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(Message started by: rbarreira on Mar 21st, 2012, 12:16pm)
Title: What would you ask an Arimaa Oracle?
Post by rbarreira on Mar 21st, 2012, 12:16pm
If there was such a thing as an Arimaa Oracle that knew the solution to every Arimaa position and you had the chance to ask a few questions, what would your questions be?

The most obvious questions are of course which player wins with best play, and what are the moves in the optimal Arimaa game (with the winner winning as fast as possible and the loser delaying their loss as much as possible).

Something I would ask would be what is the most lopsided (material-wise) setup with <= 16 pieces on each side which is still a win for the weaker side.

Any ideas in this unrealistic intellectual exercise? ;)
Title: Re: What would you ask an Arimaa Oracle?
Post by Fritzlein on Mar 21st, 2012, 1:21pm
We know Arimaa is theoretically a forced win for Gold or for Silver.  Obviously the first question is who the winner is, but a close second is how long the optimal game is, where by optimal game I mean the winner playing the winning move that wins fastest, and the loser playing the losing move that loses slowest.  If the length of the optimal game is astronomical, it means that Arimaa is a practical stalemate with theoretical best play.  Wouldn't it be a hoot if the optimal game ended due to lack of a legal move, which was due to the repetition rule?  Third question is what are the setups of each player in the optimal game.

I guess all three of my questions are included in your "moves of optimal game", but I would take satisfaction from any of the three answers without knowing the other two.  :)

If our Arimaa oracle could take it, I would ask about alterations to the rules, i.e. what happens to the optimal game with just a ko rule and no super-ko rule, what happens if both sides start with only one HDC (13-piece Arimaa), what happens if a lion replaces one of the horses, and what happens in some of the crazy variant proposals.  If the Arimaa oracle could answer for any variant of Arimaa, I would claim chess is an Arimaa variant and ask questions about chess. ;D
Title: Re: What would you ask an Arimaa Oracle?
Post by hyperpape on Mar 21st, 2012, 2:49pm
What proportion of reasonable setups are a win for Gold/Silver? I'll let the Oracle tell me what reasonable means.

Title: Re: What would you ask an Arimaa Oracle?
Post by 99of9 on Mar 21st, 2012, 6:07pm
I'm amazed that you've moved on to arimaa variants already.  Of course the oracle would deny all those requests, because after all, it is an ARIMAA oracle!  Even still, there are a lot of interesting things about arimaa and it's history that should be asked.  Here's one:

At what stage in each game did the eventual winner obtain a winning position that they never gave up.

(As a consequence we would find out which players have ever played a perfect game.)
Title: Re: What would you ask an Arimaa Oracle?
Post by rbarreira on Mar 22nd, 2012, 4:02am

on 03/21/12 at 18:07:10, 99of9 wrote:
At what stage in each game did the eventual winner obtain a winning position that they never gave up.

(As a consequence we would find out which players have ever played a perfect game.)


Ah very interesting, I like this one. It would be interesting to see what's the longest sequence that was executed perfectly by a player. Not necessarily perfectly in terms of winning the fastest but just always playing winning moves (I guess that's what you meant).
Title: Re: What would you ask an Arimaa Oracle?
Post by hyperpape on Mar 22nd, 2012, 11:32am
Hmm, that leads to another question: was Hanzack getting outplayed in the opening, or is Nombril's theory right?
Title: Re: What would you ask an Arimaa Oracle?
Post by omar on Mar 22nd, 2012, 11:55am
What's your ELO rating?

I know it's probably not a question that has a straight forward answer, but I've always been fascinated by what happens to ratings as the level of play approaches perfection. There is something calculus like about it. Initially it would seem that the answer is infinity since the Oracle plays perfectly, but as you approach perfect play from non-perfect play say by adding another ply of search you can see that the rating is limited if the length of the optimal game is limited.

