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Topic: (no) absolute score values for pieces? (Read 39559 times) |
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Fritzlein
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Arimaa player #706
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Re: (no) absolute score values for pieces?
« Reply #60 on: Mar 18th, 2006, 7:45pm » |
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EMHHDDCCR vs. EMRRRRRRRR = +134
EMHHDDCCR vs. EMRRRRRRR = +174
EMHHDDCCR vs. EMRRRRRR = +215
so far I agree with your web page
EMHHDDCCR vs. EMRRRRR = +257 , not +215 as the web page says. To break it down, it is (for the traps) 57+38+25+17+11+7+ (for gold's 1 extra rabbit) 600/9 - (for silver's -1 extra rabbits) -1 * 600/17.
FAME is admittedly very weird, but at least it likes making extra captures in this situation; something is wrong with the calculation on your web page.
Here's a genuine weirdness with FAME:
EMHHDDCCR vs. ER = +652
EHHDDCCR vs. ER = +640
It only lowers Gold's evaluation by 12 points to throw away a camel. Although it leaves Silver with only -5 rabbits instead of -6, it simultaneously weakens Gold's defense from 17 to 15, and against negative offense, FAME thinks a weaker defense is better!
To stop that silliness, each negative leftover rabbit should have a fixed value of, let's say, 40 points to the other team regardless of the size of the larger army. Not that it matters much, but why not patch holes that are easy to patch? There will still be enough unpatchable holes left. 
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Janzert
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Arimaa player #247
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Re: (no) absolute score values for pieces?
« Reply #61 on: Mar 18th, 2006, 9:38pm » |
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on Mar 18th, 2006, 7:45pm, Fritzlein wrote:
EMHHDDCCR vs. EMRRRRR = +257 , not +215 as the web page says. To break it down, it is (for the traps) 57+38+25+17+11+7+ (for gold's 1 extra rabbit) 600/9 - (for silver's -1 extra rabbits) -1 * 600/17. |
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Oops, I was breaking out of the matchups as soon as one side ran out of pieces.
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Nooo, I thought I finally had it.  640 not 633? Rabbits vs nothing count for matchup and leftover?
85 + 57 + 38 + 25 + 17 + 11 + 7 = 240
240 + ((600/(1+(2*1)))*1) - ((600/(1+(2*7)))*-5) = 640
Did you happen to check the other ones at all? In particular the first two are from your examples after making the last modification to the formula and I still get the differring results.
Janzert
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Fritzlein
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Arimaa player #706
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Re: (no) absolute score values for pieces?
« Reply #62 on: Mar 18th, 2006, 9:59pm » |
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on Mar 18th, 2006, 9:38pm, Janzert wrote:
Nooo, I thought I finally had it. 640 not 633? Rabbits vs nothing count for matchup and leftover?
85 + 57 + 38 + 25 + 17 + 11 + 7 = 240
240 + ((600/(1+(2*1)))*1) - ((600/(1+(2*7)))*-5) = 640
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Oh, whoops, it should be 633. You are right. The 7 point bonus for controlling the 8th trap goes to no one.
Quote:| Did you happen to check the other ones at all? In particular the first two are from your examples after making the last modification to the formula and I still get the differring results. |
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Sorry, I didn't see the other examples when I replied before.
EDRR vs. ECCR = 85 - 57 + 600/7 - 600/6 = 14
EDRRR vs ECCRR = 85 - 57 + 2*600/8 - 2*600/7 = 7
Looks like your web page is right and the numbers I published before are wrong. Apparently I was mistakenly reducing the denominator by one, i.e. 85 - 57 + 600/6 - 600/5 = 8 != 14. Thanks for checking so meticulously. By now you know my system better than I do.
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| « Last Edit: Mar 18th, 2006, 10:06pm by Fritzlein » |
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Janzert
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Arimaa player #247
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Re: (no) absolute score values for pieces?
« Reply #63 on: Mar 18th, 2006, 10:49pm » |
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on Mar 18th, 2006, 9:59pm, Fritzlein wrote:
Oh, whoops, it should be 633. |
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Whoo, I think I finally got it right then.
Quote:| By now you know my system better than I do. |
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Heh, not even close. Just finally got through enough trial and error to get to the right spot. At least I hope it's the right spot.
Janzert
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IdahoEv
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Arimaa player #1753
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Re: (no) absolute score values for pieces?
« Reply #65 on: May 1st, 2008, 3:12am » |
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on May 1st, 2008, 2:26am, 99of9 wrote:
Wow, that's pretty thorough! I wouldn't bother with the RabbitCurve systems unless it entertains you to do so. They were merely experiments to see if the curve could help the system but they quite clearly didn't so they've never seen any contemplation beyond a single experiment...
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aaaa
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Arimaa player #958
Posts: 768
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Re: (no) absolute score values for pieces?
« Reply #66 on: May 1st, 2008, 9:38am » |
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Some systems out there would gladly trade a horse for a cat and a rabbit in direct contravention of classical ("Fritzleinian"?) Arimaa theory, but my analysis of game data does appear to bear that out.
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Fritzlein
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Arimaa player #706
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Re: (no) absolute score values for pieces?
« Reply #67 on: May 1st, 2008, 1:54pm » |
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Sorry, what does your analysis of game data bear out? That CR is better than H or the reverse? What set of games/positions is that based on?
