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clauchau
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(no) absolute score values for pieces?
« on: Aug 27th, 2003, 2:42pm »
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If we pursue the chess tradition and evaluate positions by summing up individual scores assigned to every piece on the board, weighted according to positional factors, should we look for absolute values like rabbits are worth 1, cats 1.8, ..., camels 7, elephants 10?
 
It can't be that simple, because trading the two camels is exactly the same as trading the two elephants for example - the Silver and White players are left with the same power. Absolute static scores would mislead a bot into favoring one trade over the other and overlooking some other advantage.
 
I vote for a non-materialistic approach! Any taker?
 
Claude
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clauchau
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Re: (no) absolute score values for pieces?
« Reply #1 on: Aug 28th, 2003, 4:26am »
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I wrote:
Quote:
trading the two camels is exactly the same as trading the two elephants

 
Hmm, well, this actually is no valid argument against individual static scores for the animals, I'm sorry. Other things being equal, the difference of total scores would exactly be the same and wouldn't show any unwanted artifact as I first suggested.
 
Claude
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clauchau
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Re: (no) absolute score values for pieces?
« Reply #2 on: Aug 28th, 2003, 4:56am »
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rabbits are worth 1, cats 1.8, ..., camels 7, elephants 10?

 
Aha, a valid case against those values is when your opponent is missing two adjacent species - for example cats and dogs. Whether your are left with one of them doesn't make any difference then. A cat or a dog are worth the same in the absence of opposing animals of the same rank.
 
A naive materialistic bot would think there is a difference.
 
Claude
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99of9
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Re: (no) absolute score values for pieces?
« Reply #3 on: Aug 29th, 2003, 11:22am »
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I think rabbit's are an interesting case in valuation.  When you have 8 rabbits, losing one is no big deal, but when you have only one, then it is often the most valuable piece on the board!
 
Even valuing the rabbit's position is extremely difficult, because it really depends what's in front of it, not how far up the board it has made it so far.
 
PS nice forum omar  Wink
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99of9
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The 99 System
« Reply #4 on: Aug 29th, 2003, 12:36pm »
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This scoring system shall forever hereafter be referred to as The 99 System Smiley
 
Piece Value
Elephant 13
Camel 8
Horse 5
Dog 3
Cat 2
1st Rabbit 1
2nd Rabbit 2
3rd Rabbit 3
4th Rabbit 4
5th Rabbit 5
6th Rabbit 6
7th Rabbit 7
8th Rabbit 99

 
Each side in Arimaa starts the game with a total material value of 168.  This includes 41 for all the noble animals, 28 for the first 7 rabbits, and 99 for the final rabbit.
 
This system is especially designed to value material at the start of the game.
 
For example (the first four of these examples, being equalities, also apply vice versa):

  • I would be happy to start a game without my elephant (13), if you gave up both your camel and a horse (8+5).  
  • I would be happy to start a game without my camel ( 8 ), if you gave up both a horse and a dog (5+3).
  • I would be happy to start a game without one horse (5), if you gave up both a dog and a cat (3+2).
  • I would be happy to start a game without one dog (3), if you gave up both a cat and a rabbit (2+1).
  • I would be happy to start a game without my elephant (13), if you gave up 5 rabbits (1+2+3+4+5>13).  Controversial!!!
  • I will play you in a game where one side only has  one elephant plus one rabbit (13+99), and the other has only 3 rabbits (6+7+99).  I don't mind who gets what.  As long as I get to play gold Wink Even more controversial!!!

 
  • A brief treatise on the value of rabbits:

The value of the last rabbits to be taken away is higher than the value of the earlier rabbits to be taken away.  I am only happy for you to take away my last rabbit if I can take away all of your pieces in return Smiley, hence it is valued at 99, higher than the value of all other pieces put together.  If you're still confused about rabbit values, and happen to be an absent minded scientist, then think of removing electrons from an atom... the first are easy to remove, and take little energy, however the last ones to remove, are very strongly bound, and require a very large energy payment.
« Last Edit: Aug 29th, 2003, 1:01pm by 99of9 » IP Logged
leo
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Re: (no) absolute score values for pieces?
« Reply #5 on: Aug 29th, 2003, 11:48pm »
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Having only two rabbits left, I'd tend to value both at least 30. Is it too much? If so, why?
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Re: (no) absolute score values for pieces?
« Reply #6 on: Aug 30th, 2003, 12:00am »
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What's a camel worth when frozen or blocked or on trapping prevention? Sure, if we can discern values for the piece types, they're just one factor in the evaluation of the actions.
 
I like to picture the whole of the pieces of one player as a protoplasm whose shape and inner tensions determine its health and strength. But don't ask me to put that into code yet  Undecided
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99of9
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Re: (no) absolute score values for pieces?
« Reply #7 on: Aug 30th, 2003, 9:13am »
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What's a camel worth when frozen or blocked or on trapping prevention?

