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        Arimaa >> General Discussion >> Drawing
        
(Message started by: 722caasi on Mar 24^th, 2008, 5:53pm)

Title: Drawing
Post by 722caasi on Mar 24^th, 2008, 5:53pm

I think that if all of both sides' rabbits are taken, it should only be a draw if both sides have the the same strongest piece.

what do you think?

Title: Re: Drawing
Post by The_Jeh on Mar 24^th, 2008, 6:53pm

It will almost always be the case that both players will have their elephants left. What if one player has only an elephant, while the other has all his other pieces? Then it's likely that neither would make any progress towards an immobilization through total capture. I used to be skeptical of the rabbit extermination victory, but now I am all for it.

Title: Re: Drawing
Post by Janzert on Mar 24^th, 2008, 8:03pm

Just from the stand point of having a single unified set of rules for both tournament and casual play, I would like to see the rabbit extermination rule applied to all games.

Janzert

Title: Re: Drawing
Post by Fritzlein on Mar 24^th, 2008, 8:52pm

I also see value in a unified set of rules. It's the final step in a long transition from the play-testing and experimentation stage to wide-spread play in different venues.

When a game is first being designed, everything is fair game, and you can change rules at the drop of hat. As the design takes shape, you can still make changes, but you start to have good features you don't want to mess up. After a while you don't want to fix anything that isn't broken. But nothing is broken any more, and the game has been much engaged as it is. We are finally getting past all of those stages and on to a new one, where lots of people have become familiar with the rules and adapted to them, so making a change can be an inconvenience to a lot of people.

Very concretely, we've seen what having two sets of rules did to Clueless2006. That poor bot tries to play in the game room with tournament rules, but thinks it has won when it captures all opposing rabbits, and therefore loses its will to play on. Another example that will occur in the future (I hope) is that there will be more than one place to play Arimaa on-line, so non-uniform rules could break compatibility between the two venues.

If Omar decides that he wants to keep draws around (which I don't really care for), then I support having the draw in every game everywhere, including tournaments. The chess world manages to hold tournaments even with lots of draws; we could surely manage with one per ten thousand games. At least that way the rules would be the rules. I think Arimaa is destined for the big time no matter how rabbit elimination is treated, but it would be a slight drag on the spread and acceptance of Arimaa to have multiple rules, and a slight boost to have a single, universal set of rules that doesn't change, and doesn't need to change.

Finalizing the rules is just a part of Arimaa growing up.

Title: Re: Drawing
Post by omar on Mar 25^th, 2008, 1:31am

I've always felt that a "well designed" game should give an equal chance to both players such that a perfectly played game results in a draw. I've also felt that the margin of draw should be very slim so that very few games would ever result in a draw. Not that I would ever play anything close to a perfect game, but for the design of a game I've thought that these are good ideals to have :-)

Then theory meets reality. In knock out style tournaments it can be very inconvenient to have draws. It can requires having extra games and that can really mess up the schedule. So in the Arimaa match rules I had to introduce the extermination rule so that draws can be avoided.

Recently, Karl pointed out to me that just because a game allows for drawn positions, it doesn't necessarily mean that perfect play will result in a draw. Very interesting. So it is possible then to have a game where non-perfect play can result in draws, but perfect play leads to a win for say the first player. An example is connect four. This means that the game designer isn't off the hook just by allowing drawn positions; the game still has to be solved to say if it is ultimately a draw or not. Bummer. But of course not allowing any drawn positions definitely means the game will never be a draw.

My current position has been to allow for both drawn games and non-drawn games by announcing before the game if the extermination rule is active or not. Why not let the tournament director or event organizer decide if they want to allow draws or not. That gets the game designer off the hook :-)

But over time I've been finding that in all the tournaments I host that I am opting to not allow draws. Even in the 2008 Open Classic which used a Swiss format I opted to not allow draws. A game which does not allow draws does make things a lot easier. You would not believe how much code I've written to handle draws; most of which has hardly ever been used.

