Arimaa player #6590
2010_04_19: Fritzlein on "Arimaa vs Chess&quo
« on: Apr 12th, 2017, 11:18am »
I just noticed convinceme.net was down so I thought I would repost Fritzlein's response to the topic "Arimaa vs. Chess". I saved it since I thought it was quite good.
Apr 19, 2010
Of taste, there is no arguing, but Arimaa and chess are so similar that people who like one usually also like the other. They can be played with the same equipment. Each game lasts about 40 moves on average, and thus requires about the same amount of time and energy to play. They are both abstract strategy games, that is to say finite, two-player games of perfect information, with no chance elements. In neither game can there be complaints from the loser that he got unlucky or was conspired against. People who like that sort of game generally agree with each other on the essence of gaming excellence, which enables them to constructively debate whether Arimaa or chess has more of it.
1. Elegance (for beginning players)
Complex and unintuitive rules are a nuisance. Newcomers to a game should as quickly as possible pass the stage where they attempt to make illegal moves, are confused as to the conditions of capture, and are unsure about when the game is over. Sadly, neither chess nor Arimaa has particularly elegant rules compared to, say, Hex or Connect Four. Relative to each other, however, Arimaa is slightly more elegant than chess.
Arimaa capture, dislodgement, and immobilization are unintuitive, but are compensated by the simplicity of every piece moving the same way, unlike chess where each of the six piece types has a unique move. Furthermore, the six types of chess moves are arbitrary and unrelated rather than part of a set that can be summarized. Arimaa rules can be completely described in fewer words, in part due to the absence of special moves such as castling, double pawn moves, promotion, and en passant capture.
Verdict: Arimaa and chess are both inelegant, but chess is more so.
2. Depth (for continuing players)
No matter how well one plays a game, it should be possible to improve at it by dint of further play and study. Improvement can be objectively measured by Elo ratings: a player who wins three-quarters of his games against another player is said to be one class interval higher, reflected in 200 Elo points higher rating.
Chess ratings range from about 400 to 2800, whereas Arimaa ratings range from about 1000 to 2600. Thus chess has about twelve class intervals of depth, whereas Arimaa has only eight. This comparison is, however, deceptive.
The expansion of chess ratings to its current range took centuries to accomplish. Before the advent of scholastic chess, whereby kindergarteners of no particular aptitude were encouraged to take up the game, chess ratings below 1000 were rare. It is only the great popularity of chess that has made it obvious how badly it is possible to play.
On the upper end of the scale, too, it is only centuries of study that have made such high chess ratings possible. Chess Elo ratings have only existed since 1970, but the advent of strong chess computers has recently made it possible to evaluate earlier recorded games somewhat objectively. Based on games played one hundred years ago, it is plausible that nobody then played above a skill that would be rated 2500 on the current scale.
Thus Arimaa has already, in less than eight years since its invention, demonstrated about as much depth as chess had demonstrated by the year 1900, when chess had been played and studied for over two centuries. Furthermore, the range of Arimaa ratings is still expanding at a rate of about 100 Elo points per year. If the Arimaa community does not soon hit a wall of how well it is possible to play, Arimaa will eventually surpass chess in its range of Elo ratings.
Verdict: Chess has greater proven depth, but Arimaa has a good chance to reveal greater inherent depth than chess within the next decade.
3. Draws (for championships)
The presence of draws makes it difficult to hold elimination tournaments, because additional games must be played to break ties, or to stage fair World Championship matches, because some player must get the advantage of winning a tied match. In addition, most spectators find draws unsatisfying.
Chess is rarely drawn among beginners, but between equal grandmasters over half of chess games are drawn. Various changes to chess tournament structure have been attempted to reduce the percentage of draws, but to no avail. Apparently only a change to the rules of chess per se would eliminate draws, but chess experts vigorously resist any measure that would invalidate any of their hard-earned expertise. Thus the draw problem remains.
Arimaa has not yet been drawn, ever, in tens of thousands of games. Given that chess draws become much more of an issue at higher levels of play, it is reasonable to wonder whether Arimaa will also develop a drawing problem along with greater depth. The trajectory so far, however, is encouraging. Not only are games between top Arimaa players not ending up drawn, they are trending no closer to drawish positions than beginner games.