I did this with tic-tac-toe once and also tried it with connect-4. I think the rating of the game Oracle gives you some sort of measure of the depth of the game or probably more like  the number of ranks it has.
Title: Re: What would you ask an Arimaa Oracle?
Post by aaaa on Mar 22nd, 2012, 5:19pm
I think a more robust argument in favor of a perfect player having a finite rating is the fact that a random player always has a non-zero chance of beating anyone, including a perfect player, thus precluding the possibility of their rating difference being infinite.
Title: Re: What would you ask an Arimaa Oracle?
Post by clyring on Mar 22nd, 2012, 8:32pm
-How many different equally optimal lines are there for the first X moves of the game? It is possible that in many positions there are multiple legal moves which all win equally quickly or lose equally slowly, especially when taking transpositions into account. I would be curious about how often this happens and how many optimal moves there are in such positions as well as how often the moves lead into independent variations rather than just transpositions.
Title: Re: What would you ask an Arimaa Oracle?
Post by Arimabuff on Apr 3rd, 2012, 9:11am

on 03/21/12 at 13:21:32, Fritzlein wrote:
We know Arimaa is theoretically a forced win for Gold or for Silver.  Obviously the first question is who the winner is, but a close second is how long the optimal game is, where by optimal game I mean the winner playing the winning move that wins fastest, and the loser playing the losing move that loses slowest.  If the length of the optimal game is astronomical, it means that Arimaa is a practical stalemate with theoretical best play.  Wouldn't it be a hoot if the optimal game ended due to lack of a legal move, which was due to the repetition rule?  Third question is what are the setups of each player in the optimal game.

I guess all three of my questions are included in your "moves of optimal game", but I would take satisfaction from any of the three answers without knowing the other two.  :)

If our Arimaa oracle could take it, I would ask about alterations to the rules, i.e. what happens to the optimal game with just a ko rule and no super-ko rule, what happens if both sides start with only one HDC (13-piece Arimaa), what happens if a lion replaces one of the horses, and what happens in some of the crazy variant proposals.  If the Arimaa oracle could answer for any variant of Arimaa, I would claim chess is an Arimaa variant and ask questions about chess. ;D

Could you please explain what a lion can do?
Title: Re: What would you ask an Arimaa Oracle?
Post by Arimabuff on Apr 3rd, 2012, 9:16am

on 03/21/12 at 13:21:32, Fritzlein wrote:
...I would claim chess is an Arimaa variant and ask questions about chess. ;D

About as much as ping pong is a soccer variant. ;D
Title: Re: What would you ask an Arimaa Oracle?
Post by Adanac on Apr 3rd, 2012, 9:36am
I always wonder about weird things.  I’d like to know, if Gold begins the game without an elephant, and
Silver begins by removing 7 rabbits, then cats, then dogs, etc., how many pieces would Silver need to remove before Gold begins the game with a forced victory?  My guess is 9 but I’d like the Oracle to tell me the real answer.  I’d be shocked if the answer is 7 or 10, less surprised if it’s 8.

If Gold begins the game without any horses or camel and Silver starts with only 1 rabbit, who has the advantage?

Is it a better strategy to attack first or wait until the opposing elephant is distracted and then counter-attack with the camel?

Am I really supposed to play 3. Be2 in the King’s Gambit.  Oops, wrong game :)
Title: Re: What would you ask an Arimaa Oracle?
Post by Fritzlein on Apr 3rd, 2012, 9:57am

on 04/03/12 at 09:11:58, Arimabuff wrote:
Could you please explain what a lion can do?

A variant I proposed was to break the tie between the two horses, so instead of the piece strength being 1,1,2,2,2,8, it would be 1,1,1,1,2,2,8.  I thought I would call the new level a lion.

elephant > lion > camel > horse > 2 dogs > 2 cats > 8 rabbits.

This can still be played with a chess set by inverting one rook.
Title: Re: What would you ask an Arimaa Oracle?
Post by Arimabuff on Apr 3rd, 2012, 12:41pm
Ok, so a lion beats a camel but is beaten by an elephant. I think I saw in one of the old Tarzans ( with Weissmuller) a lion attack an elephant but I don't remember who won.
Title: Re: What would you ask an Arimaa Oracle?
Post by Adanac on Apr 3rd, 2012, 12:48pm

on 04/03/12 at 12:41:27, Arimabuff wrote:
Ok, so a lion beats a camel but is beaten by an elephant. I think I saw in one of the old Tarzans ( with Weissmuller) a lion attack an elephant but I don't remember who won.


