the chess family of games. Chess, shogi, and xiangqi have all proven extremely deep over centuries. There is no way to know whether Arimaa can hold up as well under intensive study and millions of plays until we try. All we can know about Arimaa's depth so far is that the end is not yet in sight.

However, there are superficial ways in which Arimaa outstrips the chess family. Most obviously, the pieces in Arimaa all have the same, simple movement of stepping one square orthogonally. When I learned chess as a child it was difficult for me to remember which piece moved in which way. Shogi, with its various promotions, is even worse on this score. You have to pay a higher up-front cost to experience the joy of shogi.

The more complicated part of the Arimaa rules is capturing by pushing or pulling into a trap square, rather than capturing by simple replacement. I admit it is easier to understand taking a piece by stepping on it. However, the form of the capture rule in Arimaa contributes greatly to Arimaa's strategic depth. In Arimaa, as in Go, there are many situations in which captures can be delayed, but shouldn't be, i.e. it is better to cut one's losses and play elsewhere. On the other hand, there are also plenty of positions in which a capture can and should be postponed indefinitely by the defender. Being able to distinguish these two cases is a significant part of Arimaa strategy just as judging life and death in Go is critical.

One common criticism of shogi is that the opening phase is boring, with little contact between the two sides. It appears strategically necessary to defend before attacking, because you will be in big trouble if your opponent gets pieces in hand before your king is in a fortress position. Arimaa, in contrast, usually has contact between the two armies on the second move after the setup. Agressive players have a viable option of immediately taking the fight to the other side of the board with multiple pieces.

Chinese chess at the top level is a bit drawish (four defenders are forbidden to leave the home half of the board), and chess even more drawish. I see Amy doesn't abhor draws, but many people do, so much that the Mtel Masters chess tournament, currently underway, forbids draws by agreement. The virtual lack of draws in Arimaa makes it more exciting for spectators, if nothing else.

Another common critcism of chess is that extensive memorization of openings is required, and the higher the level of play, the more is required. Perhaps Arimaa will eventually fall into stereotyped openings as the game becomes better understood, but I suspect the lack of standard opening lines is not merely a result of Arimaa's youth. Each player sets up their sixteen pieces arbitrarily within their home two ranks. Fischer Random chess has only 960 opening positions, all symmetrical, while Arimaa has millions of opening positions, often unbalanced. For example, it is increasingly common to see Arimaa setups with one elephant centralized and the other on a wing, or one camel centralized and the other on a wing. Unbalanced setups not only provide a variety of openings, they also grant the two sides different strategic objectives right out of the gate.

My final comparison is very subjective: I have a vastly different experience internally when I play Arimaa than when I play chess. Despite several years of studying chess, I never got beyond approaching chess in highly tactical terms, i.e., "If I do X, then he can do Y, then I can do Z," etc. In Arimaa I am virtually forced not to think that way, because there are about 15,000 possible moves in the average position. It is common for my opponents to make moves I haven't considered at all, even in postal games where I may have studied the position for over an hour. Therefore out of necessity I have to evaluate Arimaa moves on vague terms such as "influence", "initiative", "mobility", and so on. I am simply unable to cover enough of the bases with I-do-he-does thinking to rely on it.

Don't get me wrong: I'm not saying Arimaa is all strategy and no tactics. On the contrary, Arimaa is a highly tactical game. It is merely that when my opponent in chess makes a move I didn't consider, I'm 90% likely to have blundered, whereas when my opponent in Arimaa makes a move I didn't consider, I'm only 10% likely to have blundered.

In the 1999 chess game Kasparov vs. The World, Kasparov said that he "lost control" of the game in the middlegame. He didn't mean he was losing, he meant the position was so complex and the lines so varied, he just had to play his best move and hope he didn't stumble into disadvantage "by accident". Well, I'm currently the world's #1 Arimaa player by more than 100 points, and I feel that I "lose control" of nearly all of my Arimaa games. I can almost never be sure that my opponent has no counterplay, or that my plan is stronger, faster, and better. There's no way to play other than to take a good guess at a move and hope.

