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        Arimaa >> General Discussion >> RFC: Two Capturing Variants
        
(Message started by: lothario on Dec 1st, 2012, 1:37pm)
Title: RFC: Two Capturing Variants
Post by lothario on Dec 1st, 2012, 1:37pm
TLDR: Two Arimaa capturing variants, based on surrounding enemy pieces anywhere on the board, are proposed.  Interesting implications are traced out.  Feedback welcome.

I've been playing with two variants of the Arimaa capturing rules.  I think they yield interesting games that give Arimaa a more offensive feel, but still keep capturing significantly more difficult than Chess.  I would love to get impressions and feedback from others who are more experienced.

(These two variants change Arimaa gameplay to such an extent that it is an entirely different game.  The best I can hope for is that Omar will consider making these modified capture rules an option, and let the community decide whether it is an overall improvement.  That being said, I have no pretensions that either of these variants will ever be adopted into Arimaa, given the existing body of games and theory, and the fact that I'm just an uppity whippersnapper amateur who doesn't know his place :) )

The thought that began this diversion was to see if I could (1) merge some flavor of Go's capturing into Arimaa, (2) remove the trap squares, (3) make Arimaa less defensive, and (4) keep Arimaa more strategic than tactical.  Above all, I want to keep Arimaa's beautiful and fascinating "emergent strategies" (for lack of a more precise term); things like frames, hostages, forks, etc.

Both variants remove the capture squares; all squares on the board are identical.

Version 1 -- Simple Surround Capture:

   * A piece is captured and removed from play if and only if every adjacent square (N,S,E,W) is occupied by a piece of the opposite color.

     Edge and corner captures follow naturally from the above description: edge pieces can be captured by just 3 opposing pieces, pieces in the corner can be captured by just two enemy pieces.  It is easier to capture a piece in the corner than on the edge; easier on the edge than in the middle of the board.  So the edges and corners retain some of the original feel of the trap squares, as it is risky to be near the edge or corners when enemy pieces are nearby.

Version 1 implications (with my arbitrary scoring of each):

     * -1: Captures, overall, are much easier to do, leading to more material being traded earlier in the game, and simplifying the game perhaps too quickly.

     * +-0: Rabbits, dogs, and cats are more powerful; elephants, camels and horses are weaker.  This makes the game more Chess-like: similar to how a pawn can capture a Queen or deliver checkmate, with this rule as few as two rabbits can capture any enemy piece located in a corner.    
       
     * +1: The capital pieces (elephant, camel, and horses) can't confidently charge into enemy territory alone or in an EH-attack.  The "rabbit pulling" openings would be a much riskier approach, since it would be fairly easy to capture a capital piece that is already near the edge with just 3 enemy pieces.  I imagine that the capital pieces would have incentives to stay relatively close to home, and fewer lone-wolf raids would occur.  Attacks would tend to be with groups of pieces for safety.

     * +0.5: The total strength of an army is weighted strongly towards total number of pieces, and less determined by the strength of the individual pieces.  So a net trade of an elephant for 4-5 other pieces may be worthwhile.

     * +1: Positional play is still incredibly important -- clumps of like-colored pieces determine local strength.

     * +1: This brings in the Go concept of "shape" into Arimaa.  Three like-colored pieces surrounding an empty square create a trap square on that position, anywhere on the board, ready to capture anything that is pulled / pushed there by a 4th piece.

     * +1: Center-edge-corner strategies: the center is the "safest" area, since 4 pieces are required to capture an enemy piece in the center.  The edges are more risky, since only 3 pieces are required to capture.  Corners are the most vulnerable.  There is an interesting interplay in that edges and corners are increasingly far from the center, so easy capturing at the edge / corner has to be balanced against the loss in mobility.  I imagine that this will push the capital pieces towards the center where they are most mobile and more difficult to capture, and push the minor pieces / rabbits to the edge corners, where they can easily capture other pieces.  This has a strong Go flavor to it.

     * +1: Deadlocked positions are less likely to happen: huge intertwined piles of pieces constantly positioning in the rear flanks to shove through a rabbit would likely not happen as much, since this sort of position would lead to easy captures.  I can see there being a "wedge" strategy, where an unbroken line of capital pieces lead the way (can't be easily pulled into a capture position) with rabbits following.  To break up the wedge, the enemy would have to attack the weaker flanks, pulling off weaker pieces and capturing them to get to the rabbits.