I didn't realize that lions attacked elephants until I saw that "Planet Earth" series narrated by David Attenborough.  :o
Title: Re: What would you ask an Arimaa Oracle?
Post by Arimabuff on Apr 3rd, 2012, 12:49pm
What I would ask an Arimaa Oracle is if, long after we're all dead, say two hundred years from now, Arimaa will still be played and by how many people around the world? (I almost wrote one hundred years but chances are that some of us may still be alive by then.)
Title: Re: What would you ask an Arimaa Oracle?
Post by Arimabuff on Apr 3rd, 2012, 12:59pm

on 04/03/12 at 12:48:59, Adanac wrote:
I didn't realize that lions attacked elephants until I saw that "Planet Earth" series narrated by David Attenborough.  :o

I think an angry as well as hungry lion could do a lot of damage to an elephant if he manages to ride it rodeo style and plant his enormous fangs as and claws in the elephant's neck. The only way for the elephant to get rid of the lion would be to roll on his back and try to crush it but I don't know if they can do that.
Title: Re: What would you ask an Arimaa Oracle?
Post by Fritzlein on Apr 3rd, 2012, 1:32pm

on 04/03/12 at 12:59:16, Arimabuff wrote:
I think an angry as well as hungry lion could do a lot of damage to an elephant if he manages to ride it rodeo style and plant his enormous fangs as and claws in the elephant's neck. The only way for the elephant to get rid of the lion would be to roll on his back and try to crush it but I don't know if they can do that.

We had a discussion about elephant vs. lion before.  I stick by my guns that a lion, no matter how hungry/angry, could not take out fully grown elephant.  The only reason it would be a draw is that a lion could dodge any elephant charge and run away, but a lion that gets in too close will get smacked down by a very strong trunk.  Lion claws are sharp, but elephant hide is thick!
Title: Re: What would you ask an Arimaa Oracle?
Post by Adanac on Apr 3rd, 2012, 2:33pm

on 04/03/12 at 13:32:01, Fritzlein wrote:
We had a discussion about elephant vs. lion before.  I stick by my guns that a lion, no matter how hungry/angry, could not take out fully grown elephant.  The only reason it would be a draw is that a lion could dodge any elephant charge and run away, but a lion that gets in too close will get smacked down by a very strong trunk.  Lion claws are sharp, but elephant hide is thick!


According to this article lions attack elephants more often than I would have expected by attacking in packs, mostly against young, isolated elephants, and almost always at night.  It ain't easy hunting elephants  :P

http://johnhawks.net/weblog/reviews/life_history/risk/lion_elephant_predation_2006.html

"On only one occasion was a lion injured by an elephant in these hunts. In that case, the elephant collapsed on top of the lion. The resulting injury to the head was therefore recorded as accidental rather than as a result of a counterattack by the elephant."  That must have hurt!!


It doesn't really matter though.  Weaker pieces can take out stronger pieces in Arimaa so long as the stronger piece is standing on a trap :)  So lions killing elephants won't invalidate Fritz's new piece hierarchy.

And this is getting waaay off topic but check out "Battle at Kruger" on YouTube for a wild video clip involving lions.
Title: Re: What would you ask an Arimaa Oracle?
Post by 99of9 on Apr 3rd, 2012, 7:10pm
There's a reason they're called King of the Jungle... you're supposed to represent them with the chess king.
Title: Re: What would you ask an Arimaa Oracle?
Post by Fritzlein on Apr 3rd, 2012, 9:08pm
Thanks for the link, Adanac.  The information is interesting, especially the part about lions almost always escaping uninjured, which I wouldn't have expected.  But maybe I should have expected it.  I remember being awed by a nature documentary about a desert cat taking out a poisonous snake by patiently waiting for an opening for a lighting-quick scratch, followed by more waiting, etc., and by nimbly jumping out of the way whenever the snake would try to strike back.  Also I imagine that an elephant could be injured yet recover, whereas an injured lion is as good as dead since it can't hunt, so it would make sense that lions would only attack when they had a low probability of injury.

