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Title: Handicap Order - what beats what? Post by mistre on Apr 17th, 2008, 3:50pm It took a while and was tedious, but I took the values from each of the 3 material evaluators - http://arimaa.janzert.com/fame.html and ranked each major type of handicap. I say major, because I calculated there are actually 815 different handicap combinations (keeping at least 1 rabbit). For this exercise, I did not include any combination that included both non-rabbit pieces and rabbit pieces. This dropped the number to a more manageable 108 combinations. My reasoning for not including the rabbit/non-rabbit combinations is that typically when handicap botbashing, you will start with the heavy pieces first and only add rabbits at the end. So I don't think there would be any reason to compare something crazy like HDCR and CRRRRRR. I did leave in rabbit-only handicaps to see how they compared. After I ranked all 108 combinations for each evaluator, I summed the rankings to give a composite score. I think this is more accurate than just doing a 2/3 majority rule (this was the tiebreaker). Some interesting findings: H = CC. FAME and DAPE (opt) prefer CC, while DAPE prefers H. The average rankings for all 3 makes the comparison equivalent. 7 rabbits = MHC. This would make a neat asymmetrical handicap match. In Arimaa, E = MHC2 Here is the entire list from lowest handicap to highest. R C D RR RRR CC H DC DD RRRR HC DCC HD M DDC RRRRR HCC HH HDC MC HDD MD DDCC HHC RRRRRR HHD MCC HDCC MH HDDC MDC MDD HHCC HHDC MHC RRRRRRR MDCC MHD HHDD HDDCC MDDC E MHCC MHH HHDCC MHDC EC HHDDC MHDD MDDCC ED MHDCC MHHD ECC MHDDC EH HHDDCC EDC EDD MHHCC MHHDC EHC EHD MHHDD MHDDCC EDCC EDDC EHH EM EHCC MHHDCC EHDC EHDD MHHDDC EMC EMD EHHD EHDCC EHDDC EMCC EMH EHHCC MHHDDCC EMDC EMDD EHHDC EHHDD EMHC EHDDCC EMDCC EMHD EMDDC EHHDCC EMHCC EHHDDC EMHDC EMHH EMDDCC EMHDD EMHHC EMHDCC EMHDDC EHHDDCC EMHHD EMHHCC EMHDDCC EMHHDC EMHHDD EMHHDCC EMHHDDC EMHHDDCC Edit: I found 3 more, there is 111 listed now. 3 more to find. |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 18th, 2008, 6:45am You did a great job here! maybe you should put a link in the handicap rules part of the botbasher page to this list. |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 18th, 2008, 6:55am on 04/17/08 at 15:50:51, mistre wrote:
Only in relative terms. ;) |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 18th, 2008, 7:09am on 04/17/08 at 15:50:51, mistre wrote:
Actually there should be 2x2X3X3X3=108-1 = 107 (If you exclude "nothing" from the list) combinations, if you don't count the rabbits. Plus 1 to 7 rabbits (since you need at least one rabbit to win) = 107 + 7 = 114 combinations. However, your list has only 108 items, therefore there must still be 6 combinations missing. |
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Title: Re: Handicap Order - what beats what? Post by chessandgo on Apr 18th, 2008, 11:24am Thanks for this interesting list, Mistre. I went trough the start of the list, and I disagree with a few things. For instance, it does not make sense, in my opinion, that H<CC while HH>HCC. Having a piece less makes the number of pieces even more important. I'm not sure what I'd prefer between H and CC, but I definitely prefer having HCC to HH. Similarly, M and HD are probably roughly equal, but MD should be worth less than HDD, by the same principle that the less pieces you have, the more their number is important relatively to their strength. Or are there theoretical arguments for the converse ? |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 18th, 2008, 11:35am on 04/18/08 at 11:24:17, chessandgo wrote:
I my view the NUMBER of pieces outweighs their relative strengths in game endings when what's important is the ground you're covering. In the beginning of a game, it's pretty much the reverse. We all know how deadly it can be if you block someone's elephant even if you commit half of your pieces to the task! While in the end of a game, an elephant can't even outrun two distant rabbits. Therefore, you may try to think of these pieces as in the context of a cluttered board and it might change your perspective a little. |
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Title: Re: Handicap Order - what beats what? Post by mistre on Apr 18th, 2008, 11:59am Chessandgo - Thanks for your comments. The results are only as good as the three current models. What I think this list does for the first time though is combine all 3 model evaluators into one composite ranking. |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 18th, 2008, 1:36pm on 04/18/08 at 11:59:34, mistre wrote:
I think this is the right thing to do. If we try to make a list by taking each individual's opinion, it’ll take ten years to come up with an order that everyone will hate. So you might as well refer to an objective indicator like this one and stick to it. |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 18th, 2008, 2:09pm on 04/18/08 at 11:59:34, mistre wrote:
Yeah, and I freely admit that FAME stinks. The best I can say for it is that FAME is better than a static piece evaluation, which is what I was competing against when I designed it. Oh, and it is well-defined. Chessandgo is absolutely right that after a trade of H for CC, the side with the cats benefits more from trading H for H. I'm pretty sure H > CC but I don't know about HH for HCC. It's painful to imagine having that kind of discussion a hundred times to get the handicap order right. :P |
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Title: Re: Handicap Order - what beats what? Post by mistre on Apr 18th, 2008, 4:25pm on 04/18/08 at 14:09:02, Fritzlein wrote:
The worst thing about FAME is that once you get to multiple piece handicaps it thinks they are equivalent. For example, it ranks the 4-piece handicaps EHCC through EMHH as equal. This first occurs with HDC and HDD. |
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Title: Re: Handicap Order - what beats what? Post by aaaa on Apr 18th, 2008, 5:11pm I'm planning to come up with my own material evaluator in the form of a multilayer perceptron based on game statistics. Here's hoping it will have better output than garbage. |
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Title: Re: Handicap Order - what beats what? Post by 99of9 on Apr 18th, 2008, 7:06pm on 04/18/08 at 11:24:17, chessandgo wrote:
Yes, I have a theoretical argument for the converse. I agree with you that as both player's pieces are reduced, the number of pieces of pieces starts mattering more. BUT, there is also something in the detail about which pieces you have. It's good to have a piece equal to the pieces your opponent has an excess of. One horse can partially neutralize an opponent with two horses, but zero horses cannot neutralize an opponent with one horse. So after an H for CC trade, I would agree that it is beneficial for the CC player to trade rabbits, but it could well be beneficial for the H player to trade away one of his H's for the last of his opponent's. (This is the reason for the "Equals" term in DAPE, which depreciates the value of a piece according to how many opponent's pieces are equal to it.) |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 18th, 2008, 9:17pm on 04/18/08 at 19:06:51, 99of9 wrote:
That's a good point, and one that would weigh even more heavily if the camels were missing. Maybe I'll have to reconsider my intuition. |
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Title: Re: Handicap Order - what beats what? Post by Janzert on Apr 18th, 2008, 10:39pm on 04/17/08 at 15:50:51, mistre wrote:
While I don't want to step into the middle of the controversy over what order things should be ranked in, I do think this approach is flawed because of the way I currently present the material eval scores on that page. The scores shown are normalized for the first rabbit captured (i.e. all the methods show 1.0)1. But the three methods still operate on different scales (i.e. once there is only a rabbit left FAME gives 162, DAPE 284 and DAPE(eo) 56). This means that for the high end sacrifices with the above summation method you are essentially giving DAPE 1.75 times the weight of FAME and 5 times the weight of DAPE(eo). So for the current numbers a simple count as 99 originally proposed is almost certainly better. I have several times in the past thought about rescaling the numbers so the could be more directly compared. But the problem is that while it's very natural to say that the first rabbit should be 1.0 there isn't any similiar self apparent spot to pin the top end. Or looked at another way the current numbers directly mean DAPE thinks one rabbit remaining is like 284 initial rabbits while DAPE(eo) thinks it's like 56 initial rabbits. Scaling the methods to all go 1 through 100 or some such makes the numbers a little more abstract but more directly comparable. Maybe I'll just modify it to show both the current (initial rabbit) number and a new (scaled range) number. Janzert 1 The actual raw values for the initial rabbit are 33.69 for FAME, 4.28 for DAPE and 10.44 for DAPE(eo). So had the raw numbers been left on the page DAPE would have had a smaller weighting while FAME and DAPE(eo) would have had larger weightings in the above calculation. |