     * +1: 4 pieces in a capture position in the middle of the board are themselves vulnerable to capture, and thus not particularly stable.  Bringing in more pieces to strengthen the capturing configuration is expensive and exposes weaker pieces to being pulled off and captured themselves, creating lots of competing positional and strategic opportunities that is always changing and dynamic.

     * -1: The existing hostage strategy no longer applies, given that the trap squares are removed.

     * +1: Without the trap squares, the capturing rule is much simpler, simplifying the rule set.  In my opinion, the removal of the trap squares makes the modified game more uniform and less arbitrary, giving the game more of a Go feel and improving the game's elegance.

Version 2 -- equal / stronger surround capture:

   * A piece is captured and removed from play if and only if every adjacent square (N, S, E, W) is occupied by a piece of the opposite color of equal or greater strength.

Implications:

   * +1: This version keeps the game closer to existing Arimaa.  Capital pieces are still much stronger than weaker pieces.  
     
   * -0.5: Elephants are even stronger than they are in existing Arimaa, as it is impossible to remove an elephant from the board.  
     
   * +0: Camels can only be captured in the corners, making their capture much more difficult, and thus making Camels more equal in power to Elephants, and less of a liability.  A horse capture in the middle of the board requires the opposing 2 horses, camel, and elephant to pull it off.

   * +1: A piece's safety from capture is guaranteed if it is equal or stronger than all enemy pieces in its local neighborhood, making it relatively easy for humans to determine if a piece is safe for the near future.

   * +1: I can imagine there being a situation like an "edge hostage" or a "corner hostage", where, e.g., a nascent capture of a frozen silver horse is threatened near the edge of the board if gold can get his camel / horse to the edge in time to capture the frozen silver horse before it is freed.

Thoughts? Criticisms?  I'm interested enough in this to write up a Bot that plays both of these variants, but it won't be very good without a corpus of games from which to learn.
Title: Re: RFC: Two Capturing Variants
Post by Arimabuff on Dec 1st, 2012, 11:42pm
I think the first thing you should do is what Omar did with Arimaa, IE find half a dozen of friends that have some experience in board games and play with them these variants on a chess board. You may quickly find out that neither of these variants are suitable for an interesting game. Omar tried many different versions of Arimaa before finding the correct one. It would be a shame to waste time and effort on a bot and then find out that the game is not even playable, wouldn't it?
Title: Re: RFC: Two Capturing Variants
Post by lothario on Dec 2nd, 2012, 3:17pm

Quote:
I think the first thing you should do is what Omar did with Arimaa, IE find half a dozen of friends that have some experience in board games and play with them these variants on a chess board. You may quickly find out that neither of these variants are suitable for an interesting game.

Yes, all good points.  I've playtested the second variant, "stronger/equal strength surround capture" enough times that I enjoy it as much as, if not more than, standard Arimaa.  I am fairly confident that it has as much strategic possibilites to be a variant on par with existing Arimaa.  Although, I'm willing to admit that my desire to see this new capture rule as an option is clouding my objectivity :)

After playing again today, here are some of the nice features of the "stronger/equal surround capture" variant:
  • Subjectively, the capture rules feel more natural and intuitive, which I like aesthetically.  Any square on the board can lead to capture, with strong strategic differences between the center / edge / corners.
  •  Capturing in the middle of the board is quite difficult, and rarely happens, due to the need to coordinate 4 pieces, at least one of which is often vulnerable to the enemy's strong pieces.  Captures are pushed to the edges and corners, since it requires fewer pieces to accomplish.
  • One wants the capital pieces in the center to be most effective, but given the difficulty to pull off captures in the center means they often have to commit to an edge / corner to remove material.  There is a constant positional tension between center mobility and committing pieces to the edge / corners.  I really like this tension.
  • The "feel" of camel / horse hostages is still there, just modified somewhat.  Camels can only be captured in a corner, and require both the opposing camel / elephant to pull it off, so it is more difficult to do.  Almost all horse captures are at the edges, and once one side commits big pieces to a horse capture, the other side is almost always able to inflict heavy damage of its own on the other side of the board.  Again, the central mobility / edge capturing tension is very strong.
  • It is easy at a glance to see if a piece is in immediate danger of capture: "are there enough pieces of equal / greater strength nearby to kill this piece in the next turn?"  I feel this makes capturing more strategic, more positional, and less tactical.  The often frustrating "gotcha!" captures that happen against bots in existing Arimaa (due to tactical flaws in my positions) seem to be unlikely here.