On the other hand, the article doesn't exactly settle the head-to-head dispute of who gets to push whom around on the Arimaa board, because the fights were always multiple lions against lone elephants, and usually smaller ones at that.  And even with many lions against one elephant, the success rate was low if the one elephant was an adult male.  "Many attempts to kill adults bulls were made in 1996, when we saw lions attacking elephant bulls almost nightly although only one hunt was successful."

One of my fellow Peace Corps volunteers in Africa once saw what happens when, instead, it is the elephants that work together.  She saw a herd of elephants watering at a river when a pride of lions showed up and also wanted to drink.  The elephants became agitated and eventually charged en masse.  The lions wanted no part of it; they lit out in all directions without even the pretense of resistance.  In daylight, at least, the elephants owned the scene.

The King of the Jungle is indeed king when attacking from behind in the dark with advantage in numbers, but...
Title: Re: What would you ask an Arimaa Oracle?
Post by omar on Apr 6th, 2012, 11:42pm

on 04/03/12 at 09:57:19, Fritzlein wrote:
A variant I proposed was to break the tie between the two horses, so instead of the piece strength being 1,1,2,2,2,8, it would be 1,1,1,1,2,2,8.  I thought I would call the new level a lion.

elephant > lion > camel > horse > 2 dogs > 2 cats > 8 rabbits.

This can still be played with a chess set by inverting one rook.


If you want to stick with the current theme of domesticated mammals, a bull might be better. Although I don't know if it would be stronger or weaker than a horse.
Title: Re: What would you ask an Arimaa Oracle?
Post by The_Jeh on Apr 7th, 2012, 12:04am

on 04/06/12 at 23:42:34, omar wrote:
If you want to stick with the current theme of domesticated mammals, a bull might be better. Although I don't know if it would be stronger or weaker than a horse.


Based on this video (viewer discretion advised), I would have to say a bull. http://www.liveleak.com/view?i=e5c_1225826191. When it comes to battle, having horns and a lot of mass is an advantage. I certainly can't see a way for a horse to win, though it probably could outrun the bull to escape for a draw.

In terms of sheer strength, I would guess a bull would be stronger on average, although for all I know a draught horse could match or exceed it.
Title: Re: What would you ask an Arimaa Oracle?
Post by arimaaphile on Apr 7th, 2012, 8:58pm
O, Arimaa Oracle!

I did not come from a far away country to ask you question about moves, pieces, maths, search trees! Tell the future!

Tell me, what will happen to our game once computers start winning humans like in chess, regularly, and most of the time?
Will our Arimaa survive and continue as an independent game   leaving behind computer-bound twist/identity? Or will it go down to history as (un)successful experiment whose rules will be taught only to remember what not to do in fight against computers?

Tell me, o Arimaa oracle, what will happen after Arimaa singularity arrives!  
Title: Re: What would you ask an Arimaa Oracle?
Post by clauchau on Apr 17th, 2012, 9:18am
Nice questions.

I would ask the Oracle some kind of shortest theory = some highly structured science about distinguishing in efficient time between winning moves or board positions and loosing ones, and about evaluating their optimal distance to the end.

There might be no such theory significantly smaller than merely enumerating unrelated individual cases, so I would also ask for the best playing engine using 1KB and 1ms, the best using 10KB and 1ms, the best using 1KB and 10ms, and so on.
Title: Re: What would you ask an Arimaa Oracle?
Post by tize on Apr 17th, 2012, 3:43pm
A similair question: How small can you make a "perfect" arimaa bot with the current hardware?
Where I define perfect as given a position where at least one winning move exist then the bot should return a non-empty subset of those moves, and if no winning moves exist then no moves should be returned.
Title: Re: What would you ask an Arimaa Oracle?
Post by Arimabuff on Apr 19th, 2012, 12:50pm

on 04/17/12 at 15:43:08, tize wrote:
A similair question: How small can you make a "perfect" arimaa bot with the current hardware?
Where I define perfect as given a position where at least one winning move exist then the bot should return a non-empty subset of those moves, and if no winning moves exist then no moves should be returned.

