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IdahoEv
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Fairy Pieces
« on: Apr 10th, 2006, 2:00pm » |
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As an amateur game designer myself, it doesn't take long with any new game before my brain starts musing on the topic of "hey, I wonder what else we could do with this...?"
(Note that this is no way disrespectful of Omar's beautiful creation. As someone who's designed several games, I can say that Arimaa is practically the holy grail: it manages to be both fun and strategically deep in an extremely simple set of rules that can be learned in minutes. And, it's an abstract strategy game - the hardest kind to design; flavor and story are crutches that nearly all game designers depend on.)
Anyhow, on an airplane this past weekend, I couldn't play, so instead my mind was mulling over Arimaa. Practically the only thing that has ever nagged me about the design is the near invulnerability of the elephant; I feel like the strategic depth would increase if the elephant weren't so invincible. So, tapping into a particular cultural legend about elephants, I came up with two possible fairy pieces for Arimaa:
The Mouse:
The mouse is an officer, moves like any other non-rabbit piece, and cannot score goals. For purposes of pushing, pulling, and freezing, it is "smaller" than all Arimaa pieces, including the rabbit ... except for the Elephant. It is accounted larger than the elephant, and can freeze, push, or pull the elephant.
The Rat:
Identical to the mouse, except that it is accounted as the "same size" as a rabbit, i.e. it cannot push, pull, or freeze a rabbit, and vice versa.
I came up with the rat when I worried that it might be too easy to just push the enemy mouse near your rabbits and never worry about it again, making it fairly impotent. Playtesting would be necessary to tell which of these was the more interesting piece.
A few thoughts on possible ways you would use these:
- A single rodent replaces the camel.
- Two rodents replace the cats
- N rodents replace N rabbits, with the number being up to the player (thus dramatically increasing the size of the opening book). You get to trade off the ability to fight the opposing elephant vs. the ability to make goal threats.
The first two options retain the feature that the game can be played with a chess set.
Just thoughts ... hope the purists aren't too offended. 
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Fritzlein
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Re: Fairy Pieces
« Reply #1 on: Apr 10th, 2006, 2:36pm » |
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Your propopsed rule ideas are very interesting, and it would be fun to experiment with them. I remember as a child when almost the only game I knew was war (a card game of no skill), I thought it was dumb that nothing could take the top card, so you could only lose that card as a concealed card in a war. I always preferred to play that an ace beats everything except a joker, a joker beats everything except a deuce, and a deuce loses to everything except the joker. Thus my deuce was your mouse. This change made the game much more dramatic, and made a comeback possible from the weakest of positions.
on Apr 10th, 2006, 2:00pm, IdahoEv wrote:| Practically the only thing that has ever nagged me about the design is the near invulnerability of the elephant; I feel like the strategic depth would increase if the elephant weren't so invincible. |
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I think that a rodent or two in Arimaa would increase the drama of the game. However, I suspect it would correspondingly lower the strategic depth, and make it rather easier for computers to beat humans.
At present humans can outplay bots at all phases of the game except goal search, which is the most drastic and tactical part of the game. As bots improve, I can imagine them also surpassing us at wide open games when many pieces are threatened, although we can presently dominate such positions. What I have the hardest time imagining is how computers will beat us in games where the elephants become deadlocked around the same trap.
The very fact that the two elephants are equal and invincible slows the game down and makes it more strategic. No matter what you threaten to capture with your elephant, I can make it safe with my elephant. This means that to make progress when our elephants are deadlocked, you have to overload my elephant by operating in antoher quadrant to create a second threat. Computers are just hopeless at this. Either they are too passive, and you can increase the pressure on them until they crumble, or the bots are too aggressive and you can pick off a piece they unwisely expose.
The fact that any piece in chess can kill any other piece makes chess fast and tactical. Chess wouldn't be strategic at all if facing pawns could capture each other too, but luckily for chess the pawns can deadlock. In Arimaa, the fact that neither elephant can hurt the other and they can stalemate each other makes Arimaa much more strategic than it would be if, say, equal pieces could push and pull (but not freeze) each other.
