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(Message started by: JimmSlimm on Aug 9th, 2013, 7:31am)
Title: Who would win if...
Post by JimmSlimm on Aug 9th, 2013, 7:31am
In the final move, who would win if..

1. I push an opponent rabbit to goal at the same time as I step one of my own rabbits to the goal line?

2. I immobilize myself at the same time as making opponent immobilized

3. I capture the last opponent rabbit at the same time as suiciding my own last rabbit

Would it be a draw in all cases?
Title: Re: Who would win if...
Post by supersamu on Aug 9th, 2013, 7:47am
There are no draws in Arimaa since a rule change.

According to this site: http://arimaa.com/arimaa/learn/rulesIntro.html
Here is the relevant part copied:

The order of checking for win/lose conditions is as follows assuming player A just made the move and player B now needs to move:

 - Check if a rabbit of player A reached goal. If so player A wins.
 - Check if a rabbit of player B reached goal. If so player B wins.
 - Check if player B lost all rabbits. If so player A wins.
 - Check if player A lost all rabbits. If so player B wins.
 - Check if player B has no possible move (all pieces are frozen or have no place to move). If so player A wins.
 - Check if the only moves player B has are 3rd time repetitions. If so player A wins.

1. The player who just moved would win.
2. The player who just moved would win.
3. The player who just moved would win.

I think that answers your question.
Title: Re: Who would win if...
Post by JimmSlimm on Aug 9th, 2013, 7:58am
Thanks mate :)
Title: Re: Who would win if...
Post by aaaa on Aug 9th, 2013, 9:45am
Self-immobilization no longer necessarily directly ends the game.
Title: Re: Who would win if...
Post by clyring on Aug 9th, 2013, 9:54am
Funnily enough I was just thinking about this and was soon to post a thread about how the very existence of an order of checking as a part of the game itself bothers me. It would be easier and simpler to just say that one can only win after making a move.

Being that the player on move cannot retreat his own rabbits from the goal line, uncapture the opponent's last rabbit, or eliminate the opponent while suffering a goal, this could only conceivably alter results in the exceptionally rare situations where one player can sacrifice his last rabbit and/or push an opponent's rabbit to goal to immobilize the opponent and would simplify the technical details of the rules.
Title: Re: Who would win if...
Post by supersamu on Aug 9th, 2013, 11:02am

Quote:
Self-immobilization no longer necessarily directly ends the game.


Yes, as you can see from the checklist. Or did you refer to something different?


Quote:
[...] It would be easier and simpler to just say that one can only win after making a move.  

Being that the player on move cannot retreat his own rabbits from the goal line, uncapture the opponent's last rabbit, or eliminate the opponent while suffering a goal, this could only conceivably alter results in the exceptionally rare situations where one player can sacrifice his last rabbit and/or push an opponent's rabbit to goal to immobilize the opponent and would simplify the technical details of the rules.


So what happens if Player A on his move sacrifices his last rabbit, while Player B has still all pieces on the board. You want Player B to make a move, even if regardless of Player Bīs move he canīt change the outcome of this game?
Wouldnīt it be easier to rearrange the checklist?
That would be a rulechange in Arimaa. I think it makes sense that the first thing to check is if rabbits are on the goal line or not and if rabbits are present or not, because advancing a rabbit to goal is what Arimaa is about, and not immobilizing the opponent.

I suggest that you open up a thread to discuss this or we discuss here further. It is your choice, clyring.
Title: Re: Who would win if...
Post by rbarreira on Aug 10th, 2013, 5:27am
To me, self-immobilization seems like a meaningless concept. After you make a move, you can never make another move as it's the other player's turn.

The repetition rule further strengthens this, as it's dependent on who played a certain move.

I like to think of immobilization as something that is checked at the beginning of a player's turn.
Title: Re: Who would win if...
Post by arhart on Aug 10th, 2013, 11:58am

Quote:
I like to think of immobilization as something that is checked at the beginning of a player's turn.


Agreed, and I think that's consistent with the order of checking:
 - Check if a rabbit of player A reached goal. If so player A wins.
 - Check if a rabbit of player B reached goal. If so player B wins.
 - Check if player B lost all rabbits. If so player A wins.
 - Check if player A lost all rabbits. If so player B wins.
[end of play A's turn; beginning of player B's turn]
 - Check if player B has no possible move (all pieces are frozen or have no place to move). If so player A wins.
 - Check if the only moves player B has are 3rd time repetitions. If so player A wins.