 
That's like asking "What's a queen worth when the king's in checkmate?".
 
We're just talking about valuing material here.  Valuing position is another very important question, but it's certainly a different question.
 
Quote:
Having only two rabbits left, I'd tend to value both at least 30.

 
Well the last is clearly worth more than the second last, since it determines whether you can even possibly win the game.  I believe the second last is not worth 30.  For example, if you think it is worth more than an elephant plus a camel plus a horse plus a dog (13+8+5+3) ... I'll play you where I have all those pieces and one rabbit, and you just have two rabbits Smiley.
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clauchau
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Re: (no) absolute score values for pieces?
« Reply #8 on: Aug 30th, 2003, 6:06pm »
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As you suggested 99of9, those values may weigh little compared to other factors after a few moves have been played.
 
But they are real and interesting statistics to make and may help design an handicap scheme.
 
I'll have fun making experiments about them when/if my non-materialistic Quantum Leapfrog bot is finished.
 
Claude
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clauchau
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Re: The 99 System
« Reply #9 on: Aug 30th, 2003, 6:37pm »
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on Aug 29th, 2003, 12:36pm, 99of9 wrote:
The 99 System: Elephant 13, Camel 8, Horse 5, Dog 3, Cat 2 [...]

 
The values of rabbits change according to how many are left and I think you also need similar variable values for the stronger animals. For example consider a game starting with
 
1 Elephant + 8 Rabbits  vs  1 Camel + 1 Horse + 8 Rabbits
 
which is fair according to your system (140 vs 140). It would exactly be the same as a game starting with
 
1 Elephant + 8 Rabbits  vs  1 Dog + 1 Cat + 8 Rabbits
 
but your system now scores this as unfair (140 vs 132).
 
Claude
« Last Edit: Aug 30th, 2003, 6:39pm by clauchau » IP Logged
99of9
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Re: (no) absolute score values for pieces?
« Reply #10 on: Aug 30th, 2003, 6:58pm »
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... which is fair according to your system  ...
... but your system now scores this as unfair ...

 
Your quantum leapfrog will understand this, it is in a quantum state which is a mixture of fairness and unfairness.
 
But seriously, of course you are right, this is only a first approximation.
 
If you do want to correct it, you need to use the 99 shuffle up process... another exceedingly brilliant but as yet unpatented invention.  It's a little hard to explain though, so I might leave it for another post.  Oh, that and I'm also not quite sure yet whether it should be called shuffle up or shuffle down...
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leo
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Re: (no) absolute score values for pieces?
« Reply #11 on: Aug 30th, 2003, 8:57pm »
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on Aug 30th, 2003, 9:13am, 99of9 wrote:

We're just talking about valuing material here.  Valuing position is another very important question, but it's certainly a different question.

 
Sorry, I'm obsessed with the "action potential" of the pieces and I'm not familiar with traditional piece value.
 
Quote:

I believe the second last is not worth 30.  For example, if you think it is worth more than an elephant plus a camel plus a horse plus a dog (13+8+5+3) ... I'll play you where I have all those pieces and one rabbit, and you just have two rabbits Smiley.

 
I see what you mean. Thanks for you reply.
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fotland
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Re: (no) absolute score values for pieces?
« Reply #12 on: Sep 1st, 2003, 4:24pm »
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Bomb has fixed values for all pieces except rabbits.  When there are fewer on the board, they are worth more.  Not just because when the last one is gone ther is no way to win.  Rabbits are essential for blocking forward progress of other rabbits, so even an 8 to 4 excess of rabbits is a huge advantage.  At some point there just aren't enough pieces left to block the goal.
 
My values are almost the same as 99of9:
 
1, 2.5, 3, 5, 9, 13.
 
I agree that fixed values are not correct, but in actual games there is not so much opportunity for strange trades, so it doesn't make much difference.
 
In any case, just evaluating material will give a very weak player.
 
David
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99of9
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Re: (no) absolute score values for pieces?
« Reply #13 on: Sep 2nd, 2003, 11:36am »
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...  Not just because when the last one is gone ther is no way to win.  Rabbits are essential for blocking forward progress of other rabbits, so even an 8 to 4 excess of rabbits is a huge advantage.  At some point there just aren't enough pieces left to block the goal. ...

 
This is true, but of course rabbits are no better at this than any other piece.  In fact they are often worse.  So really all pieces should increase in value with decreasing density.
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99of9
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Re: (no) absolute score values for pieces?
« Reply #14 on: Sep 2nd, 2003, 11:38am »
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on Sep 1st, 2003, 4:24pm, fotland wrote:

My values are almost the same as 99of9:
 
1, 2.5, 3, 5, 9, 13.

 
Can I sue?  (no claiming bankruptcy when bomb thrashes humanity come February) Smiley
 
99
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