Also over time my view of a "well designed" game has been changing to that of a "practically well designed" game. I'm starting to appreciate the view that it doesn't matter so much if the game is ideally a draw, but rather what matters more is that for non-perfect play the game should be balanced for both player. In other words for non-perfect play one side should not have a significant advantage over the other. Thus, a "practically well designed" game does not allow for draws and is well balanced at high level, non-perfect play. I think I would be very content with Arimaa not allowing for draws if we find that even at very high levels of play both sides have a fairly equal chance of winning.

This slow and eventual change of view reminds me of when I was so reluctant to introduce an exception rule of not allowing rabbits to move backwards. I was hung up on that for a while until I finally realized that it was needed to prevent the game from ever going back to a previous state.

So effective July 1st 2008, we will officially switch to using the extermination rule in all games.

We won't know for a long time yet if Arimaa is well balance for both players at high levels of play. We are starting to collect such games with all the postals and tournaments we have going now, but we will need a lot bigger sample to say for sure. In the future if we find conclusively that Arimaa is favored towards one side or the other by more than 2%, I want to reserve the right to try a significant rule change to the setup which I think may help to make it more balanced.

1w Gold places only two pieces: E and R
1b Silver places only four pieces: e, r, m, and r
2w Gold places: M, R, H, R
2b Silver places: h, r, h, r
3w Gold places: H, R, D, R
3b Silver places: d, r, d, r
4w Gold places: D, R, C, R
4b Silver places: c, r, c, r
5w Gold places: C, R and takes two steps
5b Silver takes four steps
6w Gold takes four steps
6b Silver takes four steps

All placement is within the players first two rows.

This slows down the setup stage a bit, but not too much. If it makes the game more equal, then I think it is worth it. Of course there is no guarantee that this will make things more balanced, but we won't know until we try. It will be a real pain at that time to make such a significant change, so lets just hope that Arimaa is well balanced as it is :-)

Title: Re: Drawing
Post by arimaa_master on Mar 25^th, 2008, 7:08am

on 03/25/08 at 01:31:46, omar wrote:

So effective July 1st 2008, we will officially switch to using the extermination rule in all games.

Great! Thanks Omar.

Title: Re: Drawing
Post by arimaa_master on Mar 25^th, 2008, 7:11am

on 03/25/08 at 01:31:46, omar wrote:

We won't know for a long time yet if Arimaa is well balance for both players at high levels of play. We are starting to collect such games with all the postals and tournaments we have going now, but we will need a lot bigger sample to say for sure. In the future if we find conclusively that Arimaa is favored towards one side or the other by more than 2%, I want to reserve the right to try a significant rule change to the setup which I think may help to make it more balanced.

1w Gold places only two pieces: E and R
1b Silver places only four pieces: e, r, m, and r
2w Gold places: M, R, H, R
2b Silver places: h, r, h, r
3w Gold places: H, R, D, R
3b Silver places: d, r, d, r
4w Gold places: D, R, C, R
4b Silver places: c, r, c, r
5w Gold places: C, R and takes two steps
5b Silver takes four steps
6w Gold takes four steps
6b Silver takes four steps

All placement is within the players first two rows.

This slows down the setup stage a bit, but not too much. If it makes the game more equal, then I think it is worth it. Of course there is no guarantee that this will make things more balanced, but we won't know until we try. It will be a real pain at that time to make such a significant change, so lets just hope that Arimaa is well balanced as it is :-)

My point of view is that arimaa is already perfectly balanced therefore I am against any setup changes. ;)

Title: Re: Drawing
Post by mistre on Mar 25^th, 2008, 8:36am

Here are my views on the subjects:

Rabbit extermination rules - all for it. Since I started playing Arimaa, I wondered why this wasn't already in place as an easy fix for draws. In my mind, it is just another way to win like immobilization. This will make for some interesting bot bashing and could re-spark interest in a challenge of some sort.