I admit, this is all speculation on my part, and we would actually have to playtest the different versions of your rodent rules to see what they did to the game dynamics. I have, however, seen the balance and depth knocked out of a few games by players adding rules to make the play more dramatic and interesting. Things that make a game "cooler" for the first dozen times you play usually seem to make you not want to play more than a dozen times that way. Just my intuition.
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jdb
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Re: Fairy Pieces
« Reply #2 on: Apr 10th, 2006, 3:21pm » |
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An interesting idea!
I think that a rodent would dramatically increase the value of a hostage. Lets say gold takes a silver horse hostage. Normally silver sends in his elephant and creates a stable position. If gold had a rodent handy, silver's elephant would need some help to protect the hostage.
The lone elephant play would also be very difficult since the rodent could venture about and freeze it.
However there would certainly be new strategies that make use of the rodent too. Two or three rodents could attack an elephant and cause alot of trouble. It would also be easier to blockade the elephant since the rodents could assist by positioning the elephant on the desired square.
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Fritzlein
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Re: Fairy Pieces
« Reply #3 on: Apr 10th, 2006, 3:41pm » |
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on Apr 10th, 2006, 3:21pm, jdb wrote:The lone elephant play would also be very difficult since the rodent could venture about and freeze it.
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Good point. Lone-elephant attacks are definitely out if there are two rodents on defense. I wonder what sort of attacks are still feasible. I was blathering about rodents making the game faster and more tactical, but suddenly I wonder if they would make it hard to go on offense at all. Perhaps some kind of swarming attack could still work if it involved a rodent in the attacking force, but it isn't clear to me why the more-numerous defenders wouldn't always win.
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| « Last Edit: Apr 10th, 2006, 3:42pm by Fritzlein » |
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IdahoEv
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Re: Fairy Pieces
« Reply #4 on: Apr 10th, 2006, 7:14pm » |
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I think the lone-elephant sort of position was the item that inspired the concept. The fact that an elephant can hunt completely alone without worry feels "too simple" to me.
Fritzlein's points on how the balance of the elephants creates strategic depth are excellent, and no doubt demonstrate a more thorough understanding of the game than I possess.
Intuitively, to me, the struggle to create two simultaneous threats doesn't feel particularly deep, since the game essentially always comes down to that particular goal: make two threats, since the enemy E can always keep one safe. My thought was to 'complexify' the situation by requiring the player to pay attention even to the "automatically safe" trap normally defended by the E; all positions require defense at all times.
But I do see how that may qualify as 'more complex' only to a human. The rodent concept may be adding tactical complexity at the expense of strategic. To a relative noob like me (especially since I think I'm better at strategy than tactics), that would seem on the surface like a deeper game.
I do think, however, that the option to replace N rabbits with N rodents would add depth (but of which sort?) in the sense that a game with 8 rabbits and 0 rodents is a fundamentally different game than one with 4 and 4; material-based strategic evaluators would need to be very different. I suspect in a game with 4 rodents, the camel is probably more valuable than the elephant, but rabbits are suddenly priceless. Computer strategies would need to become at least a little more adaptive, and opening books would get an additional factor of N larger.
Maybe this is worth investigation in Zillions of Games at some point.
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Fritzlein
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Re: Fairy Pieces
« Reply #5 on: Apr 10th, 2006, 8:44pm » |
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on Apr 10th, 2006, 7:14pm, IdahoEv wrote:| I think the lone-elephant sort of position was the item that inspired the concept. The fact that an elephant can hunt completely alone without worry feels "too simple" to me. |
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I see the problem there. If it had turned out (or still turns out) that lone-elephant is the dominant opening strategy that squeezes out all more ambitious strategies, that could sap Arimaa of some of its current excitement. It was good news for Arimaa that I didn't win the World Championship with my lone-elephant openings, and that Robinson, Adanac, and PMertens, who took the medals, all play more varied and aggressive openings.