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Title: Re: Handicap Order - what beats what? Post by mistre on Apr 18th, 2008, 11:00pm Janzert, Let me clarify my ranking method. I did not use overall raw numbers but rankings instead. I ranked all 108 (now 111) handicaps 1 through 111 for each of the three measures. I then summed that number for each measure. The handicaps were then ranked from lowest total score to highest total score. So overall raw numbers didn't matter, just what order each of the 3 evaluators placed each handicap. |
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Title: Re: Handicap Order - what beats what? Post by 99of9 on Apr 18th, 2008, 11:22pm Ahh, thanks for the clarification mistre, that sounds like a much better method than what I (and Janzert) assumed you were doing. In fact I think I even agree with you that it is a better method than my "majority of evals" method (although yours is obviously much more time consuming). |
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Title: Re: Handicap Order - what beats what? Post by chessandgo on Apr 19th, 2008, 3:38am on 04/18/08 at 13:36:17, Arimabuff wrote:
on 04/18/08 at 11:59:34, mistre wrote:
Well, I wasn't suggesting to the least extent that the ranking should be any different, you did a great job, Mistre. Just wanted to profit from this thread to hear from other players how they approach unbalanced trades. |
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Title: Re: Handicap Order - what beats what? Post by chessandgo on Apr 19th, 2008, 3:43am on 04/18/08 at 19:06:51, 99of9 wrote:
Yes, thanks for this point, Toby. But as Karl says, I would consider this to be significant only if the camels were gone. Moreover, if camels get traded, the number of pieces decreases again, making the extra piece even more interesting ... in my opinion. But I see your point. So do you think an early exchange of HH vs HCC favorizes the side with hcc down ? |
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Title: Re: Handicap Order - what beats what? Post by 99of9 on Apr 19th, 2008, 5:17am on 04/19/08 at 03:43:40, chessandgo wrote:
I'm not sure. It's close. All I'm saying is that there's something in each player's favour. I agree that the factor is much stronger when the camels are missing (all 3 evals also agree on this). But even the fact that a camel trade is now favourable for the hcc player makes his position a little easier, because the other player has to watchfully prevent a camel trade. |
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Title: Re: Handicap Order - what beats what? Post by Janzert on Apr 19th, 2008, 5:51am on 04/18/08 at 23:00:25, mistre wrote:
Ahh, yes that does sound like a better method. Janzert |
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Title: Re: Handicap Order - what beats what? Post by woh on Apr 19th, 2008, 6:50am Great list, mistre! on 04/17/08 at 15:50:51, mistre wrote:
I believe those are MHHC EHHC EDDCC |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 19th, 2008, 1:47pm on 04/18/08 at 23:00:25, mistre wrote:
So am I correct to state that we can't infer from your list whether EMHHDDCCRRRRR or EMHHDDCRRRRRRR is the greater handicap? I looks like, in order to get a relative ranking between the two, you would have to rerun with 113 handicaps in the list. Would it also be correct to say that adding alternatives could change the relative rankings of items that are already in your list? For example, in the partial lists ABC ACB ACB your method would have C ahead of B overall, but if new alternatives came in like ABDEFC ADEFCB ADEFCB then the combined ranking would have B ahead of C, right? I guess my point is that relative values of handicaps is an unstable way to do it, so to be fair one would presumably have to have _all_ handicaps in the list, or else raise the question of why one list and not another. |
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Title: Re: Handicap Order - what beats what? Post by aaaa on Apr 19th, 2008, 2:07pm Take the ranking generated by a Condorcet method with the chosen material evaluators being the voters and the 971 possible handicaps being the candidates. Problem solved. |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 19th, 2008, 2:43pm on 04/19/08 at 13:47:57, Fritzlein wrote:
Karl I believe that for handicaps where the pieces are all but depleted we should see it the other way around, that is in this case whether having only CR in your camp is better than RRR. I think it makes things clearer to see. If we have only either an army of three rabbits to fight or a cat and a rabbit, we all know which one is best don't we? I think when we consider it on the side of the handicap MHHDDCRRRRRRR versus MHHDDCCRRRRR the program will suffer from side effect miscalculations, due to the big accumulation of pieces that adds each its own uncertainty. When you look it as RRR versus CR it suddenly makes it look plain and simple but maybe that’s not what we want? I say it makes sense to look at things from their clearer and simpler perspective, that’s how we’ve been taught to organize our thoughts. |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 19th, 2008, 2:53pm If my previous post is correct, the question of whether CR beats RRR was not decided at the time that Arimabuff and 99of9 set their respective records against Gnobot2005P1. That means we now need to decide which is better, either directly, or by deciding on a methodology and accepting the result. That is tricky enough, but there is an added complication that we are setting the finish line after the race has been run. Arimabuff stopped running after reducing the handicap to CR, because he thought the race was over. Unless Gnobot2005P1 can be beaten with only RR, the race is really over now, and decision we make will determine who holds the all time record. We can't decide that RRR was the greater feat now without being unfair to Arimabuff. On the other hand, we can't start the discussion knowing what we have to conclude, or it isn't a real discussion. The more I think about whether CR or RRR is better, the more it seems to me that the two records are incommensurate, and the Hall of Fame should therefore reflect both. More generally, one handicap should not replace another in the Hall of Fame unless one handicap includes all the pieces of the other, plus more, or the two handicaps are equal in number of pieces and one is strictly better in strength. To illustrate my reasoning, consider the following examples. In the first pair of boards (Silver to move) CR is clearly weaker than RRR +---+---+---+---+---+---+---+---+ 8 | | | | | | | | | +---+---+---+---+---+---+---+---+ 7 | | | | | | | | | +---+---+---+---+---+---+---+---+ 6 | | | * | | | * | | | +---+---+---+---+---+---+---+---+ 5 | c | | | M | E | | | r | +---+---+---+---+---+---+---+---+ 4 | R | | | H | H | | | R | +---+---+---+---+---+---+---+---+ 3 | | | * | D | D | * | | | +---+---+---+---+---+---+---+---+ 2 | | | | C | C | | | | +---+---+---+---+---+---+---+---+ 1 | | R | R | R | R | R | R | | +---+---+---+---+---+---+---+---+ a b c d e f g h +---+---+---+---+---+---+---+---+ 8 | | | | | | | | | +---+---+---+---+---+---+---+---+ 7 | | | | | | | | | +---+---+---+---+---+---+---+---+ 6 | | | * | | | * | | | +---+---+---+---+---+---+---+---+ 5 | r | r | | M | E | | | r | +---+---+---+---+---+---+---+---+ 4 | R | | | H | H | | | R | +---+---+---+---+---+---+---+---+ 3 | | | * | D | D | * | | | +---+---+---+---+---+---+---+---+ 2 | | | | C | C | | | | +---+---+---+---+---+---+---+---+ 1 | | R | R | R | R | R | R | | +---+---+---+---+---+---+---+---+ a b c d e f g h In the second pair of boards (Silver to move), CR is clearly stronger than RRR +---+---+---+---+---+---+---+---+ 8 | | | | | | | | | +---+---+---+---+---+---+---+---+ 7 | r | c | | | | | | | +---+---+---+---+---+---+---+---+ 6 | R | R | * | | | * | | | +---+---+---+---+---+---+---+---+ 5 | | | | M | E | | | | +---+---+---+---+---+---+---+---+ 4 | | | | H | H | | | | +---+---+---+---+---+---+---+---+ 3 | | | * | D | D | * | | | +---+---+---+---+---+---+---+---+ 2 | | | | C | C | | | | +---+---+---+---+---+---+---+---+ 1 | | | R | R | R | R | R | R | +---+---+---+---+---+---+---+---+ a b c d e f g h +---+---+---+---+---+---+---+---+ 8 | | | | | | | | | +---+---+---+---+---+---+---+---+ 7 | r | r | r | | | | | | +---+---+---+---+---+---+---+---+ 6 | R | R | * | | | * | | | +---+---+---+---+---+---+---+---+ 5 | | | | M | E | | | | +---+---+---+---+---+---+---+---+ 4 | | | | H | H | | | | +---+---+---+---+---+---+---+---+ 3 | | | * | D | D | * | | | +---+---+---+---+---+---+---+---+ 2 | | | | C | C | | | | +---+---+---+---+---+---+---+---+ 1 | | | R | R | R | R | R | R | +---+---+---+---+---+---+---+---+ a b c d e f g h We can't say in advance what combination of pieces is going to be most useful, because we don't know in advance what portion of the bot's army will be deployed, whether it will advance rabbits sooner or later, on one side of the board, or both, etc. The material handicap formulas weren't designed for extreme situations such as a whole army against three little pieces. A handicap win is only possible because the bot doesn't use its whole army. If we use the formulas at all in this case, it might make more sense to ask whether RRR or CR is stronger against an opposing army of RRR. But then for a different bot that used its pieces differently, the true difficulty of each handicap would be reflected by a different formula. Why not use a partial order (as we mathematicians call it) and keep both records where there is no clear order between them? One might say that we would have too many records per bot, but in practice I doubt it would get beyond two or three. Under my proposal we can't say whether a handicap of M or RRRR is better, but if both are possible then probably so is MRRR, which trumps them both. If we ended up with cases where MD was possible and also HH, but not MH, then why do we need to split hairs? Why not recognize both? My hunch is that this will result in basically two handicap records per bot: a strength handicap and a numbers handicap. On the one side you'll be trying to win with just EMR, and on the other trying to win with just CRRRRRRR or something like that. For the bots that get extremely bashed, the two may even converge. What do you guys think? Is it worth a try? |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 19th, 2008, 3:02pm on 04/19/08 at 14:07:32, aaaa wrote:
