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Subject: Mouse Variant? rss

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Mi Myma
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Does anyone have any info about a variant I heard about called the "mouse"? IIRC, one of the rabbits is replaced by a mouse - smaller than all the other animals (can be pushed/pulled by rabbits), it can move backwards and doesn't count for victory if it gets to the other side. However - and this is the kicker - it can push the Elephant!

Anyone know any further details? Have I got it right? I didn't make it up, but I haven't heard anything about this for a long time.
 
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Fritz Juhnke
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My personal expectation is that having a mouse would take some of the depth out of Arimaa, because it takes away semi-permanent elephant configurations. However, for those who enjoy experimenting, we have the following discussion:

http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1174411328

http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1173723636

http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1144695637

Peace,
Fritz
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Greg Magne
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The elephant is a bit of an anomaly in that it’s the only piece that cannot be frozen, pushed or pulled and it’s virtually impossible to capture outside of a catastrophic error by your opponent. Some people don’t like this inconsistency and have suggested the game would be better if the elephants had to endure the same risks as other pieces. However, I think that the indestructible nature of the elephant is what makes the Arimaa opening playable.

The opening phase generally consists of 2 elephants that charge the enemy while the other 30 pieces huddle near their home traps because it’s too dangerous to venture to the opposite side – until a weakness appears in the enemy camp and the opportunity to charge ahead presents itself. If you introduce a piece that can threaten an elephant then the opening phase would become even more passive and it might become impossible to launch an attack into enemy territory with any pieces, other than rabbit pulls on the perimeter (and games take forever to play with that style!) Intuitively, it might seem that a camel & mouse invasion would be effective but in practice it doesn’t seem to work at all. The mouse is too weak to be an effective attacker and once it’s neutralized by the non-elephant pieces the defending elephant can pursue the invading camel. And that camel will be doomed if it’s own elephant is now unable to protect it for fear of its own safety – attacking would become much more difficult and more riskier in a game whose current rules are already challenging enough for the attacking-style player.

A great way to dominate an Arimaa game is to advance most of your army forward so that your pieces are contesting both opposing traps while your half of the board is free of enemy pieces. It’s quite possible to do so against a passive defender that leaves even slight weaknesses for you to exploit. However, it’s quite difficult to achieve such a position against a strong defender. Try advancing a horse onto a strong square (for example, a gold horse on b6, c7, f7 or g6 is extremely powerful if supported by a friendly elephant or, alternatively, supported by a 2nd strongly placed piece plus a swarm of lesser pieces) against a strong defensive player and you’ll quickly learn how difficult it is. Now try to attack against a strong defensive player if your elephant can’t even safely stand on the d6 or e6 squares! I wouldn’t necessarily say that Arimaa is a defensive game by its nature, but I would say that full-scale attacks are difficult to execute and come with very high risks. The indestructible elephant piece seems essential and I wouldn’t ever want to change that rule.

As an aside (and I might be the only person in the world who believes this judging from the response on the Arimaa.com forum), I think that Arimaa might become a more offensive-style game if there were 2 elephants rather than one. That might seem counter-intuitive because surely it would become extremely difficult to capture enemy pieces, right? But actually, full-scale aggressive attacks become much easier and both sides could attack right from the opening moves. I think the games would be much faster this way. But Arimaa was also designed to be difficult for computers to play and I think the current rules achieve that by making it hard to attack rather than easy.
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Mi Myma
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That was an excellent answer, Greg. I appreciate the insight.

It's just in my nature to come up with variants for games that I get interested in. I didn't come up with the mouse, obviously, but I did think of one other thing, which is probably not a good idea for the game, but might make an interesting experiment:

What if there were no "ties" between animals? After some thought, I came up with this scheme (which I haven't tried, and like I said, it's probably not a good idea, let alone an improvement to the game): One player's Elephant beats the other player's Elephant, but the second player's Camel, Horses, Dogs, and Cats beat the first player's. The Rabbits are unchanged. Which player do you think has the advantage in that case? If it's not balanced, what combination of "tiebreakers" would be balanced?
 
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Fritz Juhnke
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grmagne wrote:
As an aside (and I might be the only person in the world who believes this judging from the response on the Arimaa.com forum), I think that Arimaa might become a more offensive-style game if there were 2 elephants rather than one. That might seem counter-intuitive because surely it would become extremely difficult to capture enemy pieces, right? But actually, full-scale aggressive attacks become much easier and both sides could attack right from the opening moves.

Sure, if there were two elephant on both sides, then the players could fearlessly advance from the outset. But that doesn't mean either player could capture pieces or force a rabbit to goal. If neither player fears advancing, why won't they both charge forward, meet halfway, and stalemate? What would prevent the game from becoming a huge quagmire?

Phil Fleischmann wrote:
What if there were no "ties" between animals?

I once actually proposed reducing the number of ties in Arimaa by converting a horse on each side into a lion, so there are fewer ties. But even that slight tipping of the balance from defense to offense has proved unnecessary. If it ain't broke, I don't want to fix it.

Quote:
After some thought, I came up with this scheme (which I haven't tried, and like I said, it's probably not a good idea, let alone an improvement to the game): One player's Elephant beats the other player's Elephant, but the second player's Camel, Horses, Dogs, and Cats beat the first player's. The Rabbits are unchanged. Which player do you think has the advantage in that case? If it's not balanced, what combination of "tiebreakers" would be balanced?

I suspect the side with the stronger elephant would have the advantage despite losing all other ties, but even if I am wrong, the game almost certainly wouldn't be balanced. In general, games between unequal forces are essentially impossible to balance, e.g. Maharja & the Sepoys, monster chess, Tablut. The inherent inequality creates an interesting tension, but among grandmasters one side will win every game.
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