At present the balance between lone-elephant opening and elephant-horse openings seems very interesting to me, and very unclear. The elephant-horse attack is the more forcing of the two, and compels the lone elephant to hurry home, but who stands better in the resulting position? If the top players don't agree, it's hard to call it "simple".
Indeed, there even is a persistent fringe that is willing to attack with the camel in some way, including Adanac and Blue22 in my postal tournament games. This is further evidence that we haven't by any means plumbed the depths of Arimaa opening strategy, never mind the strategy of the full game.
Perhaps I try so hard to be clear in my writing about Arimaa, I give the false impression that the game is pretty well understood by now. But it is definitely not the case that all of us are trying to do the same thing, and whoever does it better wins. On the contrary, we're often trying to do very different things. In many of my games I discover that my opponent and I are angling for the same position! For example he will give up a horse hostage and think he is winning, whereas I will take the horse hostage and think I am winning. Or perhaps he will give up a camel hostage for a cat capture and think to have gained, whereas I will take the camel hostage for a cat capture and think to have gained.
It seems to me very exciting that semi-stable positions (such as frames and hostages) can tip in either direction. I love it that I can sit down to either side of a position in which an elephant holds a horse hostage while the other elephant guards, and from either side thrash the best computer players. The excitement inherent in semi-stable positions is likely to be more enduring than the sort of excitement that prevents semi-stable positions from arising in the first place.
Quote:| Intuitively, to me, the struggle to create two simultaneous threats doesn't feel particularly deep, since the game essentially always comes down to that particular goal: make two threats, since the enemy E can always keep one safe. |
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Wait, wait, there a certain amount of complexity involved in even creating the first threat. And after the first threat is created, the one which ties both elephants down near the same trap, the second threat is vastly more subtle.
If you think the second threat is boring, take a look at game 24224, the fifth game in this year's Challenge match. Adanac attacked c3 with EH, so Bomb took the horse hostage. That created a first threat on each side and an elephant deadlock by move seven. Then Adanac attacked f3 with his camel for the second threat. Would this game be a rehash of his crushing win in game 23918? No! Bomb switched wings with its elephant, throwing the board into chaos and gaining an advantage in the process.
The "create a second threat" phase of the game is usually intense because the deadlocked elephants are free to run across the board at any time and smash up the second sphere of action. The elephants are preoccupied, not frozen. In fact, it is basically only computers that let you execute the second threat. Human opponents will see the writing on the wall in advance, and complicate the situation because it is their only chance. Add to this the common possibility of undermining the first threat (e.g. breaking a frame, or flooding an elephant that holds a camel hostage), and you've got a lot going on.
Quote:| My thought was to 'complexify' the situation by requiring the player to pay attention even to the "automatically safe" trap normally defended by the E; all positions require defense at all times. |
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I can see the urge to 'complexify', but if your new rule means that the primary situation never stabilizes, you might just have simplified the strategy by eliminating the second threat. If Arimaa contained only one hot zone at a time, it might become primarily a tactical game. Particularly if there were continual capture threats, it might become hard to build up incremental (strategic) advantages. Arimaa might devolve into a situation where you either have a forced capture or you have nothing to hang your hat on, because the situation is too unstable.
By all means, if Arimaa is boring to you as it stands, try to inject some excitement. I don't think the rodent rules will necessarily make a less deep game. We would have to play it to see. I certainly couldn't have predicted the subtlties inherent Arimaa just from reading the rules, so I shouldn't pretend to know how altering the rules would alter the game.
But for my money, it will be soon enough to tweak the rules when everyone agrees on the best strategy to the standard game, and when winning at Arimaa becomes only a matter of blunder-free execution of things that everybody knows. For as long as we have World Championship games in which the spectators can't agree who is winning, why they are winning, and what a good move would be, then I say Arimaa doesn't need to be spiced up. 
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IdahoEv
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Re: Fairy Pieces
« Reply #6 on: Apr 11th, 2006, 2:40am » |
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Just to clarify - I don't have any feeling whatsoever that Arimaa needs to be tweaked or complexified; as I said up top, I think Omar has quite achieved the holy grail in game design here. Mostly I just think about variations because it's an interesting exercise (to me) to do so.