Are you ranking each smaller army by how much it is less than a full army? That provides clarity, but as Arimabuff points out, the greater the mismatch, the more likely the numbers are to be meaningless. FAME, at least, wasn't designed for extreme situations. Or do you mean ranking each army head to head? As Arimabuff suggests, we could enter CR vs. RRR directly into each evaluator. Unfortunately, FAME can have circular preferences, i.e. head-to-head preferences don't produce a strict ordering of all possible armies. For example, CCR > MR > DRR > CCR. So there may be more accuracy of the formulas that way, but less overall clarity. |
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Title: Re: Handicap Order - what beats what? Post by aaaa on Apr 19th, 2008, 3:11pm on 04/19/08 at 15:02:07, Fritzlein wrote:
You might want to let additional material evaluators weigh in then, like optimized FAME, RabbitCurveABC, LinearAB, etc. |
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Title: Re: Handicap Order - what beats what? Post by mistre on Apr 19th, 2008, 3:16pm Wow, a lot was said since I signed off yesterday... After some more thought, I don't plan on re-working my ranking analysis to see if RRR or CR remaining is better. As Karl said, I can't just add those two scenarios to the list without adding all other 700+ scenarios that mix rabbits/non-rabbit pieces. My original list is far from perfect, but I stand by using it over just 2/3 majority of evals. For 99% of the cases, it should work just fine. For a case like RRR vs CR remaining, it will not and we need another solution. aaaa mentions using the condorcet model. I don't know how to use that, so if anyone wants to give it a go with all 971 combinations, be my guest. |
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Title: Re: Handicap Order - what beats what? Post by aaaa on Apr 19th, 2008, 3:20pm on 04/19/08 at 15:02:07, Fritzlein wrote:
No. We call it a handicap because one is playing with less than a full army against the full one of the opponent, so determining how large the handicap is would logically entail quantifying the resulting disadvantage between the two armies. |
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Title: Re: Handicap Order - what beats what? Post by aaaa on Apr 19th, 2008, 3:27pm on 04/19/08 at 15:16:30, mistre wrote:
Give me the evaluation functions you want to count (preferably a large and odd number, like, say, 5) and I'll try to give you the relative ranking as given by the Schulze(margins) method. |
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Title: Re: Handicap Order - what beats what? Post by mistre on Apr 19th, 2008, 3:31pm on 04/19/08 at 06:50:54, woh wrote:
Great eyes, Woh! I appreciate it! Next time I get a chance, I will add the missing handicaps. |
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Title: Re: Handicap Order - what beats what? Post by aaaa on Apr 19th, 2008, 6:19pm Unfortunately, using the 3 material evaluators on Janzert's page gives me a considerable amount of ties. Nevertheless, here is the result I get: 001. No handicap 002. R 003. C 004. D 005. RR 006. CR 007. DR 008. RRR 009. H 010. CC 011. CRR 012. DC 013. DRR 014. CCR """. DD """. HR """. RRRR 018. CRRR 019. DCR 020. HC 021. CCRR """. DCC """. DDR """. DRRR """. HRR 026. HD 027. CRRRR """. DCRR """. HCR """. M """. RRRRR 032. DDC 033. HCC """. HDR """. MR 036. DCCR """. DDRR """. HRRR 039. CCRRR 040. DRRRR 041. HCRR """. HDC 043. DDCR 044. CRRRRR """. DCRRR """. HDD """. HH """. RRRRRR 049. DCCRR """. DDRRR """. HCCR """. HDRR """. MC 054. HRRRR """. MD """. MRR 057. DDCC """. HHR 059. CCRRRR """. MCR 061. DRRRRR """. HDCR 063. DDCRR """. HCRRR 065. RRRRRRR 066. HHC """. MH 068. DCRRRR """. MCC """. MDR 071. HDDR 072. HHD 073. HCCRR 074. DCCRRR """. HDRRR """. MRRR 077. CRRRRRR 078. DDCCR """. HDCC """. HHRR """. MDC 082. E 083. DDRRRR """. HRRRRR 085. HDDC 086. MCRR 087. HDCRR 088. DDCRRR 089. DRRRRRR """. HHCR 091. HCRRRR 092. MDD 093. RRRRRRRR 094. CCRRRRR """. MHR 096. HCCRRR 097. MCCR """. MDRR 099. HDDRR 100. DDCCRR """. HHDR """. HHRRR 103. HDCCR """. MRRRR 105. HHCC 106. DCRRRRR """. HDRRRR """. MHC 109. CRRRRRRR """. DCCRRRR """. MDCR 112. ER """. HRRRRRR 114. HDCRRR 115. HDDCR 116. HHDC """. MCRRR 118. HHCRR 119. MDDR """. MHD 121. DDRRRRR 122. DDCRRRR 123. DRRRRRRR """. EC 125. MCCRR """. MDCC """. MDRRR 128. CRRRRRRRR """. HHDD """. MHRR 131. HDDRRR 132. CCRRRRRR """. HDDCC 134. HDCCRR 135. HCRRRRR """. HHDRR 137. DDCCRRR """. HCCRRRR 139. CCRRRRRRR """. HHCCR 141. MRRRRR 142. HHRRRR 143. ED 144. MHCR 145. MDCRR """. MDDC 147. DCRRRRRR 148. DRRRRRRRR 149. HDDCRR """. HDRRRRR 151. HHCRRR 152. DCRRRRRRR """. HHDCR """. MCRRRR """. MHH 156. ERR """. HDCRRRR 158. DCCRRRRR """. DCCRRRRRR """. HRRRRRRR 161. MDDRR """. MHDR 163. MHCC 164. HHDDR 165. MCCRRR 166. DDRRRRRR """. HDCCRRR """. MDCCR """. MHRRR 170. ECR 171. HDDRRRR """. HHCCRR """. MDRRRR 174. HHDRRR 175. HDDCCR 176. HHDCC 177. EH 178. MDDCR 179. DDCRRRRR """. DDCRRRRRR """. DDRRRRRRR """. HCRRRRRR 183. MDCRRR """. MHCRR """. MRRRRRR 186. MHDC 187. DDCCRRRRR """. HHDDC 189. DDCCRRRR """. HDDCRRR 191. HRRRRRRRR """. MHHR 193. EDR 194. HHDCRR 195. ECC """. HHCRRRR """. HHRRRRR 198. HCCRRRRR 199. HCCRRRRRR """. HCRRRRRRR 201. MDDRRR """. MHDD """. MHDRR 204. MCRRRRR 205. HDRRRRRR 206. CCRRRRRRRR """. ERRR """. MDCCRR """. MDDCC """. MHCCR 211. EDC """. HHDDRR 213. MHHC 214. HDCRRRRR """. HDDCCRR """. HHDRRRR """. MCCRRRR """. MHRRRR 219. HHCCRRR """. MHHD 221. HDCCRRRR 222. HHDCCR 223. ECRR 224. MDRRRRR 225. MDDCRR """. MHDCR 227. HDDRRRRR 228. DCRRRRRRRR """. HDCRRRRRR 230. HDCCRRRRR """. MHCRRR 232. EDD """. MDCRRRR 234. HDDRRRRRR """. HDRRRRRRR 236. HDDCRRRRR 237. EHR """. HHDDCR """. MHHRR 240. DCCRRRRRRR """. HHDCRRR 242. HDDCRRRR 243. MDDRRRR 244. EDRR 245. MHCCRR """. MRRRRRRR 247. ECCR """. MDCCRRR """. MHDDR """. MHDRRR 251. MDDCCR 252. HHRRRRRR 253. HHCRRRRR """. HHDDRRR 255. MHDCC 256. EHC """. HDDCCRRRR 258. HHCCRRRR """. MHHCR 260. DDRRRRRRRR 261. HHDCCRR """. MDDCRRR 263. DDCRRRRRRR """. MCCRRRRR """. MHRRRRR 266. ERRRR """. HDDCCRRR """. MCRRRRRR """. MHDCRR 270. HHDDCC 271. EDCR """. HHDRRRRR 273. MHHDR 274. MHCRRRR 275. MHDDC 276. DDCCRRRRRR 277. HCRRRRRRRR 278. HCCRRRRRRR """. HHDCRRRR """. HHDDCRR 281. ECRRR """. MDCRRRRR """. MDRRRRRR 284. EHD 285. MHHRRR 286. MHCCRRR """. MHHCC 288. HHCCRRRRR """. MHDDRR 290. EDDR 291. HHCRRRRRR """. MDCCRRRR """. MDDCCRR """. MHDRRRR 295. HHRRRRRRR """. MRRRRRRRR 297. MDDRRRRR """. MHDCCR 299. EHRR 300. EDCC """. HHDCRRRRR """. HHDRRRRRR 303. MCCRRRRRR 304. MHHDC 305. EDRRR 306. ECCRR """. HHDCCRRR """. HHDDRRRR """. MCRRRRRRR 310. HDRRRRRRRR 311. HHDDRRRRR """. MDDCRRRR """. MHHCRR 314. MHDCRRR """. MHHDD 316. HDCRRRRRRR 317. HHDCCRRRR """. MDCCRRRRR 319. HDCCRRRRRR """. HHDDCCR """. MHDDCR 322. EHCR """. HDDRRRRRRR 324. MHCRRRRR 325. EDDC 326. EDCRR """. HDDCRRRRRR """. MHHDRR 329. HHDDCRRR """. MDCRRRRRR """. MDDCCRRR """. MHRRRRRR 333. MDRRRRRRR """. MHCCRRRR 335. ERRRRR """. MDDCRRRRR """. MHDDRRR 338. MHHRRRR 339. MHDCCRR 340. EM 341. MDDRRRRRR 342. HHDDCRRRR 343. DCCRRRRRRRR """. MHDRRRRR 345. MHHCCR 346. ECRRRR 347. EHH 348. EHDR """. MHDCRRRR 350. HDDCCRRRRR 351. EHCC """. MHDDCC 353. EDDRR 354. MDDCCRRRR 355. MHHCRRR 356. MHDDCRR 357. EDCCR """. EHRRR 359. ECCRRR 360. HHDDCCRR 361. EDRRRR """. MHHDCR 363. MHDCCRRR 364. DDCRRRRRRRR 365. HHDDCCRRR 366. HHRRRRRRRR 367. EDDCR """. EHDC """. MHDDRRRR 370. HCCRRRRRRRR """. HHCRRRRRRR """. MHCCRRRRR """. MHHDDR 374. EHCRR 375. MHCRRRRRR """. MHHDRRR 377. MCCRRRRRRR 378. DDCCRRRRRRR """. EDCRRR 380. HHCCRRRRRR """. HHDRRRRRRR 382. MHHCCRR 383. EMR """. MHRRRRRRR 385. HHDCRRRRRR """. MCRRRRRRRR 387. MHDRRRRRR 388. ERRRRRR """. MHDCRRRRR 390. MHHRRRRR 391. MHDDCCR """. MHHDCC 393. HHDDRRRRRR """. MHDDCRRR 395. EHDRR 396. EDDRRR """. EHHR """. HHDCCRRRRR """. MHDDRRRRR 400. EHCCR """. EMC """. HDCRRRRRRRR 403. ECRRRRR """. EHDD 405. EDCCRR """. MDRRRRRRRR """. MHDCCRRRR """. MHHCRRRR 409. MDCCRRRRRR """. MHHDDC 411. HDDRRRRRRRR """. MDCRRRRRRR """. MHHDCRR """. MHHRRRRRR 415. EDDCC 416. EHRRRR """. MHHCRRRRR 418. HHDDCRRRRR """. MDDCRRRRRR 