Author |
Topic: Puzzle (Read 1463 times) |
|
jdb
Forum Guru
Arimaa player #214
Gender: 
Posts: 682
|
Using the 2006 Championship rules, can you create a position where the winning side has NO PIECES left?
Please include the position before the winning move and the winning move.
Part 2) What is the greatest number of pieces the losing side can have remaining?
|
|
 IP Logged |
|
|
|
Adanac
Forum Guru
Arimaa player #892
Gender:
Posts: 635
|
 |
Re: Puzzle
« Reply #1 on: Dec 13th, 2005, 12:41pm » |
 Quote  Modify
|
on Dec 13th, 2005, 10:24am, jdb wrote:Using the 2006 Championship rules, can you create a position where the winning side has NO PIECES left?
Please include the position before the winning move and the winning move.
Part 2) What is the greatest number of pieces the losing side can have remaining?
|
|
Part 1) 1w Rc5 Eh3 1b rg3 2w rg3w rf3x Eh3w Eg3w Ef3x Rc5n Rc6x
Part 2) If silver has 8 non-rabbits on the board, it's ordinarily a draw but in the 2006 Championship it's a loss.
Did I get it right?
|
|
IP Logged |
|
|
|
RonWeasley
Forum Guru
Harry's friend (Arimaa player #441)
Gender:
Posts: 882
|
|
Re: Puzzle
« Reply #2 on: Dec 13th, 2005, 12:44pm » |
Quote Modify
|
I think Ryan_Cable's post on the "rules question" thread is one answer. I won't give it away here so others can think about the puzzle. My guess to part 2 is 8. All the non-rabbits. If I'm wrong call me thick as a brick! (Are you old enough to understand that?)
I hope questions like this get incorporated into the tutorial and the Wiki publications. This and the great question about how far away a piece can be to be part of a goal threat. Ideas like this are a big part of the beauty of the game.
|
|
IP Logged |
|
|
|
jdb
Forum Guru
Arimaa player #214
Gender:
Posts: 682
|
|
Re: Puzzle
« Reply #3 on: Dec 13th, 2005, 5:46pm » |
Quote Modify
|
8 is not the correct answer for part 2 
|
|
IP Logged |
|
|
|
Adanac
Forum Guru
Arimaa player #892
Gender:
Posts: 635
|
|
Re: Puzzle
« Reply #4 on: Dec 13th, 2005, 6:57pm » |
Quote Modify
|
on Dec 13th, 2005, 5:46pm, jdb wrote:| 8 is not the correct answer for part 2 |
|
"Part 2) What is the greatest number of pieces the losing side can have remaining? "
Okay, technically the answer is 16, but if I understood the intent of the question correctly:
"Part 2) If the winning side has no pieces on the board, what is the greatest number of pieces the losing side can have remaining?"
If so, I'm having a very difficult time understanding why the answer would be anything other than 8. And I thought Part 2 was the easy question 
|
|
IP Logged |
|
|
|
jdb
Forum Guru
Arimaa player #214
Gender:
Posts: 682
|
|
Re: Puzzle
« Reply #5 on: Dec 13th, 2005, 8:20pm » |
Quote Modify
|
Your interpretation of part 2 is correct.
|
|
IP Logged |
|
|
|
99of9
Forum Guru
Gnobby's creator (player #314)
 
Gender:
Posts: 1413
|
|
Re: Puzzle
« Reply #6 on: Dec 13th, 2005, 8:43pm » |
Quote Modify
|
I think the answer is 16.
An example move is:
re3s Ed3e Ee3e Ef3x Rf5n Rf6x
|
| « Last Edit: Dec 13th, 2005, 9:02pm by 99of9 » |
IP Logged |
|
|
|
Adanac
Forum Guru
Arimaa player #892
Gender:
Posts: 635
|
|
Re: Puzzle
« Reply #7 on: Dec 13th, 2005, 10:25pm » |
Quote Modify
|
on Dec 13th, 2005, 8:43pm, 99of9 wrote:I think the answer is 16.
