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(Message started by: athmwiji on May 19th, 2012, 10:09am)
Title: Arimaa variant without loops
Post by athmwiji on May 19th, 2012, 10:09am

Here is a variant meant to be similar to Arimaa, and still have have simple rules, but eliminate the possibility of repeat states without needing to include the game history.


The following Arimaa rules no longer hold:

- There is no restriction on repeating moves.  

- Passing is a legal move.

- Rabbits can move backwards.

- A player does not loose for having all eir rabbits captured.


I believe the purposes that these rules serve are covered by the following new rules.  To give the new rules I introduce two new terms.

The Net Rabbit Progress for a move is the difference in the total number of squares of all rabbits from its home row between the start and end of that move.  

A Progression is a move where net rabbit progress is positive, a piece is captured, a rabbit ends in the opponents home row, or initial setup.


The following new rules hold:

- A move with negative net rabbit progress is illegal unless a piece is captured.

- If neither player has played a progression in the previous 8 turns, then only a progression is legal.


The rule that a player looses if e has no legal moves still holds, but since a player can pass this only becomes an issue when the player must play a progression, since passing is not a progression.  Capturing your own piece is a progression, so a player may be forced to do so.

As an example,
g g Dr^ R^^
would move a silver rabbit back 1 and a gold rabbit forward 2 giving a net rabbit progress of -1+2 = +1, which would be a progression.
g g R<v H^>
would have negative net rabbit progress and no capture so it would be illegal, but
g g Rv Rvv H>*
would be legal, and would be a progression.
Moving a rabbit left or right does not contribute to net rabbit progress, and net rabbit progress does not need to be counted when a piece is captured.

The 8 turns before a progression must be played, is 4 turns for each player, so gold must play a progression on turn 6g unless one of the players plays a progression before then, on 2g-5s.

Rather than like pawns, the rabbits may be like a tightening vice that can be pushed back and forth and maybe loosened a bit when an animal is captured.

I think the most significant consequence of these rules is that it is harder to move your opponent's rabbits backward, but possible to move your own rabbits backward.  Also, I think the requirement that a progression be played once every 9 turns would generally be a minor factor except in cases of victory by immobilization, and in exceptionally long games.

Well... I have not had a chance to play with these rules yet...
What do you think?
Title: Re: Arimaa variant without loops
Post by ocmiente on May 23rd, 2012, 1:05pm
I agree that the need to have the game history can be a problem, especially when playing on a physical board.  So, I don't want to suggest that it's not worth looking for alternate rules that might solve the problem.  

With respect to your proposal, I think that any cure should be less problematic than the problem itself, and I don't see that your proposal solves it in a way that simplifies the game rules.  

Also, this proposal changes the game in a significant way, by allowing rabbits to move backwards, and not allowing pushing opponent's rabbits backward without a compensating rabbit advance.  This is a major rule change that alters the nature of the game.  

This variant does not completely eliminate history tracking, and the extra math to compute rabbit progress adds complexity.

So, I'm not sold on the idea.  Would prefer something simpler.
Title: Re: Arimaa variant without loops
Post by athmwiji on May 24th, 2012, 7:11am

I am not sure why you say this does not completely eliminate history tracking?  No rule depends on the history...

It does require counting, but a player only has to count to 4.  Players are already required to count the total number of steps animals take as part of a move.  Though now this is 3 things to count instead of just 1.

I do agree that these rules have very significant consequences for game play.  Well, there are less drastic ways to eliminate the need to track history, such as...

After move 100s, the player with more rabbits wins, and if there is a tie silver wins.

Or the number of steps per move begins to accumulate starting with
100s: 5 steps
101g: 6 steps
101s: 7 steps
102g: 8 steps
etc..

Any variant with significant randomness would also eliminate the need make repetition illegal.

But I guess the best option may depend on deeper knowledge of game play than we have now, such as which color has an advantage.

Some things I wonder
Have others considered alternatives to a super ko rule?
Why is the 3rd repetition illegal instead of the 1st?  
Is there some reason for it to be 3?

I could image the game developing into one where players move their pieces around into different defensive positions reducing their options until one player is forced to present a weakness... That may be for people more intelligent than I.


