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Topic: Re: Proposed New Material Evaluation Formula (Read 2513 times) |
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Janzert
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Re: Proposed New Material Evaluation Formula
« on: Dec 21st, 2006, 3:30pm » |
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Just a couple quick comments.
First just want to note that this isn't a material evaluator, or rather isn't just a material evaluator. Since it incorporates positional elements as well. At least if I'm understanding the description correctly.
Something that would probably help people comment on this is if you could provide some example situations and what it evaluates to. A couple of interesting ones might be; for pieces captured on each side:
M vs DCC
M vs HRR
M vs HC
H vs DR
H vs CC
H vs CR
DR vs CC
Also the initial value of each piece.
Of course since your evaluator also incorporates positional elements the score is going to vary by exact board positions but maybe you can show the range possible for each or simply use the assumption that each column is still filled.
Janzert
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The_Jeh
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Re: Proposed New Material Evaluation Formula
« Reply #1 on: Dec 21st, 2006, 4:15pm » |
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(I'm sorry about removing this earlier. I thought I'd forgotten something. Later I will add something that will take into account rabbit advancement, and I will give examples when I have time. Thank you, Janzert)
I would like to propose a new material/positional evaluation formula. Questions, comments, and criticisms are highly appreciated.
First, let me define the variables:
PieceValue = 9 - (# of pieces that can push or pull it)
Rabbits are evaluated in the same way as all other pieces.
SumPieceValue = the sum of the values of your pieces, including rabbits
RabDiff = (#ofFriendlyRabbits - #ofEnemyRabbits)
This is the rabbit difference
YC = (# of columns in which you have a piece or rabbit, or a piece higher than a rabbit in an adjacent column.)
OC = (" " " for opponent)
From these variables, your evaluation (E) is computed as follows:
E = ((SumPieceValue)(20/11)(1+RabDiff/9))^(1+YC/8-OC/8)
Under this system, both players start out with an initial E of 100. If you find any major (or minor) flaws, please post them so I can refine this formula.
The_Jeh
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The_Jeh
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Re: Proposed New Material Evaluation Formula
« Reply #2 on: Dec 21st, 2006, 4:16pm » |
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The initial values of the pieces are:
Rabbit: 1
Cat: 3
Dog: 5
Horse: 7
Camel: 8
Elephant: 9
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chessandgo
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Re: Proposed New Material Evaluation Formula
« Reply #3 on: Dec 22nd, 2006, 11:52am » |
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Hello, The Jeh. Here are some clues from what we know or think to know about material, to help you designing your evaluator.
As initial trades :
- a cat is probably worth slighly more than a rabbit, but a lot less than two rabbits
- a dog is worth less than a cat and a rabbit, less than 2 rabbits as well in my opinion.
- a horse should be worth slightly less than cat + dog, maybe about the same as dog + rabbit.
- a camel should be worth about H+D, or equivalently H+C.
As pieces get exchanged :
- intrinseque value of rabbits goes up when the number of those go down (ie a rabbit is worth more when you have only 4 rabbits left than it is at the beginning, and as an extreme case the very last rabbit is worth a lot)
- I can't make up my mind concerning relative values of rabbits and pieces, and have no idea as to what the other think : when pieces get exchanged, does the relative value of a rabbit compared to a piece go up or down ? On one hand with less pieces left rabbits are more likely to goal, but the few remaining pieces get more important as well ...
Designing a material evaluator respecting those few things seems to be a very hard job, good luck ! Several other threads in the forum contain much more developped thoughts about the suject, enjoy the reading 
Jean
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chessandgo
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Re: Proposed New Material Evaluation Formula
« Reply #4 on: Dec 22nd, 2006, 11:55am » |
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on Dec 22nd, 2006, 11:52am, chessandgo wrote:| and have no idea as to what the other think : Jean |
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*others
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The_Jeh
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Re: Proposed New Material Evaluation Formula
« Reply #5 on: Dec 22nd, 2006, 1:05pm » |
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On reflection, I think I weighted the rabbit difference too greatly, so here is the updated formula:
E = ((SumPieceValue)(20/11)(1+RabDiff/17))^(1+YC/8-OC/8)
ChessandGo, you said that the value of rabbits goes up when their number goes down. This is absolutely correct; it is an economic principle. The piece values here, though, are more of a measure of their threat, not their essentiality. A rabbit is more essential when it is the last one you have, but it is not more of a threat because of it. It is more of a threat when the number of pieces that can bully it goes down. That is what this formula measures.