Starting setups - I believe that any gold-silver advantage is so small that it is irrelevant. Gold gets to go first, but Silver gets to set-up its pieces 2nd. This provides an asymmetrical balance that would be very difficult to calculate, but in practice it works! If it isn't broke, don't fix it. Any other set-up rules would just add too much complexity with no way to measure success.

However, I would like to see the dogs and horses switched in the default set-up. Almost everyone starts their horses on B2 and G2 and therefore this would cut down on the number of pieces you have to shift in the set-up phase.

Title: Re: Drawing
Post by chessandgo on Mar 25^th, 2008, 11:12am

Very interesting, Omar. These new rules would lengthen a bit the placement process, and complicate the rules description, but they might very well make the game almost completely balanced.

I think gold has an advantage, and if we're fortunate enough for the community knowledge to explode in the coming decades, I'm sure this advantage will become relevant, so your new rules might be a great thing not to fall into the black/white paradigm that somehow lessens the interest of chess.

All in all, I like very much to know that you already have a handy solution for solving a problem that might occur in the far future ! Great :)

Title: Re: Drawing
Post by aaaa on Mar 25^th, 2008, 11:44am

Omar, now that you are tinkering with the rules anyway could you also make third repetition illegal instead of an instant loss? This will have to entail updating the immobilization detection code though.

If Gold were to have an undue advantage, then the most intuitive fix would just be to restrict his first move after the setup to just two steps; that way, as long as both players use up all their steps per move, it would mean they would switch being "up" two steps after each move.

Title: Re: Drawing
Post by jdb on Mar 25^th, 2008, 12:12pm

on 03/25/08 at 11:44:29, aaaa wrote:

I agree.

Title: Re: Drawing
Post by aaaa on Mar 25^th, 2008, 1:35pm

If this is to be the rule thread to end all rule threads, let's be thorough about it.

I agree that the scoring system should be abolished, to be replaced by a time control system, either total time used or by some sort of accelerated system. I have a slight preference for the latter because in the case of total time used, whenever someone ends up having used up more than half of the total game time, there would be a sudden, ungraceful shift in advantage between the two players.

On a more silly note: I also don't like the fact that it seems that officially at least it's not the the knight piece that is substituted for the horse.

Scour the following links for your pet peeves and let's use this opportunity to finally get rid of them:
Arimaa Game Rules (http://arimaa.com/arimaa/learn/rulesIntro.html)
Arimaa Match Rules (http://arimaa.com/arimaa/learn/matchRules.html)

Title: Re: Drawing
Post by omar on Mar 25^th, 2008, 4:21pm

on 03/25/08 at 07:11:30, arimaa_master wrote:

My point of view is that arimaa is already perfectly balanced therefore I am against any setup changes. ;)

I hope your hunch is right. My gut feel also says that it is, because it takes a little while for serious interaction (rabbit pulls or captures) to develop, thus allowing room for the initiative to flip/flop between the two sides. So if you look at it that way the alternating setup I proposed just allows more moves to pass before serious interaction develops.

I am definitely not proposing to change the setup rules anytime soon. But say 10 years from we are convinced that the Gold player has a 5% advantage, then we might begin to try this setup rule on an experimental bases and if it helps we might then consider adopting it. I'm just throwing this out right now so that we know there is a potential safety net if the game is not balanced for the two sides.

BTW, in my previous post I forgot to give credit to Karl for introducing me (offline, probably about a year ago) to the view that it doesn't matter if the game does not allow draws as long as it is well balanced for both sides. This was crucial in changing my view of a well designed game. But once you accept this you really have to scrutinize the setup stage of a game since all imbalance can be traced back to it. This got me thinking about how the setup could be made more balanced (at least have the appearance of being more balance) and lead to the setup rules described in my previous post.