(I'm the sort of person who will often play a game just ten times and then switch to designing maps/levels/mods/variants/bots because the creative challenge interests me even more than playing ...)
For toying with Arimaa's gameplay, I was drawn to the elephant because it felt unusual to me that it was so nearly invincible, and i liked the elephants-are-scared-of-mice flavor as a conceptual approach to that particular issue. I don't in any way think that's something the game needs, and I'm not suggesting this as a replacement for the official rules any more than fairy chess pieces like the Archbishop or Nightrider are intended as rules changes to be considered for adoption by the FIDE.
I do think it's quite likely your analysis of the rodents' effects on the game are correct; you pointed out some consequences of the Elephant's invulnerability that I hadn't thought of, and your arguments are pretty sound. This is just an entertaining intellectual exercise.
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Fritzlein
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Re: Fairy Pieces
« Reply #7 on: Apr 11th, 2006, 3:10pm » |
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Designing variations is indeed an interesting exercise. In fact, I understand that nearly all games (except more modern games) evolved and improved over time. Poker used to be a rather dull game, and not very deep, compared to the subtleties of seven-card stud and Texas hold'em.
In fact, Arimaa has already evolved slightly. The rule for breaking ties in elimination tournaments has changed, and the repetition rule has changed. Also the victory condition has been clarified.
By the way, new user Unic posted over at BoardGameGeek about the rules of Arimaa. (I believe he hasn't yet joined the Arimaa Forum.) His beef with the rules is that repetition should be a draw, not a loss for one player, since it is hard to keep track of who it is going to be a loss for.
I like Arimaa being essentially drawless, but I would support changing the rules in this related way: rather than making 3-fold repetition a loss for the repeating player, make it an illegal move, just like it is illegal to move into check in chess. (For the ultra-nitpicky, if your only legal moves would cause threefold repetition, then you would lose.) Rather than have 1 or 2 percent of games ending due to repetition, I think we should force those games to continue, with the server/interface enforcing the rule. That way players wouldn't have to do the bookkeeping to avoid repetition; instead they could deviate whenever required to do so by the rules.
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RonWeasley
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Re: Fairy Pieces
« Reply #8 on: Apr 11th, 2006, 3:43pm » |
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If the third repetition were an illegal move not allowed by the game interface, there would need to be some indication so the player would not mistake this for an error in the game interface.
In wizard's chess, if you try to make an illegal move, the offending piece has to clean up after the knights' horses when the game is finished.
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omar
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Re: Fairy Pieces
« Reply #9 on: Apr 12th, 2006, 1:04am » |
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Thanks for bring up this suggestion Evan. I think we think alike While developing the rules I also felt that perhaphs the elephants should not be so invincible and in fact experimented with a variation in which the eight rabbits/mice could push/pull/freeze the elephant but not any other piece. I don't remember now the exact reason, but I rejected that version and felt that the additional exception it introduced to the rules was not worth it. I never tried the variations you proposed.
Whenever a rule is changed it can significantly change the dynamics of the game. For me it is a lot easier to play lots of games against myself and get a feel for the nature of the game then to simulate in my head what effects the rule changes would have. I am very interested to try out your first two proposals since they can still be played with a standard chess set. However, I won't be able to in the near future. I would encourage you and others to try it out if you have the time. Perhaps you could report back on what you thought of it and if it seemed interesting more people would try it. If many people feel it improves the game, we could change the official rules to adopt it. I am always open to changes which could improve the game while maintaining the original objectives (playable with a chess set, difficult for computers, simple rules, interesting for humans (very subjective)).
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omar
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Re: Fairy Pieces
« Reply #10 on: Apr 12th, 2006, 1:16am » |
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on Apr 11th, 2006, 3:10pm, Fritzlein wrote:
By the way, new user Unic posted over at BoardGameGeek about the rules of Arimaa. (I believe he hasn't yet joined the Arimaa Forum.) His beef with the rules is that repetition should be a draw, not a loss for one player, since it is hard to keep track of who it is going to be a loss for.