Also, my intention is for this formula to be effective holistically, with the more secondary goal that its individual components can be useful.
Thank you for your valuable insight, ChessandGo. I will take all of it into consideration.
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Fritzlein
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Re: Proposed New Material Evaluation Formula
« Reply #6 on: Dec 29th, 2006, 9:34pm » |
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on Dec 22nd, 2006, 1:05pm, The_Jeh wrote:On reflection, I think I weighted the rabbit difference too greatly, so here is the updated formula:
E = ((SumPieceValue)(20/11)(1+RabDiff/17))^(1+YC/8-OC/8)
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That's an interesting idea, but it's hard for people to comment on any formula in the abstract. I agree with Janzert's comment below: you will get more feedback if you show people some examples of how your formula is working.
on Dec 21st, 2006, 3:30pm, Janzert wrote:Something that would probably help people comment on this is if you could provide some example situations and what it evaluates to. A couple of interesting ones might be; for pieces captured on each side:
M vs DCC
M vs HRR
M vs HC
H vs DR
H vs CC
H vs CR
DR vs CC
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Just this once, I will implement this in a spreadsheet for you, The_Jeh, but next time I'll leave the leg work to you. Here are the values of Janzert's trades plus a few more. I'll assume it is the opening, so all columns are blocked on each side. Positive numbers favor the first column and negative number favor the second column
M vs DCC -> -33
M vs HRR -> -28
M vs HC -> -18
H vs DR -> -11
H vs CC -> -9
H vs CR -> -3
DR vs CC -> +2
R -> +13
C vs R -> +4
C vs RR -> -11
D vs RR -> -4
H vs RR -> +4
H vs RRR -> -11
M vs RRR -> -6
E vs RRR -> -3
M vs HR -> -12
My initial impression is that this formula does all right with initial trades of rabbits, cats, and dogs, but undervalues horses a bit, undervalues camels a lot, and undervalues elephants to an extreme. We don't know how many rabbits for an initial elephant would be a fair trade, but it is more than three! Even a camel is clearly worth more than three rabbits, although your formula favors the rabbits, and a camel is very likely worth more than a horse and a rabbit, although the formula favors the horse and rabbit.
The concept is interesting, though, if you could fix the heavy piece valuation somehow. The elephant value hardly matters, since elephants are never traded, but the camel valuation is critical, and simply has to be fixed.
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IdahoEv
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Re: Proposed New Material Evaluation Formula
« Reply #7 on: Dec 30th, 2006, 12:19pm » |
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Am I the only one confused here by what seems to be the *second half* of a discussion thread about a new evaluation system? This thread is titled "Re: ..." as if there were an earlier message, and Janzert responds with comments about an earlier message. But I can't find the earlier message, so I am not sure what these people are talking about!
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Janzert
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Re: Proposed New Material Evaluation Formula
« Reply #8 on: Dec 30th, 2006, 1:42pm » |
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The second message is actually the original first message. 
I think The_Jeh deleted the first message without realizing I had already posted a reply.
Janzert
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The_Jeh
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Re: Proposed New Material Evaluation Formula
« Reply #9 on: Jan 1st, 2007, 1:21am » |
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on Dec 29th, 2006, 9:34pm, Fritzlein wrote:
My initial impression is that this formula does all right with initial trades of rabbits, cats, and dogs, but undervalues horses a bit, undervalues camels a lot, and undervalues elephants to an extreme. We don't know how many rabbits for an initial elephant would be a fair trade, but it is more than three! Even a camel is clearly worth more than three rabbits, although your formula favors the rabbits, and a camel is very likely worth more than a horse and a rabbit, although the formula favors the horse and rabbit.