Quote:
Funnily enough I was just thinking about this and was soon to post a thread about how the very existence of an order of checking as a part of the game itself bothers me.


It might bother me if I thought of the order of checking as part of the game; I think of it as one particular way of explaining the rules. From the perspective of someone who deals with software specifications, I'm used to a specification suggesting one implementation technique (as a means of explaining the required behavior) with the (often implicit) understanding that so long as the observable behavior is identical an implementation can be very different and still meet the specification.


Quote:
It would be easier and simpler to just say that one can only win after making a move.  

Being that the player on move cannot retreat his own rabbits from the goal line, uncapture the opponent's last rabbit, or eliminate the opponent while suffering a goal, this could only conceivably alter results in the exceptionally rare situations where one player can sacrifice his last rabbit and/or push an opponent's rabbit to goal to immobilize the opponent and would simplify the technical details of the rules.


I think there is another way of saying it which gets rid of the order of checking without changing any results (but it does distinguish between the end of one turn and the beginning of the next):
There are multiple winning conditions:
Any player with a rabbit on goal at the end of a turn has a potential win.
Any player whose opponent has no rabbits at the end of a turn has a potential win.
Any player whose opponent has no moves (repetition rule included) at the beginning of the opponent's turn has a potential win.

If at any time a player has a potential win and the player's opponent does not, the win is awarded to that player. If at any time both players have a potential win, the win is awarded to the player who just moved.

If someone would like to change the end of turn potential wins to beginning of turn potential wins, I think that simplifies the rules a bit. From a play perspective, I'd be happy with a player who manages to immobilize his opponent while sacrificing his last rabbit or pushing an opponent rabbit to the goal being awarded the win for initiative rather than a loss because the game is more about rabbits than immobilization.
Title: Re: Who would win if...
Post by aaaa on Aug 10th, 2013, 1:00pm

on 08/09/13 at 11:02:23, supersamu wrote:

Quote:
Self-immobilization no longer necessarily directly ends the game.

Yes, as you can see from the checklist. Or did you refer to something different?

No, I just want to emphasize that immobilization is unique insofar that, unlike the two other victory conditions, the fact that the last-mover wins likewise, is not a case of one rule having a higher priority than another. Before the rules were crystallized in aforementioned fashion, there have been games that ended due to self-immobilization. Here are their ids:
90, 249, 250, 258, 259, 271, 281, 337, 343, 361, 362, 380, 419, 421, 438, 482, 483, 484, 559, 571, 894 and 1153.
Title: Re: Who would win if...
Post by clyring on Aug 10th, 2013, 2:16pm

on 08/10/13 at 05:27:33, rbarreira wrote:
I like to think of immobilization as something that is checked at the beginning of a player's turn.

on 08/10/13 at 11:58:15, arhart wrote:
If someone would like to change the end of turn potential wins to beginning of turn potential wins, I think that simplifies the rules a bit.
I was originally planning on posting my idea in the form of "A player loses if and only if, at the beginning of their turn, there is an enemy rabbit on their first rank, that player possesses no rabbits, or that player can make no legal move," but then decided this would be too clunky to fit in the context of another post rather than as its own independent proposal.


on 08/10/13 at 11:58:15, arhart wrote:
It might bother me if I thought of the order of checking as part of the game; I think of it as one particular way of explaining the rules. From the perspective of someone who deals with software specifications, I'm used to a specification suggesting one implementation technique (as a means of explaining the required behavior) with the (often implicit) understanding that so long as the observable behavior is identical an implementation can be very different and still meet the specification.
Yes, but an equivalent implementation of the current rules will still bother me, just for a different reason: Why is the end of one turn different from the beginning of the next? :P

The observational differences that would occur in my proposed ruleset occur only in games where one player pushes an enemy rabbit to goal and/or sacrifices their own last rabbit, and would (formally) either last one ply longer or allow the player pushing an enemy rabbit to goal or sacrificing their own last rabbit to win by immobilization.