|
|
Oh of course, very clever indeed 
|
|
IP Logged |
|
|
|
jdb
Forum Guru
Arimaa player #214
Gender:
Posts: 682
|
|
Re: Puzzle
« Reply #8 on: Dec 13th, 2005, 10:44pm » |
Quote Modify
|
1w Re6 Rf6 Ra7 Rb7 Rc7 Rd7 Rg7 Rh7 Ea8 Mb8 Hc8 Hd8 De8 Df8 Cg8 Ch8
1b rc6 dd6
2w pass
|
|
IP Logged |
|
|
|
Ryan_Cable
Forum Guru
Arimaa player #951
Gender:
Posts: 138
|
|
Re: Puzzle
« Reply #9 on: Dec 14th, 2005, 4:32am » |
Quote Modify
|
1w Ec7
1b ra2 rb2 rc2 rd2 re2 rf2 rg2 rh2 ea1 mb1 hc1 hd1 de1 df1 cg1 ch1
2w Ec7s Ec6x
is a win by immobilization for gold, with 16 silver pieces and 0 gold pieces remaining. I think this is the same idea as jdb‘s suggestion. It might make an interesting loose Arimaa variant to have the goal be to have all of your pieces frozen or otherwise immobilized at the end of your turn. It could only work well if captures and sacrifices were forbidden.
Some other interesting positions are:
1w Rd3
1b ce4
2w Rd3w Rc3x
Gold draws the game. Any other move looses by immobilization. Interestingly, the server counts the following as a win by immobilization instead of a draw:
1w Rd3
1b ce4
2w Rd3n
2b Rd4w ce4w Rc4s Rc3x c4w
I found a class of positions that are proven infinite move draws. Place all 8 gold Rs on row 4 and all 8 silver Rs on row 5. Then place at least 1 friendly piece behind each line and have no pieces behind enemy lines, such as:
1w Ra4 Rb4 Rc4 Rd4 Re4 Rf4 Rg4 Rh4 Ea1 Mb1 Hc1 Hd1 De1 Df1 Cg1 Ch1
1b ra5 rb5 rc5 rd5 re5 rf5 rg5 rh5 ea8 mb8 hc8 hd8 de8 df8 cg8 ch8
None of the Rs can move or be moved, so no progress can be made. In fact, one can’t even suicide.
Many zugzwang positions (where both players would pass if allowed) can be constructed with only Rs, such as:
1w Ra4
1b ra5
|
| « Last Edit: Dec 14th, 2005, 6:42am by Ryan_Cable » |
IP Logged |
|
|
|
99of9
Forum Guru
Gnobby's creator (player #314)
Gender:
Posts: 1413
|
|
Re: Puzzle
« Reply #10 on: Dec 14th, 2005, 5:35am » |
Quote Modify
|
on Dec 14th, 2005, 4:32am, Ryan_Cable wrote:1w Ec7
1b ra2 rb2 rc2 rd2 re2 rf2 rg2 rh2 ea1 mb1 hc1 hd1 de1 df1 cg1 ch1
2w Ec7s Ec6x
|
|
In the tournament silver would have won straight after your 1b, because all gold rabbits are dead.
But then again, I don't understand jdb's solution either.
|
|
IP Logged |
|
|
|
Ryan_Cable
Forum Guru
Arimaa player #951
Gender:
Posts: 138
|
|
Re: Puzzle
« Reply #11 on: Dec 14th, 2005, 7:16am » |
Quote Modify
|
on Dec 14th, 2005, 5:35am, 99of9 wrote:
In the tournament silver would have won straight after your 1b, because all gold rabbits are dead. |
|
You are right the game is finished even though the server doesn‘t know it. I had wrongly believed the match rules only came into play if the game actually finished as a draw. The Arimaa Match Rules state:
Normally a game would continue when one of the players has lost all the rabbits and end in a draw if both players lose all the rabbits. However if draws are not allowed then a player may also win the game by being the first to capture all of the opponents rabbits.
Which makes more sense now that I think about it.