I guess it depends on your definition  of a winning move. Strictly speaking your very first move of the game could be a losing move and you won't know it because your opponent responded with a move that's even worse than yours etc...
Title: Re: What would you ask an Arimaa Oracle?
Post by browni3141 on Apr 19th, 2012, 2:10pm
A winning move is a move that wins the game for the side to move assuming future best play from both sides. What else would it be?
Title: Re: What would you ask an Arimaa Oracle?
Post by Arimabuff on Apr 20th, 2012, 8:23am

on 04/19/12 at 14:10:09, browni3141 wrote:
A winning move is a move that wins the game for the side to move assuming future best play from both sides. What else would it be?

What if it wins in 50 plus moves? You'll never know it. That means there's no practical way to discern certain winning moves from the losing ones.
Title: Re: What would you ask an Arimaa Oracle?
Post by clyring on Apr 20th, 2012, 6:18pm
No practical way, but if the answers could be obtained practically, there would be no need to ask an oracle.
Title: Re: What would you ask an Arimaa Oracle?
Post by Arimabuff on Apr 21st, 2012, 7:20am

on 04/20/12 at 18:18:50, clyring wrote:
No practical way, but if the answers could be obtained practically, there would be no need to ask an oracle.

We, weren't talking about the oracle. If you want to butt in a conversation, the least you could do is get up to speed on what the people are talking about or this could end up like a bad redux of an Abbot and Costello bit.
Title: Re: What would you ask an Arimaa Oracle?
Post by browni3141 on Apr 21st, 2012, 9:51pm

on 04/20/12 at 08:23:43, Arimabuff wrote:
What if it wins in 50 plus moves? You'll never know it. That means there's no practical way to discern certain winning moves from the losing ones.

I really don't know what you're trying to get at. If there are any number of winning moves, the perfect bot should return at least one of them. It doesn't matter if it wins in 3 moves or 1,000,000. It doesn't matter that it is impractical because this is a hypothetical situation.
Title: Re: What would you ask an Arimaa Oracle?
Post by omar on Apr 24th, 2012, 1:25pm

on 04/17/12 at 15:43:08, tize wrote:
A similair question: How small can you make a "perfect" arimaa bot with the current hardware?
Where I define perfect as given a position where at least one winning move exist then the bot should return a non-empty subset of those moves, and if no winning moves exist then no moves should be returned.


That's a good definition of perfect play. I think another useful definition is where the moves returned by the Oracle are sorted in order with the faster winning moves first. When no move wins they should be sorted with the slower losing moves first. Only the Oracle could achieve such super perfect play :-)
Title: Re: What would you ask an Arimaa Oracle?
Post by Fritzlein on Mar 6th, 2013, 7:46am

on 04/03/12 at 14:33:38, Adanac wrote:
According to this article lions attack elephants more often than I would have expected by attacking in packs, mostly against young, isolated elephants, and almost always at night.  It ain't easy hunting elephants  :P

http://johnhawks.net/weblog/reviews/life_history/risk/lion_elephant_predation_2006.html


Semi-relevant nature video: http://www.youtube.com/watch?v=LU8DDYz68kM
Title: Re: What would you ask an Arimaa Oracle?
Post by clyring on Mar 6th, 2013, 5:29pm
If you had looked a little bit more closely at the very post you quoted in providing that link, Fritz, you would have seen that Adanac already referred to that video. :)


on 04/03/12 at 14:33:38, Adanac wrote:
And this is getting waaay off topic but check out "Battle at Kruger" on YouTube for a wild video clip involving lions.

(Or is that why you provided an explicit link instead of a suggestion to search?)
Title: Re: What would you ask an Arimaa Oracle?
Post by Fritzlein on Jul 28th, 2016, 12:20am
Just saw a link to a video of an elephant surviving an attack by fourteen lions.

http://www.upi.com/Odd_News/2016/07/27/Cool-headed-elephant-fights-off-14-female-lions-in-Zambia/8571469624470/

For symmetry I want to see a video of a lion taking on fourteen elephants.  :D


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