420. ECCRRRR """. MDDRRRRRRR 422. EMD 423. HDCCRRRRRRR 424. MHDDCRRRR 425. MHHDRRRRR 426. EDRRRRR 427. EHDCR 428. HDDCRRRRRRR 429. EDDCRR """. MHHCCRRR """. MHHDDRR 432. EHHC 433. MHDDCCRR """. MHHDRRRR 435. EHCRRR """. MDDCCRRRRR """. MHHCCRRRR 438. EMRR 439. EDCRRRR 440. MHHDCRRRR 441. MHHDCCR 442. EDDRRRR """. EHCCRR """. EHDDR """. EHDRRR """. EHHD """. HDDCCRRRRRR 448. EHHRR """. MHCCRRRRRR """. MHHDDRRRR 451. HHDDCCRRRR """. MHDDCCRRR 453. EDCCRRR """. MHCRRRRRRR 455. EMCR """. ERRRRRRR 457. MHHDCRRR 458. EHDCC 459. EMH 460. EDDCCR """. HHCRRRRRRRR 462. MHDCRRRRRR 463. HHCCRRRRRRR 464. MHDRRRRRRR 465. EMDR 466. ECRRRRRR """. EHRRRRR 468. HHDRRRRRRRR 469. MCCRRRRRRRR """. MHHDCCRRR """. MHHDDCR 472. MHRRRRRRRR 473. ECCRRRRR """. MHDDRRRRRR 475. EDDCRRR """. HHDCRRRRRRR """. MHDCCRRRRR 478. EHDCRR 479. EHHCR 480. EHCRRRR """. MHHDDRRR 482. EMCC 483. MHHDDCRRR 484. MHHCRRRRRR 485. DDCCRRRRRRRR """. EMRRR """. MHHRRRRRRR 488. EDRRRRRR """. EHDDC """. HHDDRRRRRRR 491. MHDDCRRRRR 492. EDCRRRRR """. HHDCCRRRRRR """. MHHDCCRR 495. MHHDRRRRRR 496. EHCCRRR """. MDCCRRRRRRR 498. EMDC """. MDCRRRRRRRR 500. EHHDR 501. EHDDRR """. EHDRRRR 503. EHHRRR 504. EDCCRRRR """. HHDDCRRRRRR 506. MHHCCRRRRR 507. EDDCCRR """. EHDCCR """. MDDRRRRRRRR 510. EHHCC """. MDDCRRRRRRR """. MHHDDCC 513. EMCRR 514. EDDRRRRR """. EMHR 516. EMDD 517. MHHDCRRRRR 518. MDDCCRRRRRR 519. MHHDDCRR 520. MHDDCCRRRR 521. EMDRR 522. ECCRRRRRR 523. ECRRRRRRR 524. EHDCRRR 525. MHHDDCCRR 526. EDDCRRRR 527. EHHCRR """. EHHDC """. MHHDDRRRRR 530. EHRRRRRR """. ERRRRRRRR 532. HHDDCCRRRRR 533. EMCCR 534. EHDDCR 535. HDCCRRRRRRRR 536. EHCRRRRR """. EMHC 538. EMRRRR 539. EDCRRRRRR 540. EDCCRRRRR """. EHCCRRRR 542. MHHDCCRRRR 543. EHHRRRR """. HDDCRRRRRRRR 545. EHHDRR """. EMDCR """. EMHD 548. EHDDRRR 549. EDDCCRRR """. EDRRRRRRR """. EHDCCRR """. MHCCRRRRRRR 553. EHDRRRRR """. MHCRRRRRRRR 555. EHHCCR 556. EDDRRRRRR """. EMHRR 558. EDDCRRRRR """. EHHDD 560. EMDDR """. MHHDDCRRRR 562. MHDCCRRRRRR """. MHDCRRRRRRR 564. EMCRRR 565. HDDCCRRRRRRR 566. EHDCRRRR 567. MHDRRRRRRRR 568. MHHDDCCR 569. EHDDCC 570. EHHCRRR """. MHDDCRRRRRR 572. EHDDCRR """. EMHH 574. MHDDRRRRRRR 575. EMDCC """. EMDRRR 577. EDDCCRRRR """. EHHDCR 579. MHHCRRRRRRR 580. EMHCR 581. EHDCCRRR """. EMCCRR """. MHHRRRRRRRR 584. HHCCRRRRRRRR 585. EHCCRRRRR 586. EMHDR """. MHHCCRRRRRR 588. EHCRRRRRR """. EHDDRRRR """. MHHDRRRRRRR 591. EMDDC 592. EHHDRRR 593. MHDDCCRRRRR 594. EHHRRRRR """. HHDCRRRRRRRR 596. EHHCCRR 597. EMDCRR 598. EMRRRRR 599. EHRRRRRRR """. MHHDCRRRRRR 601. EHDCRRRRR """. EHDRRRRRR 603. ECCRRRRRRR 604. HHDDRRRRRRRR 605. EMCRRRR 606. EMHCC 607. EHDDCCR """. EMDDRR 609. EHDDCRRR """. EHHDDR """. EMHRRR 612. EHHCRRRR 613. EHHDCC 614. MDCCRRRRRRRR 615. ECRRRRRRRR """. EHDCCRRRR 617. EHDDRRRRR 618. EMHDC 619. EMHHR 620. EDCCRRRRRR """. EHHDCRR 622. EMDRRRR """. HHDCCRRRRRRR 624. MHHDDRRRRRR 625. MHHDDCCRRR 626. EDCRRRRRRR """. MDDCRRRRRRRR 628. EMHDD 629. EMDCCR 630. MHHDCCRRRRR 631. EDDCRRRRRR """. EHHCCRRR """. EHHDRRRR 634. EMHCRR 635. HHDDCRRRRRRR 636. EDRRRRRRRR 637. EMCCRRR 638. EHDDCRRRR 639. EHHCRRRRR 640. EDDCCRRRRR """. EMHDRR 642. EHDDCCRR 643. EMDDCR """. HHDDCCRRRRRR 645. EHHRRRRRR 646. EDDRRRRRRR """. MDDCCRRRRRRR 648. EMRRRRRR 649. EHHDDC """. EMDCRRR 651. EMHHC 652. EMHHD 653. EHHDDRR """. EMHRRRR 655. EHCCRRRRRR 656. EHHDRRRRR 657. EHHCCRRRR """. EHHDCCR """. EMDDRRR 660. MHHDDCRRRRR 661. EHHDCRRR 662. EMCRRRRR """. EMHCCR 664. EHDDCCRRR 665. EHDCCRRRRR 666. EHCRRRRRRR 667. MHCCRRRRRRRR 668. EHDCRRRRRR 669. EMHHRR 670. EMHDCR 671. EMDRRRRR 672. EMDCCRR """. MHDCRRRRRRRR 674. EHHDCRRRR """. EMDDCC 676. EMCCRRRR """. EMHCRRR 678. EHDRRRRRRR """. EMHDDR 680. EHRRRRRRRR 681. EHDDRRRRRR """. EMCRRRRRR 683. EHHDCCRR 684. EMDDCRR 685. EMRRRRRRR """. MHDCCRRRRRRR 687. ECCRRRRRRRR """. EMCCRRRRR """. EMHDRRR """. MHDDRRRRRRRR 691. EHDDCRRRRR """. EHHDDCR """. EMDCRRRR """. MHDDCCRRRRRR 695. EHHDDRRR """. EMDCRRRRR 697. EMDRRRRRR 698. MHHCRRRRRRRR 699. EHHDCCRRR """. EHHDDRRRR 701. EMHHCR 702. HDDCCRRRRRRRR 703. EDCCRRRRRRR """. MHHDRRRRRRRR 705. EMHHDR 706. EMHDCC """. MHDDCRRRRRRR 708. EDCRRRRRRRR 709. EMDDRRRR """. EMDDRRRRR 711. EDDCCRRRRRR 712. EHHCCRRRRR 713. EHDDCCRRRR 714. EHHCRRRRRR """. EMHRRRRR 716. EMHDDC 717. EMHRRRRRR 718. EMDCCRRRR 719. EDDCRRRRRRR 720. EMDCCRRR """. EMHCCRR 722. EHHDDCRR """. MHHCCRRRRRRR """. MHHDDCCRRRR 725. EHHRRRRRRR 726. EMHCRRRRR 727. EDDRRRRRRRR """. EMDDCCR 729. EMHHRRR 730. EHHDDCRRR """. EHHDRRRRRR 732. EMDDCRRRR 733. EHHDCRRRRR """. EHHDDCC """. EMHDCRR """. EMHDRRRRR 737. EHCCRRRRRRR 738. EMDDCRRR """. MHHDCCRRRRRR 740. EMHCRRRR """. MHHDCRRRRRRR 742. EHDCCRRRRRR """. HHDCCRRRRRRRR 744. EMHHCC 745. EHCRRRRRRRR """. EMHDDRR 747. EMHHDC 748. EMHHDD 749. EHDCRRRRRRR 750. EMHCCRRRR """. EMHDRRRR 752. EHHDCCRRRR 753. EHDDCRRRRRR """. EMDDCCRRR """. MHHDDRRRRRRR 756. EMHHRRRRR 757. EHHDDRRRRR """. EMHDCRRRR 759. EHDRRRRRRRR 760. MDDCCRRRRRRRR 761. EHDDCCRRRRR 762. EMDDCCRR """. HHDDCRRRRRRRR 764. EHHDDCCR 765. EMCRRRRRRR """. EMRRRRRRRR 767. EMCCRRRRRR """. EMHDDRRRR 769. MHHDDCRRRRRR 770. EHDDRRRRRRR 771. HHDDCCRRRRRRR 772. EHHDDCCRR """. EMDCRRRRRR """. EMHHCRR 775. EMHCCRRR """. EMHDCCR 777. EMDRRRRRRR 778. EMHHDRR 779. EHHCCRRRRRR 780. EDCCRRRRRRRR 781. EMDCCRRRRR 782. EMDDRRRRRR 783. EMHDCCRRR 784. EHHDDCRRRR 785. EHHCRRRRRRR """. EMHDCRRR 787. EMHHCRRRR 788. EDDCCRRRRRRR 789. EMHDDCR 790. EMHHDRRRR 791. EMHDDCRRR 792. MHDCCRRRRRRRR 793. EDDCRRRRRRRR """. EHHDCRRRRRR 795. EMDDCRRRRR """. EMHHRRRR 797. MHHDDCCRRRRR 798. EHHRRRRRRRR 799. EMHCRRRRRR 800. EHHDCCRRRRR 801. EMHDDRRR 802. EHHDRRRRRRR 803. EMHRRRRRRR 804. EHCCRRRRRRRR """. EMHDRRRRRR """. MHDDCRRRRRRRR 807. EHDCCRRRRRRR """. MHDDCCRRRRRRR 809. EMHDCCRR """. EMHHCCRRR 811. EMDDCCRRRR 812. EMHHDCRRR 813. EMHCCRRRRR 814. EMHHDDRRR 815. EHDCRRRRRRRR """. EHHDDCCRRR """. EMHHCCR 818. EHHDDRRRRRR 819. EMHDDCC 820. EMHDDCRR 821. EMCCRRRRRRR """. EMCRRRRRRRR """. EMHHDCR 824. EHDDCCRRRRRR """. EMHDCRRRRR """. MHHCCRRRRRRRR 827. EHDDCRRRRRRR """. EHHDDCRRRRR """. EMHDDCCRR 830. EMHHDDR 831. EMHDDRRRRR 832. EMDCCRRRRRR """. EMDRRRRRRRR 834. EMHHRRRRRR """. MHHDCCRRRRRRR 836. EMDCRRRRRRR """. EMHHCRRR 838. EHDDRRRRRRRR """. MHHDCRRRRRRRR 840. EHHCCRRRRRRR 841. EMDDCRRRRRR 842. EMDDRRRRRRR """. EMHDCCRRRR 844. EMHHDRRR 845. EHHCRRRRRRRR 846. EMDDCCRRRRR 847. EHHDDCCRRRR 848. EHHDCCRRRRRR """. EMHDDCCR 850. EDDCCRRRRRRRR """. EMHDDCRRRR 852. EMHHDCCRR """. EMHRRRRRRRR """. HHDDCCRRRRRRRR 855. EHHDCRRRRRRR 856. EMHHDCC 857. EMHHDDCRR 858. MHHDDCRRRRRRR 859. MHHDDRRRRRRRR 860. EMHHCRRRRR 861. EMHCCRRRRRR """. EMHHDDC 863. EMHCRRRRRRR """. EMHHCCRR 865. EHHDRRRRRRRR """. EMHHDRRRRR """. MHHDDCCRRRRRR 868. EHHDDCRRRRRR """. EMHDCRRRRRR 870. EHHDDRRRRRRR """. EMHDRRRRRRR 872. EMHHDCRR 873. EHDCCRRRRRRRR 874. EMCCRRRRRRRR """. EMHDCCRRRRR 876. EHHDDCCRRRRR """. EMHDDRRRRRR """. EMHHDDRR 879. EMHDDCCRRR """. EMHHCCRRRR 881. EMDCCRRRRRRR 882. EMDCRRRRRRRR 883. MHDDCCRRRRRRRR 884. EHDDCCRRRRRRR """. EHDDCRRRRRRRR """. EMDDCCRRRRRR 887. EMHHDCRRRR 888. EMDDCRRRRRRR """. EMHDDCRRRRR 890. EMDDRRRRRRRR """. EMHHRRRRRRR 892. EMHHDDRRRR 893. EHHCCRRRRRRRR 894. EMHHDCCR 895. EMHCRRRRRRRR 896. EHHDCCRRRRRRR 897. EMHHDDCCR 898. MHHDCCRRRRRRRR 899. EMHCCRRRRRRR """. EMHDRRRRRRRR """. EMHHDDCR 902. EHHDCRRRRRRRR 903. EMHHCRRRRRR 904. EMHDDCCRRRR 905. EMHHDRRRRRR 906. EMHDCCRRRRRR 907. EMHDCRRRRRRR """. EMHHDCCRRR 909. EHHDDCRRRRRRR 910. EHHDDRRRRRRRR 911. EHHDDCCRRRRRR """. EMHHCCRRRRR 913. EMHDDRRRRRRR """. EMHHRRRRRRRR """. MHHDDCRRRRRRRR 916. EMDCCRRRRRRRR 917. EMHDDCRRRRRR """. EMHHDDCRRR 919. MHHDDCCRRRRRRR 920. EMDDCRRRRRRRR """. EMHHDCRRRRR 922. EHDDCCRRRRRRRR """. EMDDCCRRRRRRR 924. EMHHDDCC 925. EMHDDCCRRRRR 926. EMHCCRRRRRRRR """. EMHHCRRRRRRR 928. EMHHDDRRRRR 929. EMHHDRRRRRRR 930. EMHDCRRRRRRRR 931. EHHDCCRRRRRRRR """. EMHHDDCCRR 933. EMHHDCCRRRR 934. EMHDCCRRRRRRR """. EMHHCCRRRRRR 936. EMHDDRRRRRRRR 937. EMHHDCRRRRRR 938. EHHDDCRRRRRRRR 939. EMHDDCRRRRRRR 940. EMHHDDCRRRR 941. EMHHCRRRRRRRR 942. EMHDDCCRRRRRR 943. EMDDCCRRRRRRRR """. EMHHDDRRRRRR 945. EHHDDCCRRRRRRR 946. EMHHDCCRRRRR 947. EMHHDRRRRRRRR 948. EMHHCCRRRRRRR """. MHHDDCCRRRRRRRR 950. EMHDCCRRRRRRRR 951. EMHHDCRRRRRRR """. EMHHDDCRRRRR 953. EMHHDDCCRRR 954. EMHDDCRRRRRRRR 955. EMHHDCCRRRRRR """. EMHHDDRRRRRRR 957. EMHDDCCRRRRRRR 958. EHHDDCCRRRRRRRR 959. EMHHCCRRRRRRRR 960. EMHHDCRRRRRRRR 961. EMHHDDCCRRRR """. EMHHDDCRRRRRR 963. EMHHDCCRRRRRRR 964. EMHHDDRRRRRRRR 965. EMHDDCCRRRRRRRR 966. EMHHDDCRRRRRRR 967. EMHHDDCCRRRRR 968. EMHHDCCRRRRRRRR 969. EMHHDDCCRRRRRR 970. EMHHDDCRRRRRRRR 971. EMHHDDCCRRRRRRR |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 19th, 2008, 7:19pm on 04/19/08 at 18:19:53, aaaa wrote:
With all due respect, that list doesn't make any sense in the extreme part of the handicaps as is often the case with formulas applied too systematically. It says that ONE CAT is weaker than TWO rabbits yet ONE CAT plus ONE RABBIT is STRONGER THAN Three rabbits. How can anybody rely on such absurd results? Either the difference between two rabbits or a cat is so insignificant that it would explain the bizarre switch or we are in the domain of the formula where the uncertainty outweighs the significant part of the number. Something like .5 give or take 1 for a number for instance. That happens all the time in mathematics, the data is so lacking in precision that you start getting results that don't make any sense. Besides another thing that makes me think that the formula is based on a systematic application that is detached from reality is that you need at least one rabbit in your pieces or you have lost the game BEFORE you even started so when you stop to think about it how can the program even judge that a lone cat is stronger than a lone rabbit when the lone cat means that you have exactly ZERO chance of winning the game? That doesn’t make any sense. I say that formula is unreliable when it comes to BIG handicaps and shouldn’t be used to settle a dispute. In fact, there is also one detail that isn’t taken into account in your formula and that is that I WAS THE FIRST to come up with my result, that should count for something. Had 99 won the three rabbit first we wouldn’t even be having this discussion. I found a solution to a problem that 99 was UNABLE to resolve with less than FOUR rabbits plus a CAT, a solution that put it down to ONE rabbit and one CAT. And I’d have known how to solve the three rabbit problem if I had been informed that it was a possibility. You keep forgetting that the only reason 99 got the three rabbit and not I, is because that I didn’t know that I needed to resolve it. This is a case that we have NEVER encountered in handicap situations. Someone not getting a record not because of lack of skill or unwillingness but because of not being made aware that he was to get it. In my game all the problems are resolved I would have found the solution even faster than 99 because I had already studied the case. I am the true holder of the record be it CR or RRR they both belong to me because I have being deceived into believing that I had won. Nobody neither 99 nor anyone else said anything about the record being beatable. In American law, you have something that can nullify a trial that is called “unfair surprise”, well that’s exactly what happened to me I have been robbed of the result because of unfair surprise and not beaten on skills but on that stupid unfair surprise and nothing else. 99 merits are exactly ZERO in that affair. If you take a look at his solution you can see that a child could have deduce is from mine. Before my attempt 99 didn’t even DARE to try with less than cat plus FOUR rabbits and all of a sudden THANKS TO ME he tries three rabbits!!! What made him make that leap of faith between FOUR rabbits plus cat to THREE rabbits without CAT. I have been dispossessed of my victory by something that disgusts me just to think about it. Ever see Amadeus? I am Mozart been stolen his final requiem by a poisonous Salieri, that’s what I am. Whatever way you look at it, the hall of fame belongs to me on that one. Salieri didn’t even know that he could do it with less than FOUR rabbits and a CAT before I came along and now since as Mozart was himself I am hated by some here, I will be deprived of my due victory because of that travesty of a contest. |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 19th, 2008, 8:31pm To sum up what I said in a few words. This case is pretty simple. I did come up with the solution to CR and that solution slightly adapted also works for RRR. I didn't play the latter NOT because I couldn't or was unwilling to but because I DIDN'T KNOW that I HAD TO. That’s the only reason. There is no way in hell that 99 could have had this RRR game if not for me being kept in the dark, be it accidentally or on purpose is not really the point. The point is that the reason why 99 played this game and NOT ME has nothing to do whatsoever with merits and everything to do with someone being deprived of his due victory. The CR belongs to me as well as the RRR which is only a variation of it. Thanks to me 99 knew how the rabbits of Gnobot would react because they reacted in both cases mine and his in a similar fashion. I am sick of having to explain again and again something that is so obvious. It doesn't matter actually if 99 did what he did on purpose or because he is just lacking of a conscience that tells him that some things cross a line. The result is that I have been deprived of my due victory in both cases. Because I didn't have the information that it was even useful for me to play this game. NOBODY here has ever been subjected to an injustice like that. Have a shred of honesty and ADMIT IT!!! The fact that you don't like me shouldn't be factored in unless you consider that Arimaa is a popularity contest where merits take a back seat. However, if you do then you are a far worse people than I'll ever be!!!! |
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Title: Re: Handicap Order - what beats what? Post by IdahoEv on Apr 20th, 2008, 1:04pm on 04/18/08 at 17:11:04, aaaa wrote:
You'll need to keep the number of nodes in that network very low, otherwise you'll overtrain badly. There just isn't enough data. The number of possible material state combinations is extremely high, and the majority of them have never occurred in any game. I discovered this when I did research in 2006 into optimizing the coefficients of material evaluators based on the game statistics. Even when there were only a few coefficients, like DAPE which has 7 coefficients, we saw some bad overtraining and/or sensitivity to data selection, and had to start implementing interesting constraints on the selection of games we used in order to get results that made any sense. At some point soon, I hope to re-run those numbers, by the way. There have been two more years of games now, it would be nice to see if the results have changed significantly. |
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Title: Re: Handicap Order - what beats what? Post by IdahoEv on Apr 20th, 2008, 1:17pm Just a quick mention that I would personally much disregard all the results in this thread that used results from the original formulations of DAPE and FAME. When I dug into this in 2006 I found that those algorithms misrepresented the results from real games relative to algorithms with correctly tuned coefficients. Using the ones on Janzert's calendar, the improvement (in terms of correctly predicting the outcome of games in the database) of optimized DAPE, or LinearAB (my function) over DAPE or FAME was significantly greater than the improvement DAPE or FAME gives over simply counting all the pieces (i.e. considering all pieces worth 1.0 point regardless of size). |
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Title: Re: Handicap Order - what beats what? Post by mistre on Apr 20th, 2008, 4:26pm If you rank the 114 major handicaps for the LinearAB function, I can redo the analysis using only LinearAB and DAPE (optimized). |
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Title: Re: Handicap Order - what beats what? Post by Janzert on Apr 20th, 2008, 4:42pm on 04/20/08 at 13:17:13, IdahoEv wrote:
I've never been convinced that this wasn't simply because of overfitting. I think the number of games and range of games we have available is still just too small to try and train a general method from. Janzert |
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Title: Re: Handicap Order - what beats what? Post by IdahoEv on Apr 20th, 2008, 7:07pm on 04/20/08 at 16:42:54, Janzert wrote:
Anything's possible. But LinearAB only has two parameters, A (the cat-to-rabbit ratio) and B (the ratio used for all subsequent levels; i.e. D/C, H/D, M/H and E/M). And it's pretty hard to overfit data with only two coefficients. Maybe when I get around to rerunning this I can use some part of the data for overfit testing during the optimization. I doubt we'll see much difference. When we looked at the particular cases that the optimized functions preferred over the guessed-at ones, they seemed pretty reasonable to me. Rather than overfitting, I think you could make a better case that the games themselves don't actually represent the true value of the pieces very well; Karl made a good argument from causality in this vein. (i.e. if getting ahead and being likely to win, or simply being a stronger player, makes certain captures more likely irrespective of winning, it would make those captures appear arbitrarily valuable in the analysis.) But that's a fundamental limitation of using statistics from the games to answer questions like these. There isn't really anything you can do about it. |
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Title: Re: Handicap Order - what beats what? Post by IdahoEv on Apr 20th, 2008, 7:21pm on 04/20/08 at 16:26:40, mistre wrote:
If you want to do it, here's how LinearAB will rank the pieces. For the case of beginning-game sacrifice, you can simply add the following values of the pieces to achieve the LinearAB score. (A=1.241, B=1.316). rabbit 1.000 cat 1.241 dog 1.633 horse 2.149 camel 2.828 elephant 3.722 (Note that this won't give you the correct LinearAB score once the opponent starts losing pieces because it will ignore 'level collapse', i.e. the fact that EHHRerrr is functionally identical to ECCRerrr. But for game-start sacrifice, there is no level collapse because the opposing team is full.) I'm sure this system misvalues elephants because the E/M ratio is fixed to B. When I made an alternate optimization that allowed E to vary independently it settled on E~7.5. I doubt that's anything like accurate, though, because there are so few actual examples of E sacrifice to compare against. |