If I were launching Arimaa today, I would include the extermination rule and the alternating setup (as opposed to the sequential setup). But its too late now for the alternating setup. Unless the current setup proves to have a noticeable imbalance there really is no need to mess with it.

Title: Re: Drawing
Post by omar on Mar 25^th, 2008, 4:33pm

on 03/25/08 at 11:44:29, aaaa wrote:

Yes, online it essentially is like this. The new interface warns about the repetition and does not allow you to send it. A properly programmed bot would also not lose by repetition. For off line games it can in rare cases be hard to detect the repetition. But even then it would be possible to have a computer referee the moves and warn of the repetition.

I will include this change too in the July 1st 2008 update.

Title: Re: Drawing
Post by omar on Mar 25^th, 2008, 7:17pm

on 03/25/08 at 11:44:29, aaaa wrote:

If Gold were to have an undue advantage, then the most intuitive fix would just be to restrict his first move after the setup to just two steps; that way, as long as both players use up all their steps per move, it would mean they would switch being "up" two steps after each move.

Actually Wayne Schmittberger had also suggested this to me shortly after seeing Arimaa back in 2003. I like this option as well since it would be much easier to adopt. In fact if it turns out that Gold has the advantage, I would prefer to try this option first.

Title: Re: Drawing
Post by 99of9 on Mar 26^th, 2008, 7:33am

on 03/25/08 at 19:17:46, omar wrote:

Great - it is way more elegant than your complicated scheme!

I would just like to note that it does not have to be 2 steps for gold, it could be 1 or 3 depending on how much advantage you think gold had with 4 steps - it just gives you a little more flexibility to correct any imbalance.

(I personally still maintain that with 4 steps gold has a small but significant advantage.)

Title: Re: Drawing
Post by jdb on Mar 26^th, 2008, 8:37am

If it turns out gold has an advantage, another way to equalize is to use the "swap rule".

Gold places his pieces and then silver has the option of placing his pieces as normal, or playing the gold pieces.

Title: Re: Drawing
Post by lightvector on Mar 26^th, 2008, 9:32am

If Gold takes 2 steps, then tempo-wise, the game is even. Silver and Gold each alternate between having taken 2 steps more than the opponent.

Except that Silver gets the advantage of the second setup, which means Silver should have a slight advantage if Gold gets only 2 steps on the first turn.

How much do people think the second setup is worth?

Title: Re: Drawing
Post by Fritzlein on Mar 26^th, 2008, 11:09am

on 03/25/08 at 01:31:46, omar wrote:

In the future if we find conclusively that Arimaa is favored towards one side or the other by more than 2%, I want to reserve the right to try a significant rule change to the setup which I think may help to make it more balanced.

If we have set the threshold for considering a rule change at Gold winning 52% of games between even players (which is equivalent to Gold being worth 14 rating points) then odds are we will be fine keeping the current rules forever. See the latest statistics here:

http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1163650023;start=15#21

Title: Re: Drawing
Post by Fritzlein on Mar 26^th, 2008, 11:26am

on 03/26/08 at 09:32:05, lightvector wrote:

How much do people think the second setup is worth?

My current thought is that the second setup is worth nothing to Silver, because I will balance my horses no matter what. Also I will always centralize my camel for defense against an EH attack on either wing, unless Gold set up unbalanced horses, which never happens these days. The fact that I don't use the second setup to adapt to what my opponent does is the reason I think Gold must have an advantage due to the first move.

However, there is a real possibility that we are wrong about opening theory. It may be that swarming attacks including the camel are good. It may be that one should attack with EH on one wing and MH on the other, in which case decentralizing the elephant and camel could be a net gain of time. Alternatively it may be that it is good to have EHH on one wing and MD on the other. It may be that only Silver can take advantage of the decentralization of the camel, because if Gold decentralizes the camel, Silver can place both horses on the opposite wing and gain advantage. Contrariwise, it may be that only Silver can gain from having unbalanced horses, because if Gold sets up with unbalanced horses, Silver can nullify it by setting up the camel on the same wing. If one is trying to measure the setup advantage in steps (i.e. does it offset a two-step tempo for Gold) it could easily be worth more than two steps. For example putting the camel two steps from where it would have been and putting a horse four steps from where it would have been could mean the second setup was worth six steps!