The concept is interesting, though, if you could fix the heavy piece valuation somehow. The elephant value hardly matters, since elephants are never traded, but the camel valuation is critical, and simply has to be fixed.
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So the formula obviously undervalues pieces more and more the higher their rank. I guess the piece values could be multiplied by or taken to the power of constants, a different one for each piece. What I don't like about that idea is that these constants would be based on opinion, rather than having mathematically derived significance. I'll try to think of another way to increase the weight of higher pieces.
Thank you very much Fritzlein. Please don't spoil me with your recrementitious generosity.
The_Jeh
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Fritzlein
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Re: Proposed New Material Evaluation Formula
« Reply #10 on: Jan 1st, 2007, 11:07am » |
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on Jan 1st, 2007, 1:21am, The_Jeh wrote:| What I don't like about that idea is that these constants would be based on opinion, rather than having mathematically derived significance. |
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Yes, it would be very appealing if the formula had no arbitrary constants. I think FAME had three arbitrary constants, so even getting that number down to two or one would be an improvement in beauty. If you manage to create a reasonable formula with no arbitrary constants I will be tremendously impressed.
Quote:| Please don't spoil me with your recrementitious generosity. |
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Thanks for introducing me to a new vocabulary word. I had to run off and look up "recrementitious". I love learning new words. I am sad, though, that it seems to mean "composed of waste matter or dross". I guess my commentary left something to be desired in comparison to chessandgo's "valuable insight". 
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| « Last Edit: Jan 1st, 2007, 11:09am by Fritzlein » |
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The_Jeh
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Re: Proposed New Material Evaluation Formula
« Reply #11 on: Jan 1st, 2007, 11:52am » |
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My "recrementitious" is supposed to mean "excess" or "surplus." (Merriam-Webster's Collegiate Thesaurus) That is a slightly more flattering connotation, I think.
The_Jeh
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The_Jeh
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Re: Proposed New Material Evaluation Formula
« Reply #12 on: Jan 1st, 2007, 2:12pm » |
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I have revised the PieceValue formula and tweaked the RabDiff component. Here are all the variables and final formula again:
PieceValue = (9 - (# of pieces that can push it))(Rank) , where rabbits have a rank of 1, cats 2, elephants 6, etc.
SumPieceValue = sum of the friendly piece's PieceValues
RabDiff = (#FriendRabbits - #FoeRabbits)
YC = # of columns in which you have a piece or a rabbit, or a piece higher than a rabbit in an adjacent column
OC = " " " for opponent
E = ((SumPieceValue)(1/2)(1+(RabDiff/|RabDiff|)(RabDiff^2/192)))^(1+YC/8-OC/ 8)
So far, there are zero arbitrary numbers. 192 is 3(8^2).
Here are the initial values if White/Black start out down by the following hadicaps. Positive differences favor white.
Handicap, Score, Difference
E/-, 73/114, -41
M/-, 80/113, -33
E/RRRR, 79/102, -23
E/RRRRRRR, 92/81, 11
The_Jeh
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The_Jeh
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Re: Proposed New Material Evaluation Formula
« Reply #13 on: Jan 1st, 2007, 4:45pm » |
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I forgot to mention, if the RabDiff = 0, do not use that portion of the formula. Otherwise, the answer will be undefined. You know what my intention was.
Also, here are some more initial scores for various handicaps for White/Black. Positive values favor white.
Handicap, Score, Difference
RRRRRRR/-, 72/126, -54
D/RR, 94/102, -8
DDCC/HH, 87/92, -5
R/-, 99/101, -2
DCC/HH, 98/86, 12
M/HH, 98/81, 17
EM/HHDDCC, 91/62, 29
The_Jeh
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The_Jeh
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Re: Proposed New Material Evaluation Formula
« Reply #14 on: Jan 1st, 2007, 4:59pm » |
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This formula is equivalent, simpler, and you don't have to worry about RabDiff being 0:
E = ((SumPieceValue)(1/2)(1+RabDiff|RabDiff|/192))^(1+YC/8-OC/8)
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