The progression variant may be interesting for its own sake.  I was considering other changes:
- A player does not win by getting a rabbit to the opponents home row.
- An animal next to a trap can choose to prevent the capture of an animal on the trap.
Players would then want to drag the opponent's rabbits to their own home row to stop them from playing a progression.  That might be more like Lose Arimaa, except players would not win by capturing their own rabbits.
Title: Re: Arimaa variant without loops
Post by ocmiente on May 24th, 2012, 12:38pm

on 05/24/12 at 07:11:02, athmwiji wrote:
I am not sure why you say this does not completely eliminate history tracking?  No rule depends on the history...


History requirement here:

on 05/19/12 at 10:09:32, athmwiji wrote:
- If neither player has played a progression in the previous 8 turns, then only a progression is legal.


This is a rather strict view of what constitutes history in that you're only tracking progression and not entire move history, so I can understand why some people not see this as history tracking.  It's just my opinion.

As far as this goes:

Quote:
After move 100s, the player with more rabbits wins, and if there is a tie silver wins.

That's pretty much already in the time keeping rules, though it's not based on turn but based on game length.  However, I don't think that's a satisfying work around for eliminating the repetition rule.  That would result in to players who were convinced that breaking the repetition would lead to a loss would just sit there repeating moves until time ran out.  

With respect to some of the other ideas you mentioned, you might like something like avalanche chess (http://www.chessvariants.org/mvopponent.dir/avalanche.html) or progressive chess (http://en.wikipedia.org/wiki/Progressive_chess).
Title: Re: Arimaa variant without loops
Post by athmwiji on May 26th, 2012, 7:21am

on 05/24/12 at 07:11:02, athmwiji wrote:
After move 100s, the player with more rabbits wins, and if there is a tie silver wins.



on 05/24/12 at 12:38:29, ocmiente wrote:
I don't think that's a satisfying work around for eliminating the repetition rule.  That would result in to players who were convinced that breaking the repetition would lead to a loss would just sit there repeating moves until time ran out.  


Repeating until 100s would be a reasonable strategy for silver, since silver would win, but not for gold.  This puts the onus on gold to be aggressive from the start.  Or later, the player with fewer rabbits.

But this leaves some questions...


Does gold have an advantage now?

If silver has an advantage maybe gold should win a tie when rabbits are equal.  From this (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1163650023) analysis it seems unclear, but I was guessing that gold does.


Even if gold does have an advantage now, would this rule give silver too much of an advantage?

This rule might be unbalancing if the best strategy in Arimaa is to maintain a strong defensive position until your opponent offers a weakness, but this does not seem to be the case.  My impression is that it is better to attack.  Given that few games last to 100s anyway, my guess is that this rule would not be unbalancing.

As long as this is a finite, deterministic, perfect information game without draw some player will have a perfect strategy, but the game may still be close to even in practice for mortal players.  
Title: Re: Arimaa variant without loops
Post by athmwiji on May 26th, 2012, 11:32am
Well, this topic has come up several times in the forum, and others have proposed alternatives.  I think I liked the following more:

From turn 1x0s the goal row is moved from row 8 to row 7-x

For example, if the game gets to 100s silver could win for having a rabbit in row 7.

In addition to making the restriction on repeat moves unnecessary, so that the full game history would not need to be included as part of the current game state, this would also limit games to a reasonable length.

Some relevant threads are:
Importance of repetition rule (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1274916361)
Arimaa Repetition rule and draws. (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1293397074)
Should the repetition rule favor attacker? (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1288827366)
Draws? (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1238448389)
Game lengths (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1262974905)
Silver defending forever? (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1250744520)
Drawing (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1206399208)
Rules Discussion (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1201845528)
Fixing the rules / eliminating draws (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1112545671)
Title: Re: Arimaa variant without loops
Post by Fritzlein on May 26th, 2012, 1:20pm
Thanks for collecting these discussion links.  If practical stalemates ever start occurring in Arimaa, it will be easiest to restart the discussion with a review of past ideas.
Title: Re: Arimaa variant without loops
Post by minderbinder on May 31st, 2012, 6:14pm

on 05/26/12 at 11:32:44, athmwiji wrote:
From turn 1x0s the goal row is moved from row 8 to row 7-x

Although I like this better than the "progression tracking" idea, I have a few concerns (presuming that these changes would happen after it is discovered that serious deadlocks are occurring in Arimaa):

1. It might give Silver a large advantage to have the last move before the row advances (and hence the first move that could benefit from this row advance).