There are several other things I really like about this variant, but I'll quit carrying on for now :)


Quote:
Omar tried many different versions of Arimaa before finding the correct one. It would be a shame to waste time and effort on a bot and then find out that the game is not even playable, wouldn't it?

I should mention that I am currently developing a bot to play standard Arimaa, and I will make it so I can swap out the capturing rules, so 90% of the development work will be shared between the versions.  The second variant will be worthless without several games to learn from, of course, but at least it will provide a starting point with a minimum of duplicated effort.
Title: Re: RFC: Two Capturing Variants
Post by Arimabuff on Dec 3rd, 2012, 3:49pm
Ever hear of Hnefatafl? It's also known as Viking Chess? Something you could picture Beowulf play. ;)

It's a game that's been forgotten for centuries and only recently rediscovered.

Anyway, it's interesting that the pieces move somewhat like Chess or checker pieces but to capture you have to surround the enemy piece with your own as in Go or your variant. It's also a game that's disymmetric, unlike Chess. I think only one side has a king and the other side has to capture it before being exterminated. Basically it's like the invasion of a kingdom by enemy forces. I don't know more about it because I played only a few games and it was years ago.
Title: Re: RFC: Two Capturing Variants
Post by lothario on Dec 5th, 2012, 8:43pm

Quote:
Anyway, it's interesting that the pieces move somewhat like Chess or checker pieces but to capture you have to surround the enemy piece with your own as in Go or your variant. It's also a game that's disymmetric, unlike Chess. I think only one side has a king and the other side has to capture it before being exterminated. Basically it's like the invasion of a kingdom by enemy forces. I don't know more about it because I played only a few games and it was years ago.

Interesting. From the wikipedia page, it says that the side with the king almost always wins and the standard rules lead to an unbalanced game.  It also looks like there isn't an established setup so perhaps other initial setups would lead to a more balanced game.

After more playtesting, I found one more interesting fallout from the "surround by equal / stronger capture" rule: if, for instance, gold captures the silver camel (in the corner, with the gold elephant and camel), then it is impossible for silver to capture gold's camel.  So once a camel is captured, the capturing side has the equivalent of 2 uncapturable elephants, guaranteed.

The tradeoff for this huge advantage is that the capturing side has to commit a camel and an elephant to a corner, far away from the center of the board.  The other side has the opportunity to take control of the center and edges while the capturing side spends time dragging a camel to the corner.


Quote:
Omar tried many different versions of Arimaa before finding the correct one...

Are you of the opinion that Arimaa's current rules are the best possible?  I think that one set of rules can be judged better or worse than another set, but that it would be impossible to find any single rule set that could be deemed the "correct" one in any objective sense.  That being said, I think Arimaa's rules are very well done, well thought out, and well balanced, as proven by its growing community.

I'd be interested to learn more about how Arimaa's rules were arrived at, and if anything like a "surround capture" was considered during the process.  Do you know if Omar wrote anything on the process of inventing Arimaa?
Title: Re: RFC: Two Capturing Variants
Post by Fritzlein on Dec 6th, 2012, 4:48pm

on 12/05/12 at 20:43:30, lothario wrote:
That being said, I think Arimaa's rules are very well done, well thought out, and well balanced, as proven by its growing community.

I agree with you that the proof of Arimaa's excellence is in growing community (including discussions, books, tournaments, etc.).  I would, however, disagree with the notion that this success is because the rules were well thought-out.  I think Omar got lucky, and insofar as it was not luck, his success was not based on having a great intuition as to what makes for good rules, not based on thinking very clearly and carefully about rules, but rather based on trying out many, many rule sets and rejecting one failure after another.  Being willing to fail repeatedly and being able to recognize failure were Omar's key virtues.  


on 12/05/12 at 20:43:30, lothario wrote:
Do you know if Omar wrote anything on the process of inventing Arimaa?

