Author |
Topic: What would you ask an Arimaa Oracle? (Read 10508 times) |
|
rbarreira
Forum Guru
Arimaa player #1621
Gender: 
Posts: 605
|
 |
What would you ask an Arimaa Oracle?
« on: Mar 21st, 2012, 12:16pm » |
 Quote  Modify
|
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? 
|
| « Last Edit: Mar 21st, 2012, 12:17pm by rbarreira » |
 IP Logged |
|
|
|
Fritzlein
Forum Guru
Arimaa player #706
Gender:
Posts: 5928
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #1 on: Mar 21st, 2012, 1:21pm » |
Quote Modify
|
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. 
|
| « Last Edit: Mar 21st, 2012, 1:27pm by Fritzlein » |
IP Logged |
|
|
|
hyperpape
Forum Guru
Arimaa player #7113
Gender:
Posts: 80
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #2 on: Mar 21st, 2012, 2:49pm » |
Quote Modify
|
What proportion of reasonable setups are a win for Gold/Silver? I'll let the Oracle tell me what reasonable means.
|
|
IP Logged |
|
|
|
99of9
Forum Guru
Gnobby's creator (player #314)
 
Gender:
Posts: 1413
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #3 on: Mar 21st, 2012, 6:07pm » |
Quote Modify
|
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.)
|
| « Last Edit: Mar 21st, 2012, 6:24pm by 99of9 » |
IP Logged |
|
|
|
rbarreira
Forum Guru
Arimaa player #1621
Gender:
Posts: 605
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #4 on: Mar 22nd, 2012, 4:02am » |
Quote Modify
|
on Mar 21st, 2012, 6:07pm, 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).
|
|
IP Logged |
|
|
|
hyperpape
Forum Guru
Arimaa player #7113
Gender:
Posts: 80
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #5 on: Mar 22nd, 2012, 11:32am » |
Quote Modify
|
Hmm, that leads to another question: was Hanzack getting outplayed in the opening, or is Nombril's theory right?
|
|
IP Logged |
|
|
|
omar
Forum Guru
Arimaa player #2
Gender:
Posts: 1003
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #6 on: Mar 22nd, 2012, 11:55am » |
Quote Modify
|
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.
|
|
IP Logged |
|
|
|
aaaa
Forum Guru
Arimaa player #958
Posts: 768
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #7 on: Mar 22nd, 2012, 5:19pm » |
Quote Modify
|
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.
|
|
IP Logged |
|
|
|
clyring
Forum Guru
Arimaa player #6218
Gender: 
Posts: 362
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #8 on: Mar 22nd, 2012, 8:32pm » |
Quote Modify
|
-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.
|
| « Last Edit: Mar 22nd, 2012, 8:35pm by clyring » |
IP Logged |
I administer the Endless Endgame Event (EEE). Players welcome!
|
|
|
Arimabuff
Forum Guru
Arimaa player #2764
Gender:
Posts: 589
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #9 on: Apr 3rd, 2012, 9:11am » |
Quote Modify
|
on Mar 21st, 2012, 1:21pm, 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. |
|
Could you please explain what a lion can do?
|
|
IP Logged |
|
|
|
Arimabuff
Forum Guru
Arimaa player #2764
Gender:
Posts: 589
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #10 on: Apr 3rd, 2012, 9:16am » |
Quote Modify
|
on Mar 21st, 2012, 1:21pm, Fritzlein wrote:| ...I would claim chess is an Arimaa variant and ask questions about chess. |
|
About as much as ping pong is a soccer variant.
|
|
IP Logged |
|
|
|
Adanac
Forum Guru
Arimaa player #892
Gender:
Posts: 635
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #11 on: Apr 3rd, 2012, 9:36am » |
Quote Modify
|
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
|
|
IP Logged |
|
|
|
Fritzlein
Forum Guru
Arimaa player #706
Gender:
Posts: 5928
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #12 on: Apr 3rd, 2012, 9:57am » |
Quote Modify
|
on Apr 3rd, 2012, 9:11am, 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.
|
| « Last Edit: Apr 3rd, 2012, 9:57am by Fritzlein » |
IP Logged |
|
|
|
Arimabuff
Forum Guru
Arimaa player #2764
Gender:
Posts: 589
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #13 on: Apr 3rd, 2012, 12:41pm » |
Quote Modify
|
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.
|
|
IP Logged |
|
|
|
Adanac
Forum Guru
Arimaa player #892
Gender:
Posts: 635
|
|
Re: What would you ask an Arimaa Oracle?
« Reply #14 on: Apr 3rd, 2012, 12:48pm » |
Quote Modify
|
on Apr 3rd, 2012, 12:41pm, 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. 
|
| « Last Edit: Apr 3rd, 2012, 12:49pm by Adanac » |
IP Logged |
|
|
|
|
Home
Help
Search
Members
Login
Register
Reply
Notify of replies
Send Topic
Print