In short, if opening theory changes to favor swarming attacks, it could easily change my conviction that Gold has an advantage into a conviction that Silver has an advantage.

Title: Re: Drawing
Post by aaaa on Mar 26^th, 2008, 1:47pm

on 03/26/08 at 08:37:23, jdb wrote:

I don't like it except as a last resort, because it would mean you would have to deliberately play suboptimally with respect to the game at the "object level".

Title: Re: Drawing
Post by omar on Mar 26^th, 2008, 11:49pm

I would also prefer not to use the pie rule. In some games it can't be avoided, but in Arimaa I think we can use other means to compensate.

If we find that Gold has an advantage then reducing the number of steps Gold may take in the first move, might be enough to fix it. Though we could reduce by 1, 2 or 3 steps depending on how much compensation is need, it would be nice to use 2.

If we find that Silver has an advantage then using the interlaced setup might be the way to fix it.

Hopefully the difference stays below 2% and we never have to worry about it.

Title: Re: Drawing
Post by aaaa on Apr 2^nd, 2008, 10:51am

I realized that there is yet another advantage of a consistent rabbit extermination rule: There could never be a superfluous move after total annihilation.

Title: Re: Drawing
Post by gatsby on Apr 8^th, 2008, 10:23am

I have recently discovered Arimaa, and I think it is a major effort in creating a game difficult for computers, as well as an entertaining challenge for humans. My congratulations to you, Omar.

I have being reading your recent post proposing your solution to an eventual problem of Gold-Silver imbalance. It is a good idea, but too complicated. I would like to post here my personal proposal, which would, by the way, elliminate every possibility of opening preparation. Current rules already make it difficult, but the setup phase can be simply considered as one more move, and consecuently standarized. My solution overcomes this, and it is as follows:

At the start of the game, every player places his eight rabbits in his nearest row of the board. The rest of the pieces will be placed randomly in the second nearest row, in such a way that Silver pieces are centrally symmetrical to Gold ones (i.e., the same setup as Gold but rotated 180∫). This is to avoid the possibility of elephant confrontation in the same file, and gives us a total of 2520 possible initial positions, a number large enough to make opening preparation impractical. After the pieces setup -and this is the important thing-, Gold starts the game by making one step. Silver then replays with two steps, and Gold, subsecuently, makes three steps. Then every side gets four steps per turn as usual. As you will observe, both Gold and Silver gets an advantage of one step right after making the first move of the game, and a two steps advantage for every move since. I think that this progressive method is fairer than an initial two steps for Gold followed by four steps for every side since then.

Lastly, I would like to join the people who thinks that threefold repetition should be declared simply illegal, and not an instant loss as it is now.

I would be glad to read your answer. Congratulations again for having created such a wonderful game!

P.D.: I write this from Leon (Spain). Please excuse me if my English is not fully correct.

Title: Re: Drawing
Post by omar on Apr 8^th, 2008, 1:19pm

Thanks for the suggestion gatsby and also for the nice comments about Arimaa.

I'm really hoping that the setup advantage of silver balances out the first move advantage of gold and that we never see a statistically significant imbalance of more than 2% for one side or the other. So if that never happens, we will never have to consider changing the setup.

If it turns out that gold has the advantage then the least disruptive solution would be to reduce the number of steps gold gets on the first move. Perhaps 2 steps or perhaps the gradually increasing number of steps for both sides as you suggested. The actual choice will probably depend on how much advantage gold has.