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But this would create a loop hole for mutually agreed draws which we try to forbid in the match rules.
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I like Arimaa being essentially drawless, but I would support changing the rules in this related way: rather than making 3-fold repetition a loss for the repeating player, make it an illegal move, just like it is illegal to move into check in chess. (For the ultra-nitpicky, if your only legal moves would cause threefold repetition, then you would lose.) Rather than have 1 or 2 percent of games ending due to repetition, I think we should force those games to continue, with the server/interface enforcing the rule. That way players wouldn't have to do the bookkeeping to avoid repetition; instead they could deviate whenever required to do so by the rules. |
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I like this much better, because I perfer to see games continue to a natural finish (goal or immobilization) rather than have an abrupt ending.
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Fritzlein
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Re: Fairy Pieces
« Reply #11 on: Apr 12th, 2006, 1:49pm » |
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To further expand on my proposal to make a third repetition illegal rather than have it be a loss:
There is often some confusion as to "whose fault" the repetition is. When I am attacking, I naturally feel that my opponent shouldn't be able to undo my moves. I feel I should be able to make the attacking move again, and my opponent should have to deviate. If I could just use this rule of thumb and not worry, there would be no problem.
Unfortunately, it isn't so easy to keep track of. Sometimes there are two slightly different ways to undo my move, so the defender can avoid repetition, but there is only one way for me to redo it, so I have to deviate to avoid losing, even though I'm on offense.
It's a bit of a hassle to keep track of which of those two situations I'm in. If I lose by repeating, it is not a strategic error, nor even a tactical blunder, it is merely a bookkeeping error because I thought my opponent was obliged to deviate instead of me.
In the game of go there is a rule that forbids you from undoing the opponent's move. The rules don't say, "If you undo the opponent's move, you lose." Here's a case where I can see the wisdom of the ancients.
For Arimaa, imagine a ridiculous rule that said, "If you move a frozen piece, you lose the game instantly." It would have no effect on strategy whatsoever, but it would require people to waste their attention making triple-sure the pieces they were trying to move were indeed eligible. The fact that the Flash interface doesn't let us move frozen pieces frees us from this hassle, and allows us to concentrate on strategy instead.
Therefore, if it isn't too hard, I'd love for the interface and/or gameserver to simply disallow three-fold repetition so that I don't have to think about it any more. There's enough to pay attention to in Arimaa without it!
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IdahoEv
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Re: Fairy Pieces
« Reply #12 on: Apr 12th, 2006, 7:29pm » |
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I concur with the thought of simply making repeats illegal; bookkeeping is a pain and should be minimized.
Also, IIRC, the repeat rule is not just consecutive repeats, but rather takes action on the 3rd repeat of any position regardless of the time during the game. If that's so, then it could be 3-4 turns down the road and you could be completely surprised when what you think is the 2nd repeat of a position (forcing your opponent to deviate) turns out to be the 3rd repeat, and you lose!
Not sure how best to do that in the interface, though. Certainly not by just eliminating the blue arrow if the position would be a repeat ... that could be quite confusing. ("Why the *&#@$ can't I move my camel there? It ain't frozen!")
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unic
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Re: Fairy Pieces
« Reply #13 on: Apr 13th, 2006, 11:18am » |
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*waves* unic here.
Making repetitions illegal moves wouldn't reduce the book-keeping for games not played on the server... or is the game designed only to be played using computers, and not in real life? (I'm currently looking for suitable toy animals to make a physical set that's nicer than a chess-set and specific to Arimaa...)
If neither player can deviate in a profitable manner, to me, a draw seems like the most logical outcome.
(On the other hand, the situation where all rabbits are captured being a draw feels counterintuitive - wouldn't it make more sense to have the one who first loses all his rabbits lose the game?)
While I'm posting anyhow - why restrict the access to the bot-developing tools and having so strict rules around bots? I've started working on a bot, but as it is now, it's unlikely to ever play on the server (unless I operate it manually) or take part in the yearly competition. Giving the game's stated goal of being difficult for bots, I would have thought developing a bot would be encouraged, not curtailed by lots of conditions and requirements?