If my opinion is considered "classical" then we have to define when my opinion is/was measured. I used to have clear preference for H over DR as an opening trade, but I now rate it nearly equal. I don't know if my change of heart is due to experience, or due to persuasion by reported statistics. I still clearly prefer H to CR, though.
I remain intrigued by the fact that my intuition is contradicted by game data, as first pointed out by IdahoEv. (And it isn't just me: ask chessandgo which side of a C for R trade he would prefer in the opening.) I am therefore quite curious about the exact nature of the data that is contradicting me.
IdahoEv has suggested that material values may be different for bots than for humans. If so, bot developers may wish to ignore the opinions of human players. (In particular, Clueless and OpFor may want to stop using FAME.)
It should be much easier to verify material values for actual bots than material values for hypothetical perfect play. One should be able to play a bot against itself with various material handicaps present from the start (e.g. H for CR) and see which side wins more often. This would at the very least separate out the causality issue, i.e. prove that the material imbalance causes the difference in winning chances, rather than the causality being reserved, or both being effects of some third cause.
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| « Last Edit: May 1st, 2008, 2:00pm by Fritzlein » |
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aaaa
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Arimaa player #958
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Re: (no) absolute score values for pieces?
« Reply #68 on: May 1st, 2008, 2:40pm » |
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You've nailed it completely with pointing out that direction of causality is key here. For example, based on my data, I can say that given a game (biased towards one played between strong players) where at one point one side missed a horse, two dogs and a rabbit while the other missed a horse, a dog, a cat and a rabbit, the former is still more likely to have eventually won the game despite being strictly worse off.
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Janzert
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Arimaa player #247
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Re: (no) absolute score values for pieces?W
« Reply #69 on: May 1st, 2008, 5:45pm » |
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Wow, very nice 99of9. I didn't realize there were anywhere near that many different methods proposed already.
Janzert
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| « Last Edit: May 1st, 2008, 5:45pm by Janzert » |
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99of9
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Gnobby's creator (player #314)
 
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Re: (no) absolute score values for pieces?
« Reply #70 on: May 1st, 2008, 6:40pm » |
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on May 1st, 2008, 9:38am, aaaa wrote:| Some systems out there would gladly trade a horse for a cat and a rabbit |
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Mostly those which were empirically optimized based on game data (by IdahoEv).
Quote:| my analysis of game data does appear to bear that out. |
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Which presumably means you were using a similar methodology to him!
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99of9
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Re: (no) absolute score values for pieces?
« Reply #71 on: May 1st, 2008, 6:47pm » |
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on Oct 13th, 2005, 9:03pm, nbarriga wrote:
By the way, my current eval function is
R=100
C=200
D=300
H=500
M=800
E=2000
If the oponent lost a complete category, the next category of my pieces is worth the average between the category and the one lost.
If i'm not making myself clear is because i'm not a native english speaker. An example: If the enemy lost both his dogs, the values for my pieces is:
R=150
C=250
D=300
H=500
M=800
E=2000 |
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nbarriga, I see you on the forum right now, so I might as well ask you this. If you would like me to implement this system on the summary page, I will need a bit more detail.
So when the enemy loses one type of piece, all values of pieces below it are promoted by half of one step? I presume enemy pieces are *not* promoted? What if the enemy loses two sets of pieces, or more?
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nbarriga
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Almost retired Bot Developer
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Re: (no) absolute score values for pieces?
« Reply #72 on: May 21st, 2008, 2:03pm » |
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Sorry, I just saw this question. The answer is, I don't remember :( I haven't coded anything for arimaa in a long while, I can paste the actual code here, but I don't even remember if tests showed if it was usefull.
this is the code, I hope it is not to criptic.
//parameters.piece_value are the values you cited
// c is side to play
void piece_value(position *p,int *real_values,int c){
//int real_values[6];
int i,j=5;
real_values[5]=2000;
for(i=4;i>=0;i--){
if(bit_count(p->bd[c^1][i+2]!=0)){//if enemy has given piece
j--;
}
real_values[i]=(parameters.piece_value[j]+parameters.piece_value[i])/2;
}
}
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aaaa
Forum Guru
Arimaa player #958
Posts: 768
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Re: (no) absolute score values for pieces?
« Reply #73 on: Jun 8th, 2009, 11:30am » |
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Here is the material evaluation function used by my bot. It is the difference between the result of the following computation for one side and that of the other:
For every friendly non-rabbit with no stronger enemy piece add 2/Q.
For every other friendly non-rabbit add 1/(Q+number_of_stronger_enemy_pieces).
Finally, add G*ln(number_of_friendly_rabbits*number_of_total_friendly_pieces).
The chosen values for the parameters are:
Q=1.447530126
G=0.6314442034
This makes the material evaluation function completely indifferent towards a trade of a dog for two rabbits.
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Fritzlein
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Arimaa player #706
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Re: (no) absolute score values for pieces?
« Reply #74 on: Jun 8th, 2009, 6:34pm » |
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Thanks for sharing, aaaa. I like the simplicity of your formula. Is there a theoretical justification, or did it simply seem to correspond to our intuition for many practical cases? Does number_of_total_friendly_pieces include the rabbits? I suppose it must or the function might be undefined. Do you have a silly acronym for it like FAME or DAPE? I hope Janzert adds it to his material calculator page so I can play around with it for minimal effort.
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