Yes, he did: http://arimaa.com/arimaa/about/

The trouble with inventing new games (or new variants of old games) is that you simply can't tell how good the game will be just from the rules.  It is impossible.  The only way to determine the quality of a game is to playtest.  But who will be willing to playtest your game?  You are excited about it because it is yours, but who else will be excited about it, and why?  Omar did a lot of his playtesting alone, and also exhausted the patience of all of his relatives he tried to rope into playtesting along with him.  He certainly wouldn't have been able to recruit me even if he had known me back then, because I already have too many good games I want to play without being bothered over a new game that might be good.

When I first learned about Arimaa, it had already been playtested on-line for a year and a half by a small group, but Arimaa was still so new and so unproven that it would never have attracted my attention based on its rules or minimal exploration.  Omar could have said Arimaa was ten times as strategic as chess, and I would have completely ignored him because there was no way for him to know, i.e. insufficient proof.  If you want to prove a game is worthy, there is simply no substitute for hordes of people trying to be best at it.  The only reason I gave Arimaa a shot in the first place was the $10,000 Arimaa Challenge prize.  Omar really had to stick his neck out financially to attract someone with my attitude.

Your variant might be the best two-player abstract ever invented, i.e. better than chess, better than Go, better than Arimaa, and better than the dozens of new abstracts invented every year.  But if it is the best, how will we ever know?  It takes an enormous amount of effort merely to find out, say, that the game is pretty good but after you get reasonably strong players it is always drawn (cf Abalone).  And no matter how much you test a game without busting it, you might always bust it by getting a little bit better.  And until we know a game won't be busted, why should we put in the effort to test it?

This is the chicken-and-egg dilemma faced by every abstract game inventor, including Omar.  I wish I had a good way out of the dilemma (particularly for Arimaa, which I personally believe deserves to push aside chess and take over its cultural status) but I don't have an answer.   :'(
Title: Re: RFC: Two Capturing Variants
Post by lothario on Dec 6th, 2012, 11:04pm

Quote:
I would, however, disagree with the notion that this success is because the rules were well thought-out.  I think Omar got lucky, and insofar as it was not luck, his success was not based on having a great intuition as to what makes for good rules, not based on thinking very clearly and carefully about rules, but rather based on trying out many, many rule sets and rejecting one failure after another.  Being willing to fail repeatedly and being able to recognize failure were Omar's key virtues.

What strikes me about your account is that it argues that Arimaa's rules came out of an exhaustive search process with a simple evaluation function rather than out of an intuitive process more characteristic of human-style reasoning. Id est, Omar was more Deep Blue than Kasparov to create a game that, by its very essence, is designed to be intuitive to Kasparov and confounding to Deep Blue!


Quote:
The trouble with inventing new games (or new variants of old games) is that you simply can't tell how good the game will be just from the rules.  It is impossible.  The only way to determine the quality of a game is to playtest.  But who will be willing to playtest your game?  You are excited about it because it is yours, but who else will be excited about it, and why?  Omar did a lot of his playtesting alone, and also exhausted the patience of all of his relatives he tried to rope into playtesting along with him.  He certainly wouldn't have been able to recruit me even if he had known me back then, because I already have too many good games I want to play without being bothered over a new game that might be good.

I have no doubt that designing strategy games takes a tremendous amount of hard work and months of playtesting.  My posts are here only to say to the Arimaa community, "hey! I might be on to something here!"  in the same vein as other rule variant threads I've seen in the past (just rabbits and cats variant, for example).  I have done what I believe to be a minimum of due diligence by playtesting and by describing the interesting features of the rule change.  My hope is that others' curiosity may be piqued by my arguing for the "equal/stronger surround capture" variation to do what I did, and try it out on a rainy afternoon with an Arimaa set.  I am playtesting it often, and beginning to engage others in doing so.  I'm planning on adapting my in-development Arimaa bot to play with this rule variant, and I would love for the opportunity to have this bot play more than just against itself and me.  But I'm certainly getting ahead of myself.
Title: Re: RFC: Two Capturing Variants
Post by Luis Bolaños on Dec 7th, 2012, 10:18am
I mentioned surround capture in this forum back in 2010 (I was "gatsby" then). Omar then told me that he had tried it during the design process (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1273854806;start=12#12) but that it didn't work too well.


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