2. What happens if both players have a rabbit on row 7 when move 101 is reached?

For now though, it seems that deadlocks are not common enough to worry about preventing infinite games.
Title: Re: Arimaa variant without loops
Post by athmwiji on Jun 3rd, 2012, 12:27pm

on 05/31/12 at 18:14:40, minderbinder wrote:
1. It might give Silver a large advantage to have the last move before the row advances (and hence the first move that could benefit from this row advance).

2. What happens if both players have a rabbit on row 7 when move 101 is reached?

My understanding would be, if both players have a rabbit on row 7 at the end of 100s then Silver wins, since winning conditions are checked for the moving player first.  This does give Silver advantage.  And, it might be a big advantage!

Well, the current match rules include an option for the maximum number of turns until the game is scored, and the scoring seems to give Silver less of an advantage.  Another option for scoring that was suggest by someone else in another thread was something like...

If the turn limit is reached,

- The player with the rabbit farthest forward wins.

- If there is a tie, then ignore one rabbit farthest forward from each player and check the remaining rabbits, repeating this until one player has a rabbit farther forward than the other player's rabbits.

- If both players have the same number of rabbits on the same rows from their respective perspectives then Silver wins.


If there is a turn limit, after which the game is scored, then I think the following rules could be dropped without breaking the game:

- There is no restriction on repeating moves.  

- Passing is a legal move.

- A player does not lose for having all eir rabbits captured.

- A player does not lose for being immobilized


In the other direction, if one wants to drop the restriction on repeating moves while changing the game as currently defined as little as possible, having a ko rule (undoing the previous move is illegal) seems less extreme then having a super ko rule (repeating a board position [3x] is illegal).
I have not played many games, but I have already gotten into a ko situation where I won the game because the other player could not repeat a position and I might have lost otherwise.  The other player, a bot, attempted to and would have benefited from undoing my previous move.  



on 05/26/12 at 13:20:21, Fritzlein wrote:
 If practical stalemates ever start occurring in Arimaa...

It seems from this that you don't fully consider the super ko rule to be valid?  I guess this means it is a way to deal with unwanted situations as long as they rarely occur, but if the rule actually becomes important to the game, then it should be replaced.  Although, these other alternatives all seem to have a similar flavor in that sense.  

My impression from this and past discussions are that most consider the super ko rule to be a potential problem only in the future if it is insufficient to reasonably limit the length of a game, but I have other reasons for not liking the super ko rule:

The game state grows, so a larger amount of data must be stored and searched to make each successive move.

It makes the game more difficult to analyze without making it more interesting to play, in my opinion.
(well, this could be considered a benefit if the difficulty encourages the development of more generally capable bots)

In a face to face game with ordinary pieces the difficulty of keeping the history in mind may cause players to make mistakes or disagree.


I should perhaps say that I mostly play Go, and I am not very familiar with Chess, so that may influence my perspective.
Title: Re: Arimaa variant without loops
Post by Fritzlein on Jun 3rd, 2012, 3:02pm

on 06/03/12 at 12:27:59, athmwiji wrote:
- A player does not lose for having all eir rabbits captured.

- A player does not lose for being immobilized

If your purpose is to change the game dynamics as little as possible while eliminating the need to keep a game history, why are you changing the winning conditions?  Do you have additional purposes behind your proposal, or am I missing the point?  I am interested in an elegant replacement for the superko rule, but I don't want to fix anything that isn't broken.
Title: Re: Arimaa variant without loops
Post by athmwiji on Jun 3rd, 2012, 7:23pm
My last post was not meant to be a single cohesive set of rules, but rather just thoughts on rules that limit game length.  The secondary victory conditions also seem to serve this purpose.  if the game length is otherwise limited, two options with conflicting motivations would be:

To make the game as simple as possible, remove any other rule that mainly serves to limit the length.

To change the game as little as possible, replace the super ko rule with a ko rule, but don't change any other rules.


I also don't like having a growing game state.  

If only the bots could play for eons... But alas memory constraints would not allow it. OTL


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