If the E is replaced with a R, I think it should be a win for gold by analogy with the case I gave above being a win rather than a draw. Still, I would like to hear an official ruling from Omar about the following in a tournament:
1w Rc5
1b ra2 rb2 rc2 rd2 re2 rf2 rg2 rh2 ea1 mb1 hc1 hd1 de1 df1 cg1 ch1
2w Rc5n Rc6x
|
|
IP Logged |
|
|
|
Janzert
Forum Guru
Arimaa player #247
Gender:
Posts: 1016
|
|
Re: Puzzle
« Reply #12 on: Dec 14th, 2005, 7:30am » |
Quote Modify
|
on Dec 14th, 2005, 4:32am, Ryan_Cable wrote:I found a class of positions that are proven infinite move draws. Place all 8 gold Rs on row 4 and all 8 silver Rs on row 5. Then place at least 1 friendly piece behind each line and have no pieces behind enemy lines, such as:
1w Ra4 Rb4 Rc4 Rd4 Re4 Rf4 Rg4 Rh4 Ea1 Mb1 Hc1 Hd1 De1 Df1 Cg1 Ch1
1b ra5 rb5 rc5 rd5 re5 rf5 rg5 rh5 ea8 mb8 hc8 hd8 de8 df8 cg8 ch8 |
|
Just to be ornery and pedantic, wouldn't this situation lead to a forced win because of the position repitition rule?
The above rabbit setup with only one friendly piece behind the line on either side being forced in around 968 moves?
Janzert
|
|
IP Logged |
|
|
|
RonWeasley
Forum Guru
Harry's friend (Arimaa player #441)
Gender:
Posts: 882
|
|
Re: Puzzle
« Reply #13 on: Dec 14th, 2005, 7:59am » |
Quote Modify
|
So it depends on the order in which the win conditions are checked. I think jdb's 16 piece solution is correct.
At the end of gold's move, his pieces are gone, but the game checks for a gold rabbit on the 8th rank or for no silver rabbits on the board. Neither is the case so silver's move begins.
At the beginning of silver's move, the game checks for immobilization. Silver is indeed immobilized and a win is awarded to gold.
If silver was not immobilized, silver would move and the game would check for no gold rabbits on the board. Because there are none, the win is awarded to silver.
It's important to know exactly how wins get awarded.
This was a great puzzle question, jdb!
|
|
IP Logged |
|
|
|
Ryan_Cable
Forum Guru
Arimaa player #951
Gender:
Posts: 138
|
|
Re: Puzzle
« Reply #14 on: Dec 14th, 2005, 8:57am » |
Quote Modify
|
on Dec 14th, 2005, 7:30am, Janzert wrote:Just to be ornery and pedantic, wouldn't this situation lead to a forced win because of the position repitition rule?
The above rabbit setup with only one friendly piece behind the line on either side being forced in around 968 moves? |
|
Yes, the repetition rule means that all Arimaa games must have a finite number of moves. Infinite move draw is an informal term for games which are limited by only the repetition rule but do not have obviously cyclic repetition.
With only one piece on each side there are 24^2 = 576 possible positions. Since the threefold repetition rule includes side to move, I think the game could last at most 6*576 = 3456 moves. (It seems that the server scores the loss on the third repetition, which is actually the fourth time the position occurs.) Of course, even if both sides have all 8 noble pieces the number of positions is still finite. Specifically there are (24!/(24-8)!/(2*2*2))^2 = 8.79*10^20 positions.
All of these cases are much longer than our normal game time limits, so the game will be decided by score, which results in a draw if both sides have matching noble pieces. However, I would still consider the game to be an infinite move draw even if the score gave one side the win.
on Dec 14th, 2005, 7:59am, RonWeasley wrote:At the end of gold's move, his pieces are gone, but the game checks for a gold rabbit on the 8th rank or for no silver rabbits on the board. Neither is the case so silver's move begins.
At the beginning of silver's move, the game checks for immobilization. Silver is indeed immobilized and a win is awarded to gold.
If silver was not immobilized, silver would move and the game would check for no gold rabbits on the board. Because there are none, the win is awarded to silver. |
|
Yes for a regular game that is correct, but a tournament game ends on the move that a player looses his last R. If silver had a move he would win immediately without needing to move. The question is does the match rule check for loss of final R before or after the game rule checks for immobilization? The server only implements the game rules not the match rules, so it doesn’t answer this exact question. However, we do know that the server checks for immobilization before it checks for draws. Since the match rule was implemented to resolve draws and is not intended to change a win for one player into a win for the other player, I think situation I gave in my last post should be a win for gold, but it is legally ambiguous.
|
|
IP Logged |
|
|
|
|
Home
Help
Search
Members
Login
Register
Reply
Notify of replies
Send Topic
Print