What is astonishing in this context is that upsets aren't more common. Better players win most of the time, and the ratings are spread out over quite a range. Better judgement wins games, although why this should be so is a mystery. Apparently you don't have to consider all the options to play well. I have won games of Arimaa in which I did not once foresee the position two moves in advance (i.e. what the position would be after my move, his move, my move, his move.) I can't say the same of chess.

All of the objective reasons aside, I believe I am addicted to Arimaa rather than chess mostly because, "I didn't see that move," doesn't translate so directly into, "I lost the game."
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Jim Getzen
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Well, you've persuasively answered my question. I'll definitely take another look at Arimaa.
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I just wanted to provide a link to a fine series of articles in Wikipedia on the subject of Arimaa. (I'm thinking that based on prose style, not to mention the fact that you are the leading Arimaa player, these articles may have been written by you, Karl.)

Here it is: http://en.wikipedia.org/wiki/Arimaa

Although, speaking strictly for myself, one of the joys of chess is studying its extensive literature, it is also enjoyable to break new ground in a rich, yet largely unexplored field, like Arimaa.
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Fritz Juhnke
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Sexy Amy wrote:
(I'm thinking that based on prose style, not to mention the fact that you are the leading Arimaa player, these articles may have been written by you, Karl.)

I'm guilty as charged, although it is more accurate to say I am the primary author of those pages. On Wikipedia folks feel free to pitch in with their own $0.02, so any given paragraph might have come from someone else.
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Fritz Juhnke
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As a footnote to evaluating Arimaa by J. Mark Thompson's criteria, he says:

"A game's drama might be measured roughly by matching a strong player against a weak player, and having them switch sides after the strong player achieves an advantage. In a dramatic game the strong player will still have a chance of winning."

Just by coincidence, I came across a game of Arimaa between two novices, in which black had resigned on the twenty-first move. I offered to play on against the winner from the resigned position, and came back to win in sixteen more moves.

http://www.greylabyrinth.com/discussion/viewtopic.php?t=9203

That's about as close as it gets to Thompson's definition of drama!
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ronaldinho @boardspace.net
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Interesting, but I am still a bit skeptical. Still, I am curious to try this game out.
 
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Erik Karlsson
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There is no need for scepsis. Find a roughly equal chess player and give the game a go. All you need is a chessboard, some patience and www.arimaa.com for the rules.
Personally i love arimaa. Why? It gives a feeling of space, of room and above all; freedome. Arrange the pieces the way you want, alla according to the original rules. Much like Go arimaa has an immense depth but without the...constrains... of chess.
 
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Francisco Alcala
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Arimaa is a great game. It is really interesting from any point of view, and I hope that it will stand the test of time.

However, I have seen in previous comments comparisons of Arimaa against Chess or other chess variants. In my opinion, Arimaa is not a chess variant, and the only relation I can found is that Arimaa can be played with a Chess set.

My point is: while Chess is a game where you want to capture a certain piece (the King), Arimaa is a game where you want to place one of your weakest pieces at your enemy's back row. Mechanics are different, so Arimaa is closer to Epaminondas or Halma than to Chess. The same can be said about comparing Arimaa with Go. Benchmarking a game against other games with different mechanics is not fair; it is also not ideal.

Of course, I'm not saying that Arimaa is an inferior game because it is not "chess-like". Arimaa is an excellent game that belongs to another family of abstracts. This game is probably the best board-crossing abstract game around.
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Fritz Juhnke
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I agree that Arimaa isn't very much like chess in terms of how it plays, and it is even less like Go. Leaving aside the equipment (chess) and the piece names (Shou Dou Qi), what other game is most similar to Arimaa in terms of how it feels to play? To me Arimaa is like nothing else, but my experience isn't very wide. Halma seems very different, because there is no capture, and the pieces never regroup backwards for defense. Maybe Epaminondas is the closest match, although I have only played it a couple of times, and thus have no feeling for its strategic depth and variety.
 