If it turns out that silver has the advantage then I think fixing it will require changing the setup stage. But I think we will find ourselves in a strange predicament. We will have various proposals on how to fix it, but how will we know which one to chose. We really should try out those various proposals experimentally and pick the one which balances both sides the best. But that of course will require a lot of games to determine and probably won't be possible. Also the current rules will probably be so entrenched by then that there will be a large resistance to change even if it could make things better.

What would really be great is if we could find a method to somehow compute the imbalance for a given set of rules. This would allow us to try and determine if we are headed for disaster with the current Arimaa setup and if so allow us to test different proposals to fix it. I remember seeing some thread where Fritzlein suggested trying to run a lot of games between random bots to see if there is any imbalance in such games; but can't seem to find that posting now. Anyways, I would be interested to hear any suggestions on this.

Title: Re: Drawing
Post by Fritzlein on Apr 8^th, 2008, 2:08pm

We don't yet suffer from standardized openings. If some day in the far future Arimaa loses its freshness due to stereotyped openings, then it would be an attractive solution to give the two sides random but equal setups, and balance tempo by reducing steps in the initial move(s). But if we do that, why put all the rabbits on the back row? I think it would be much more interesting to randomize the entire setup.

For the present, I would strongly object to enforcing random but equal setups, because we don't yet know whether Silver can use the second setup to advantage. If Silver can gain tempo from the setup, a very interesting dynamic will be created that I would like to see played out. Let's not try to fix the opening when so far is it not broken; first let's try to figure out how to play this game.

Title: Re: Drawing
Post by aaaa on Apr 8^th, 2008, 2:14pm

If a random element were to be added to Arimaa, it would, for me personally at least, seriously detract from its attractiveness.

Title: Re: Drawing
Post by gatsby on Apr 9^th, 2008, 9:37am

I quote Fritzlein: "If some day in the far future Arimaa loses its freshness due to stereotyped openings, then it would be an attractive solution to give the two sides random but equal setups, and balance tempo by reducing steps in the initial move(s). But if we do that, why put all the rabbits on the back row? I think it would be much more interesting to randomize the entire setup."

Simply because a rabbit placed in front of another piece would obstruct it and force the player to advance the rabbit, which could be inconvenient in the early stages of the game. Also, I think it is more elegant to place in the first row the pieces whose objective is to step through the entire board to goal.

But all of this is, of course, hyphotetical.

Title: Re: Drawing
Post by 99of9 on Apr 9^th, 2008, 10:09pm

on 04/08/08 at 14:14:09, aaaa wrote:

If a random element were to be added to Arimaa, it would, for me personally at least, seriously detract from its attractiveness.

Me too. Particularly because we know that some setups are better than others, this would be like giving a player a random handicap.

Title: Re: Drawing
Post by Arimabuff on Apr 10^th, 2008, 2:41am

on 04/08/08 at 14:14:09, aaaa wrote:

If a random element were to be added to Arimaa, it would, for me personally at least, seriously detract from its attractiveness.

I agree as well, Arimaa would stop being a game like Chess, Go or Checkers and enter into that category of any game where you have to roll the dice to know what to do next (like Monopoly for instance).

Title: Re: Drawing
Post by omar on Apr 11^th, 2008, 1:00am

I think what gatsby is suggesting is somewhat similar to Chess 960 (Fischerandom chess). Only the starting setup position is randomly picked and it is the same for both players. One player does not a different position than the other. I think this still would be considered a fair, deterministic game. However, I think I would still prefer giving the players the flexibility to chose their own setup, even at the expense of a slight imbalance.

As a side note; while designing Arimaa I did consider at one point using a dice to determine the number of steps a player gets on each turn :-)

Title: Re: Drawing
Post by Arimabuff on Apr 11^th, 2008, 7:27am

on 04/11/08 at 01:00:51, omar wrote:

I believe that at its beginning when it was still called Chaturanga, Chess was played between four opponents (hence the doubling of most pieces), based on alliances and part of it was determined by the roll of a dice.