Verdict: Chess has a severe draw problem. Arimaa has no draws whatsoever, and no danger signs of draws arising as play improves.
4. Balance (for championships)
If the first and second players of a game do not have equal chances, an unattractive element of luck enters the game, namely the luck of who is chosen to play first. Chess points fall about 55% to the first player and 45% to the second player at all levels of play. The disparity is perhaps tolerable in Swiss or round-robin tournaments, as long as each player gets to play first in roughly the same number of games. In elimination tournaments or World Championships, however, the disparity is unacceptable, and colors must be exactly equalized, which is a nuisance.
Arimaa, in contrast, is so finely balanced that the results so far do not vary from 50% by a statistically significant amount. Indeed, the Arimaa community is not yet certain whether the first player or the second player has an inherent advantage. It is presently suspected that, at the highest levels of play, the second player has a slight advantage. If that proves true, one would expect the second player's winning percentage to get higher and higher as the players get better. For now, however, even at the highest levels, there is so little advantage to playing first or second that colors do not have to be equalized to have a fair match.
Verdict: Chess is somewhat imbalanced. Arimaa is excellently balanced so far, although a slight balance problem (less than that of chess) may emerge as play improves.
5. Memorization vs. Thought (for fun)
People who love to memorize don't play strategy games; they recite digits of pi. Yet in any competitive sport, people will do whatever they must do to gain an advantage. All high-level chess players memorize standard openings, not because they like to, but because they must. Chess grandmasters only gain the privilege of thinking if they survive fifteen or so moves of opening theory.
In Arimaa, each player sets up his own sixteen pieces however he chooses in his home two ranks, thus each player has 64,864,400 options on his first move, compared to 20 options for each chess player's opening move. This freedom has so far prevented any Arimaa opening theory from developing. For example, after the two players in the final game of the 2010 Arimaa World Championship had set up their pieces, they were already in a position that had never been seen before.
It is possible that increasing expertise will eventually force Arimaa players to resort to standard setups, but even then they will have about 500 times as many options per move for continuing as chess players have. Therefore it is unlikely that memorization of openings will ever become an essential skill for Arimaa the way it is for chess.
Verdict: Substantial memorization is required to play high-level chess. No memorization is required to play high-level Arimaa so far, and it probably never will be.
6. Computation vs. Intuition (for fun)
Strategy gamers love to play the moves that feel right, and are put off when they must act like a computer, looking at many possible moves, many possible replies, and so on. Much of the fun of chess is that it is highly intuitive. Good players can look at a board and simply know which move is best without considering all the possible moves or considering all the possible replies. Nevertheless, chess is somewhat susceptible to computation. If one player moves quickly by intuition while the other takes the time to grind through some computation, the plodder will win more often.
In Arimaa, computation is essentially impossible, because the average position has over seventeen thousand move options, compared to about thirty-five move options for chess. In Arimaa, you can't look at all of your opponent's possible moves, or even any significant percentage of them. Instead you must guess based on general tactical and strategic principles, and hope for the best. Chess grandmasters have been known to announce combinations seven moves deep, whereas Arimaa experts seldom see more than two moves ahead. Indeed, Arimaa experts correctly anticipate the very next move of their opponent less than 25% of the time.
In a related phenomenon, computers play chess better than any human, but play Arimaa three classes lower than the Arimaa World Champion. The power of chess computers is a great asset for analysts who want to know the "correct" move in any given position, but also creates such a temptation to cheat that players in live chess tournaments can hardly be permitted to go to the bathroom.
Verdict: Chess is more susceptible to computation than Arimaa.
In summary, I believe that Arimaa has more of each element of greatness in an abstract strategy game than chess has. The only point of superiority that chess retains in my mind is that the greatness of chess has been proven beyond question, whereas the greatness of Arimaa is still hypothetical based on its short history and present trajectory.
The purpose of argument is to draw distinctions, as I have just done. Yet it feels strange to dwell so much on differences between games which are essentially so similar. Both Arimaa and chess are fabulously rich and infinitely replayable. Both are adequate to provide a lifetime of enjoyment to anyone who devotes himself to their study. When faced with such an embarrassment of riches, an individual gamer's choice of whether to play Arimaa or chess (or both!) had best be a matter of personal taste.