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Snowball
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One game rated, Arimaa.
Is it some kind of sect? devil
 
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Fritz Juhnke
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HavocIsHere wrote:
Is it some kind of sect? devil

If you give Arimaa a hundred plays or so, you will start to understand the religious aspects...
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Fritzlein wrote:
If you give Arimaa a hundred plays or so, you will start to understand the religious aspects...

Playing a single game 100 times is a rare feat. I can only think of 6 games I've played 100+ times.
 
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Fritz Juhnke
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spearjr wrote:
I can only think of 6 games I've played 100+ times.


That's part of my point. I can only think of a handful of games I would want to play 100 times, even if I could spend all day every day on gaming. The only games I have played 100+ times are Arimaa, chess, poker, bridge, Boggle, and Titan, with the first four definitely outstripping the latter two in quality.

Games like Quarto and Abalone can be thrilling at first, but then you seem to slide into state where you aren't learning anything new as you play, and the game loses interest, and you start inventing variant rules because the original game is played out.

There's a difference between a game being fun because the [mechanics, components, theme, vagaries of chance] seem exciting on the first play, and a game being fun because you learn and learn and learn and then it seems there is yet more to learn.
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Russ Williams
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This is an interesting article that makes me curious to try the game, but is it really a review? If so, it's possibly the most indirect/abstract game review I've ever read, as I have no concrete idea how the game actually works, other than that it involves using a standard chess board and pieces...

(I would also say that the article's various assertions about what makes an abstract game good/interesting/etc are just as true if you remove the word "abstract" from those sentences.)
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Fritz Juhnke
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Thanks for the feedback. This is the only "review" I've done for BGG, so I didn't know what was expected. I guess I got caught up in saying what a great game Arimaa is without first explaining what game it is. :-)

In my defense, I think people are often curious about the mechanics of a game, and then judge it based on the mechanics without ever playing it. The trouble is that a game with very cool mechanics can be boring to play (e.g. Quarto), while a game with boring mechanics can be extremely rich and varied (e.g. Go).

I'm interested to see reviews by people encountering the game for the first time, as opposed to my review after having played for years. I think depth is ultimately the most important thing, but first impressions matter too.

As for the four factors necessary to make a game good, I wish I were clever enough to think of them myself, but they are entirely borrowed from J. Mark Thompson.
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russ wrote:
This is an interesting article that makes me curious to try the game, but is it really a review? If so, it's possibly the most indirect/abstract game review I've ever read, as I have no concrete idea how the game actually works, other than that it involves using a standard chess board and pieces...

(I would also say that the article's various assertions about what makes an abstract game good/interesting/etc are just as true if you remove the word "abstract" from those sentences.)


Yes, it's a review - much more so than the rules summary that most "reviews" on here are...
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Fritz Juhnke
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2097 wrote:
Fritzlein wrote:
On the basis of my limited knowledge of Go, I don't know of any shortcomings it has which Arimaa could claim to remedy.


I can think of at least one: arimaa doesn’t need komi, at least not according to the current stats.
We’ll see how it works out over time.

(Disclaimer: I like go, have never played arimaa.)

Good point. One can claim that komi is an inelegant hack to the rules of Go. I fear, however, that even with that awkward add-on, the rules of Go are more elegant than the rules of Arimaa. :'(
 
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Fritz Juhnke
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PollutedMonkey wrote:
Thanks for the review. Arimaa deserves to become a classic.

I wrote this review five years ago, and every year since then Arimaa has inched closer to classic status. The game still hasn't been busted by a simple idea or dominant strategy, and that isn't because nobody is trying; there have been over 40,000 games played on Arimaa.com this past year. One of the reasons I hope to live another twenty years is to see what Arimaa's cultural status will be by then.
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