on 08/09/13 at 11:02:23, supersamu wrote:
So what happens if Player A on his move sacrifices his last rabbit, while Player B has still all pieces on the board. You want Player B to make a move, even if regardless of Player Bīs move he canīt change the outcome of this game?
Surely if the game reaches such a point the final ply would be seen by both players as merely a formality. I would expect the player on the losing end of this situation to resign, and from the winning side I would rather be happy about the win my opponent has just handed me than bother complaining about the two seconds it takes to enter any one-step move and claim the win... ;)

on 08/09/13 at 11:02:23, supersamu wrote:
I think it makes sense that the first thing to check is if rabbits are on the goal line or not and if rabbits are present or not, because advancing a rabbit to goal is what Arimaa is about, and not immobilizing the opponent.
You could very well argue this, but that will never change that Arimaa means something completely different to me. To me, Arimaa is not about goals, it is not about elimination, it is not about immobilization, it is not about capture, and it has nothing to do with rabbits. Arimaa is first and foremost about subtle and beautiful situations and patterns emerging from a set of simple rules.
Title: Re: Who would win if...
Post by arhart on Aug 10th, 2013, 3:24pm

on 08/10/13 at 14:16:29, clyring wrote:
"A player loses if and only if, at the beginning of their turn, there is an enemy rabbit on their first rank, that player possesses no rabbits, or that player can make no legal move,"

Elegant. In practice it would not be "only if" because of time controls :-(


on 08/10/13 at 14:16:29, clyring wrote:
Arimaa is first and foremost about subtle and beautiful situations and patterns emerging from a set of simple rules.

Well-said!
Title: Re: Who would win if...
Post by kzb52 on Aug 10th, 2013, 8:10pm
I also have been wondering about the rules.  I think the current chart in the rules is very good for simplifying the clunky system down.  However, it doesn't strike me as being useful or easy to understand.  In fact, I think the following is almost as clear as the current rules.

The current rules state that if Player A just moved then:

Player A.......Player B.........Winner
Goals...........Goals..............A
Goals...........Eliminates.......Impossible  (That would require player A to have a rabbit on the goal line and have no rabbits left)
Goals...........Immobilizes.....A  (Player A goals in a way that leaves him with no legal moves.  Naturally A wins since it's not even B is the one who moves next.)

Eliminates.....Goals..............Impossible  (Opponent can't goal w/o rabbits)
Eliminates.....Eliminates.......A
Eliminates.....Immobilizes.....A  (Player A eliminates in a way that leaves him with no legal moves)

Immobilizes...Goals.............B  (If you push an enemy rabbit to its goal in an effort to immobilize your opponent, you lose)
Immobilizes....Eliminates......B  (If you sacrifice your last rabbit to immobilize, you lose)
Immobilizes....Immobilizes....A

I don't understand why sacrificing your last rabbit to immobilize loses while sacrificing your last rabbit to eliminate wins.  I think the current system is built on the idea that goaling is more important than eliminating which is more important than immobilizing.  I think clyring is right to simplify the rules by saying that you can only win on your turn, and that all three victory conditions are "equal."



Quote:
It would be easier and simpler to just say that one can only win after making a move.


Taking that idea (and arhart's notion of potential wins - which I unoriginally rename victory conditions), I think the following lines are simpler, clearer, and more logical than the current rules.  I also think that there is significant room to improve the phrasing.

In Arimaa, a player goals if one or more of his rabbits finishes a turn on the opposite side of the board.
A player eliminates if all his opponents rabbit's are captured.
A player immobilizes if his opponent is on move but has no legal move to make.
Goaling, eliminating, and immobilizing are the three victory conditions in Arimaa.
A player wins immediately if he achieves one or more victory conditions after his turn.

These rules assume that terms like 'opposite side' 'captures' and 'legal move' are well defined elsewhere in the rules.  The bold situations in my original chart are now wins for A instead (and also the winner would have to play an extra move if his opponent plays suicidally).  The only alternative I can see to the last line is to have 4 rules along the lines of:

A player can only be immobilized after an opponent's turn, while either player can achieve any other victory condition(s) after any turn.
A player wins immediately if he achieves one or more victory conditions after his move and his opponent has achieved no victory condition.
A player wins immediately if he achieves one or more victory conditions after his opponent's move and his opponent has achieved no victory condition.
A player wins immediately if both players achieve any combination of victory condition(s) after his move.


The first line is to emphasize the meaningless-ness of self-immobilization while reminding everyone self-goaling and self-elimination exist so that if an opponent self-immobilizes the game doesn't end instantly, but if he self-eliminates, it does (as in the current system).
Title: Re: Who would win if...
Post by Arimabuff on Aug 11th, 2013, 3:40pm
Immobilization is only relevant if it's your turn to move, if it's your opponent's turn to move, it doesn't matter if you can move or not, because your opponent could make a move that would free one of your pieces for example.


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