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Fritzlein
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Re: Fairy Pieces
« Reply #14 on: Apr 13th, 2006, 1:56pm » |
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on Apr 13th, 2006, 11:18am, unic wrote:
Hi, unic! Welcome to the wild, wonderful, wacky world of Arimaa.
Quote:| Making repetitions illegal moves wouldn't reduce the book-keeping for games not played on the server... |
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True, but making threefold repetitions into draws also wouldn't reduce the bookkeeping for live games. You would still be in the same situation as a live game of chess in which (unless the players record the moves) it's hard to know whether a position is occurring for the third time with the same player to move, especially in some endgames. Then consider the bookkeeping needed to enforce the fifty-move rule in chess. Somehow live games of chess get played anyway...
To have the server do the bookkeeping for Internet games is a small convenience to make playing more pleasant.
Quote:| If neither player can deviate in a profitable manner, to me, a draw seems like the most logical outcome. |
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Are you sure a draw is most logical? If so, does it bug you that the game of go has a rule forbidding you from undoing the opponent's last move? Do the rules of go seem inelegant, because they force games to continue which would otherwise be "naturally" drawn?
Go as it stands is a drawless game, but without the ko rule (i.e. no undoing the opponent) there would be draws, because ko fights crop up which are worth more than the margin of victory, i.e. which neither player can concede and yet win the game.
Arimaa too, as it stands, is essentially a drawless game. I like that feature. I have yet to encounter an Arimaa position (either real or composed) in which it was true that neither player could profitably deviate, but if there were such a position, I would rather have a rule which forces deviation than introduce draws.
Quote:| (On the other hand, the situation where all rabbits are captured being a draw feels counterintuitive - wouldn't it make more sense to have the one who first loses all his rabbits lose the game?) |
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The rule you suggest, i.e. that losing all rabbits is a loss, was in effect for the the World Championship and the Computer Championship because they were elimination tournaments. I like the rule a lot. I personally wish it were the standard rule for all games, which would make Arimaa completely drawless.
However, the practical consequences are tiny. There have been more than 1300 rated human vs. human games on arimaa.com, and none have been drawn. The human vs. bot statistics suggest about 1 in 5000 serious games will be drawn.
(Incidentally, 2 human games have been decided by repetition of position, games 11661 and 14990, but they don't help answer a pertinent question: Are there games in which both players are stuck in repetition, so that either player loses by deviating? Chess has such postiions and declares them drawn; Go has them and forces deviation; Arimaa might not have them!)
Quote:| (I'm currently looking for suitable toy animals to make a physical set that's nicer than a chess-set and specific to Arimaa...) |
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Way cool. If you ever get an Arimaa-specific board cobbled together, please post pictures here for the rest of us to admire.
Furthermore, if you actually play Arimaa live, please modify the official rules however you like, and tell us all if your rules work out better. As Omar said just a few posts above, "If many people feel it improves the game, we could change the official rules to adopt it. I am always open to changes which could improve the game while maintaining the original objectives."
Quote:| While I'm posting anyhow - why restrict the access to the bot-developing tools and having so strict rules around bots? |
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In the beginning, there were hardly any people making bots, and Omar wanted to know any time someone started to develop one. The only restriction for getting all the tools is to let him know that you are developing a bot, right? I imagine that Omar will eventually ease up on this, especially when there are other places to play Arimaa online (GGZ Gaming Zone?), and when there are so many bot efforts he can't keep track of them all anyway. In the mean time, to tell him you are developing a bot doesn't seem like a huge concession to make, given that he invented this great game, and built a great place for us to play, and hosts the site without charging us for playing, and put up his own money for the Challenge prize, and yearly puts up his own money for the Computer Championship prizes.
I wouldn't have trouble listing a dozen things where I think, "Why does Omar have policy X? It would make more sense to have policy Y." Yet somehow, I spend half my life on Arimaa anyway.
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| « Last Edit: Apr 13th, 2006, 2:07pm by Fritzlein » |
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