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Title: Re: Handicap Order - what beats what? Post by 99of9 on Apr 20th, 2008, 8:10pm on 04/20/08 at 19:07:57, IdahoEv wrote:
I agree, and because of this limitation, I think you should be slower to "disregard" the evals which were hand optimized by experts! I'm looking forward to getting back to this conversation when you've run with more data. |
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Title: Re: Handicap Order - what beats what? Post by mistre on Apr 20th, 2008, 8:59pm Since there is disagreement on this one, I will take a back seat for now and let you guys sort out which evals are more reliable than others. Is there any way to compare their predictions with real games and see which one was better? |
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Title: Re: Handicap Order - what beats what? Post by IdahoEv on Apr 20th, 2008, 9:08pm on 04/20/08 at 20:10:03, 99of9 wrote:
Fair enough, that. |
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Title: Re: Handicap Order - what beats what? Post by IdahoEv on Apr 20th, 2008, 9:17pm on 04/20/08 at 20:59:16, mistre wrote:
Yes, it's possible, and that is in fact how the coefficients for LinearAB and Optimized DAPE were developed. Existing evals were repeatedly modified (by tweaking the numbers) and measured as to how well they predicted the eventual winner in real games from the database. That cycle was repeated until the eval functions stopped getting "better". At the end of that process on several eval functions, Optimized DAPE (as implemented on Janzert's page) was the best overall at guessing the winner among games in the history database. LinearAB was a bit behind that in 2nd place. Both did much better than the hand-coded versions. The debate is whether or not that process is valid in order to determine a material eval function. Karl and Toby are less sure about that than I am. I recognize their concerns that might make the process invalid, but I suspect it still is. There's no way to prove it one way or the other. :) |
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Title: Re: Handicap Order - what beats what? Post by mistre on Apr 20th, 2008, 9:36pm Were the game that were looked at human vs human games? bot vs bot games? human vs bot games? or all 3? I can't wait to see what your results will bring when you re-run the analysis. There are quite a few more E handicap games in the database, thanks to me. ;D |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 20th, 2008, 10:14pm on 04/20/08 at 21:36:15, mistre wrote:
If your elephant handicap games are included, it could significantly mess up the value of the elephant. You probably won a lot more than one would expect from starting down an elephant, therefore a function that is optimized to fit that data will do better if it values the elephant less than it should. As for the superiority of LinearAB in predicting winners in games databases, let's just say that when Zombie wins the Computer Championship and I am defending the Arimaa Challenge, I will have my fingers crossed that Zombie still likes trading its camel for a horse and a rabbit, and I get to make that trade at the start of every game. :-) For all their flaws, FAME and DAPE correctly prefer having the camel, while LinearAB and DAPE(eo) get it wrong. But I'm willing to believe that as more pieces get traded, FAME gets progressively less accurate, while LinearAB gets better. I mostly tuned FAME for opening trades, not midgames and endgames. |
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Title: Re: Handicap Order - what beats what? Post by IdahoEv on Apr 20th, 2008, 10:16pm on 04/20/08 at 21:36:15, mistre wrote:
Most of the analysis was done with games where both players were rated over 1600, and including HvH games and BvB games, but not HvB games because there was so much botbashing strangeness in that category and I was trying to represent the true value of the pieces to players honestly trying to win a straight-up game. :-) Some of the analysis was done both ways; with and without including HvB games. You can find the original discussion in these three threads: thread one (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1146199776), thread two (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1163044066), and thread three (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1163717031). |
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Title: Re: Handicap Order - what beats what? Post by Janzert on Apr 20th, 2008, 10:41pm The third link above should to this thread (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1163717031), I believe. If you do end up running the evaluators through new games again there are two things I would find interesting. First, some sort of cross validation where a subset of the games are used for training then the rest used for testing. An obvious application initially would be to test all the old constants on the games played since then. Second, in addition to looking at a win percentage prediction also check a straight side to win prediction. Janzert p.s. Another thing I just thought is instead of scoring evaluators per game, score them per material pattern. |
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Title: Re: Handicap Order - what beats what? Post by IdahoEv on Apr 21st, 2008, 2:45am Fixed the third link above, thanks. Cross-validation I will definitely do. on 04/20/08 at 22:41:59, Janzert wrote:
I'm not quite certain what you mean by that. All the material functions simply output a number that represents who is ahead and by how many rabbits. One could simply check whether score > 0 and assume that means "gold win", then add a point of error if silver won, and vice versa. Or you can use another function to convert the score into a probability estimate as to who is more likely to win, and score the difference, so if the eval predicts an 80% chance of a gold win, it accrues 0.2 error for every gold win from that state and 0.8 error for every silver win. In the limit of large numbers of sample cases, these amount to the same thing: the training of the coefficients will find the same solution. When the number of test cases is finite, the probability estimate will find the solution a bit faster and more reliably. Quote:
You mean so that the error function is Sum over states(error for state n), instead of sum over states(error for state n)*(number of times n has appeared)? I suppose it could. This would cause the functions to attempt to match mid-game and end-game states more strongly than early-game states (relative to the way I did it before), because later states are much less likely to be duplicated in the database. It also leaves open the question of how to score the individual states, though, when we do have multiple examples. If state N is won by gold 53% of the time and silver 47%, how much error do we accrue the training function for predicting a gold win? 0.47? 0.0? I don't intuitively see this as an improvement, though you're more than welcome to try to convince me. :-) |
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Title: Re: Handicap Order - what beats what? Post by Janzert on Apr 21st, 2008, 11:12am on 04/21/08 at 02:45:36, IdahoEv wrote:
Yes, this is what I mean. But I'm just interested in seeing the result, I didn't mean to use it for training. I'm simply wondering if some of the evaluators predict the correct side to win more frequently but when they get it wrong they get it wrong by a larger margin. Quote:
Right, although states that have occured less than some cutoff should be excluded. Perhaps better would be sum over states(error for state n) * log(number of times n has appeared) or some other sub-linear weighting. My reasoning for this is to try and see what the error is over the whole space of possible material states, rather than weighted towards how frequently those states appear in the game database. Basically I was motivated by this comment you made in that third thread. Quote:
In regards to, Quote:
I meant to use your previous formula to turn an evaluator score into a prediction percentage then directly compare the error of the actual percentage of wins in the database (e.g. since fame has a K of 2.92 the prediction for 1 rabbit loss is 0.58% which is a 0.03% error). Janzert |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 21st, 2008, 2:14pm on 04/21/08 at 02:45:36, IdahoEv wrote:
That's right, the there is the same minimum in both cases. For example, say that there have only been three material states ever, always a cat for a rabbit, and the side with the extra cat won two out of three. If my penalty function for predicting percentage P on the side with the cat is (1-P) when I am right and P when I am wrong, then my total penalty function is 2*(1-P) + 1*P = 2-P. I minimize my penalty by setting P=1, i.e. I should predict 100% for the side with the cat. Something is wrong when you are optimizing a variable P in such a way that the "optimum" value doesn't match observation. The root cause of this problem is that you are optimizing using the wrong penalty function. You should penalize square error. Then the total penalty function is 2*(1-P)^2 +1*P^2 = 3*P^2 - 4*P - 2. What is the value of P that minimizes this penalty? Astonishingly, it is P=2/3, i.e. the exact fraction of the time that the cat won. The least square error metric is a wonderful thing... Now that you have posted that detail, I see you were effectively only rewarding the function that was right the most often, and ignoring how much it was right by, even when you brought percentages into the mix. So the optimization was all provided by the few cases in the middle that are in doubt, and you were only tweaking coefficients to be right in the maximum number of close cases. I can't help but point out that we should not expect the optimized functions to do well in extreme cases (such as massive handicaps), if the function was optimized on the basis of only close cases. Moreover, since only the close cases matter, you are effectively throwing away most of your optimization data, and optimizing over a much smaller set, which one can expect to make the results less reliable. Suddenly I am extremely curious to have you re-run your optimization with percentages and the least square error function, so that the scaling actually does matter, i.e. it does matter how much one side is ahead. The results might be essentially the same, or they might be substantially different. |
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Title: Re: Handicap Order - what beats what? Post by IdahoEv on Apr 22nd, 2008, 1:47am Okay Karl, I was with you right until you said this: on 04/21/08 at 14:14:46, Fritzlein wrote:
Because what you are asking me to do here: Quote:
Is exactly what I did in 2006/2007, and I'm not following what led you to believe otherwise. The functions were all optimized by minimizing the least-squared-error, computed as the difference between the %age confidence of gold win vs. the actual game result for every state in the database. They definitely weren't optimized against only the close cases, they were optimized against all cases. (subject to the inclusion criteria described in those threads, i.e. ratings >= 1600, no HvB, no mid-exchange states, etc.). It seems to me that Janzert was asking me to ignore the % confidence and just use a binary error function, and I was explaining why I doubt that would be an improvement. |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 22nd, 2008, 7:33am on 04/22/08 at 01:47:07, IdahoEv wrote:
Oh, whoops. I thought that was what you had done, but then when you started talking about errors of 0.2 and 0.8 for an 80% prediction, then I thought I had mis-remembered. But I guess I was mistaken in my mistake. My apologies. I should have at least checked the original thread and given you the credit that I had been giving you! Given that all the material states did in fact contribute to your optimized coefficients, I'll have to think harder to explain why I don't like the results. I mean, harder than the obvious explanation that my own intuitive material evaluation is wrong. :P But, given how many things I've been wrong about in the past, why think too hard? I used to think that 99of9 was overly bold to open with two rabbits in front, but now I have four in front every game. I once said I knew I was winning because I had gotten a camel hostage by sacrificing only two cats, which I'm now confident means I was losing. My mocking LinearAB for preferring HR to M in the opening may only be fodder for history to laugh at me some more. :) |
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Title: Re: Handicap Order - what beats what? Post by Janzert on Apr 22nd, 2008, 1:05pm As the ranting seems to have died down over this, here are my thoughts on trying to rank handicaps by difficulty. These are more or less in the order they occured to me. ;) First, current evaluators were mostly developed to look at near even piece trades. So it's unsurprising to me that they give unreasonable results when used to compare large handicaps. Also all but the empirically optimized ones by IdahoEv are simply based on current intuition rather than any objective measure. Because of the way the empirically optimized ones are trained I wouldn't expect them to do any better on extreme handicaps either. So what do we actually mean when trying to rank the piece handicaps? One thought I had was to try and relate it to the probability of a game theoretic proven loss. But I can easily give a fairly simple algorithm (involving no search, a p0 bot if you will) that would beat perfect play when playing against any handicap that leaves only cats and rabbits. So on some level you could say that all handicaps leaving only cats and rabbits are equivalent (trivially provably lost). Obviously any difficulty measure needs to be able to distinguish between any, or almost any, handicap. Another aspect is that almost certainly different opponents are going to have different rankings in difficulty for various sacrifices. Almost certainly even to the point of handicap 1 being impossible and 2 being possible against opponent A but the reverse against opponent B. But of course we want to establish a general ranking that in some way represents an overall ordering of difficulty, i.e. free of 'opponent bias'. My current idea for an objective, bias free, although theoretical, measure of difficulty would be to look at certain features of the game tree derived from a given handicap. The first thought I had was to use the percentage of leaves that are wins, lower percentages being more difficult of course. This has the potential problem though of a given tree having many early critical moves followed by a period where most moves lead to wins. This could lead to it having a percentage just as high or higher than another tree that has several viable choices at every stage throughout the game and therefor easier to play. A better metric that avoids this problem would be one that looks at the interior nodes instead of just the leaves. Perhaps looking at the percentage of critical moves as the game progresses or maybe something involving the average length of critical move sequences. Another potential problem with any similar approach is that by definition 'good play' does not travel uniformly through the game tree. But I'm afraid any attempt to try and correct for that will probably lead to opponent bias in the results. Of course it is beyond any current, or apparent near future, resources to construct and/or look at the whole game tree for even a single handicap. I wonder though if some sort of random sampling could produce useful results. Anyone have further thoughts on this or other ideas? Janzert |
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Title: Re: Handicap Order - what beats what? Post by IdahoEv on Apr 22nd, 2008, 2:14pm on 04/22/08 at 07:33:49, Fritzlein wrote:
Cognitive dissonance and confirmation bias are, after all, the reason we have the scientific method. :P You can see evidence of my own biases in the newly-reconstituted Material Eval II thread, defending my evaluator against a big fault demonstrated by 99: I'm convinced I'm my own system is correct despite evidence to the contrary. :-) What I can tell you is that as of the last time I ran the data, the coefficients of LinearAB and optimized DAPE -- coefficients which lean more towards piece number and less towards piece size, relative to human expert intuition -- were definitely supported by the actual game history, both in the aggregate of all states, and in the specifics we examined like M vs. HR. I was as surprised by these coefficients as you are. One can argue that the game history doesn't actually represent the value of the pieces, and you might even be correct! But it's definitely an uphill argument. Your argument about causality is IMHO the strongest argument here. We don't know if HR captures are causing wins more often, or if winning play is causing HR captures more often. Put statistically, there's no way to tell whether the database results are measuring p(win|HR) or p(HR|win), and poor Thomas Bayes will spin pirouettes in the ground if we assume those are the same thing. But consider this: being a winning player would tend to impose your understanding of the game on the database, because you would play in the way you believe is right, and the win (since you're a strong player) would demonstrate the "rightness" of your approach, even if it's not actually optimal. So the database evidence should be skewed towards the human belief that bigger pieces are much more valuable, simply because the top players have been playing that way and winning. So maybe even LinearAB is overvaluing the big pieces! In any case, the database history is the only set of objective data we've got. Despite possible (but unproven) flaws in it, my instinct as a scientist is to trust data over human intuition. And if I'm the only bot developer taking that approach, believe me that's perfectly fine with me! If there's any modest possibility it's the correct approach, i'd certainly prefer to be the only one doing it :P Edited: Move 'grammar'. For great clarity. |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 22nd, 2008, 3:43pm on 04/22/08 at 13:05:06, Janzert wrote:
Hey, that's a pretty strong argument in favor of my proposal to list both handicaps any time the two are incommensurate! Quote:
Do we really want this even if it is wrong? If there is one bot that can be beaten more easily with RRR and another that can be beaten more easily with CR, do we want to lock ourselves into recognizing only one as the greater achievement in both cases? It seems that trying to get this definitive relative ranking is like trying to get a definitive answer as to whether a camel is worth 4 rabbits or 5. Why break your back tuning it to 4.38051 rabbits when you know it is only an average, and sometimes the camel will be worth more than that and sometimes less? Instead we try to build dynamic evaluations that recognize that how much a camel is worth depends on the situation. Instead of trying to say in advance what is best for a certain bot, we can instead keep all incommensurate handicap records, and see what all different handicaps can be achieved... |
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Title: Re: Handicap Order - what beats what? Post by aaaa on Apr 22nd, 2008, 6:25pm If we want to try to make any headway with the theory of material evaluation, we should work out the various relevant considerations that could be captured in intermediate variables. It may even be the case that four of those, namely those that stand for "army strength" and "goal threat" for both sides, may not even be enough. |
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Title: Re: Handicap Order - what beats what? Post by Janzert on Apr 22nd, 2008, 6:28pm Regarding handicaps having different difficulties against different opponents: on 04/22/08 at 15:43:26, Fritzlein wrote:
I'm not sure how the word "incommensurate"1 applies here, but I'll take a stab at interpreting your meaning to be "roughly equal" (i.e. commensurate). I think either every handicap that is accomplished has to be listed2 or you have to define a full ordering. We could judge some handicaps to be equal but the more of those there are the less useful the ordering is. But even disregarding that, I think the opponent bias is going to be larger than just roughly equal handicaps being possible against one opponent and not another. I wouldn't be surprised to see a bot against which an E handicap is possible but not a M handicap while others would more likely to have the reverse. Regarding a general list of handicaps: Quote:
Actually I think we want to answer yes to both questions or at least yes with qualifications. ;) Without a general list we have to define an ordering for each bot. I believe it is impossible to make a bot specific ordering that includes handicaps that have not yet been accomplished. Even just stating whether a handicap is possible or not would seem to be impossible, never mind creating a more fine grained ordering. This leads to the problem of defining the finish line after the race is over. Also even after various handicaps have been accomplished, I'm not sure how to simply define an objective measure of difficulty against the specific bot. Have a general list allows predefined goals and reduces the burden on the community to only make one ordering instead of one for each bot. Even if as more arimaa knowledge is gained it is decided that some specific handicap ordering needs to be changed, I think this is a better solution than trying to make separate orderings for all bots. Janzert 1 (adj) incommensurate (not corresponding in size or degree or extent) "a reward incommensurate with his effort". 2 I seem to recall a proposal a long time ago to simply list the first instance of every handicap that was done and some very vocal resistance to the idea. |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 22nd, 2008, 7:31pm on 04/22/08 at 18:28:18, Janzert wrote:
Read reply #24 in this thread to understand what I meant by incommensurate, and my proposal to deal with it. But I used the wrong word. I meant "incommensurable", meaning they can't be compared. We can know for sure that CRR > CR > RR, but we can't compare CR to RRR or DRR to CCR. My idea is not to have a separate, fully-ordered ranking for each bot, but to treat as records all handicaps for a bot that aren't clearly beaten by some better handicap. |
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Title: Re: Handicap Order - what beats what? Post by 99of9 on Apr 22nd, 2008, 7:59pm If we're willing to have more than one record per bot (I estimate 3-6 for most bots), then partial ordering is a great way to go because it removes the need to rely on any materials eval at all. Even if we go down that track, I think it is worth having the conversation about which handicaps are harder in general, but it would certainly take the angst out of that conversation. Regarding mistre's suggestion of one list per person. I agree with Arimaabuff that this is not the best way to go on the main "records" page, because the competition does help spur us on. However, I agree with mistre that this would be helpful for newer or less competitive botbashers, so I recommend setting this up as a subpage (where you can fit many more people). |
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Title: Re: Handicap Order - what beats what? Post by Janzert on Apr 22nd, 2008, 8:28pm on 04/22/08 at 19:31:13, Fritzlein wrote:
Ahh, ok. First a minor nitpick, saying we can't compare two things is saying we can't tell whether green, water or 23 grams is better. I think all handicaps are comparable, whether we can figure out if a particular handicap is better, worse than or equal to another handicap is another matter. Having records for all handicaps that are equal, within the margin of error or plain undecidable on which is better is fine with me. In actual fact I care very little how the records are listed. You say we know CRR > CR > RR and that we can't for CR-RRR and DRR-CCR. While I completely agree with you on the former and have no opinion at all on the latter, how do you decide this is the case? The method for deciding this is what interests me. Janzert |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 22nd, 2008, 8:30pm on 04/22/08 at 14:14:38, IdahoEv wrote:
I think that playing more aggressively recently has given me an insight I didn't have before into unbalanced trades. I have always been a control player rather than a race player. That is to say, I don't want to capture more of your pieces than you capture of mine; I want to capture something of yours in return for nothing. Race players, on the other hand, are willing to give in order to get. They will slug it out as long as they are getting the best of it. In the past I have been unwilling to race even when I would get the best of the race, because I didn't want to lose control. This unwillingness to race often came back to haunt me, because it isn't always possible to keep everything under control, even with a positional or material advantage. Sometimes you have to race or lose your control, but if you are willing to race, you can trade control for a race that favors you. Being able to identify and accept those favorable races actually makes control more valuable to me. In comparing M to HR as an opening trade, it is clear that the M is better for control, i.e. more likely to produce a free capture for nothing. The HR on the other hand, is better for racing and slugging it out, because every equal trade of pieces favors the HR side, most particularly a trade of H for H. The question of who the material balance favors overall can be translated into whether the M side can force the game into a control game, or the HR can force the game into a slugfest. Naturally the answer is not absolute. One can always force the game into a race if one is willing to pay a price. So maybe a better way of putting it is in terms of tradeoffs: what will the HR player have to pay to force the game into a race, and/or what will the M player have to pay to keep the game a control game. This language gives me a new way of expressing why I think M is superior to HR. Racing is, in essence, having the elephants apart. Each player tries to do damage with his own elephant rather than defend any damage the opposing elephant does. But when I have M and my opponent doesn't, I can fearlessly use my elephant to track his elephant, and defend anything his elephant tries to get started. I can become Mr. Tag-along. It doesn't bother me if both our elephants get bound up in a defensive deadlock, because I will have the strongest free piece (M) if that happens. Meanwhile my opponent's elephant can't afford to track my elephant and stop whatever I am up to. He will always have to leave, complicate, and threaten to trade. I submit that races and slugfests are easier to understand than the control game, and that the weaker the players are, the better HR fares compared to M. Even a player as strategically strong as Omar has made the mistake of racing when he is ahead by M for H, even though he wouldn't have had to race. (I specifically remember scolding him for this. :P) In a race strength is not so important, and the advantage of extra strength evaporates. I submit that the strongest players prefer M to HR, because that's what is more useful in games against each other. The more one understands the control game, the more one understands when and how not to race. You may say that I have an uphill argument because I am arguing against the data, but you also have rather an uphill argument against the intuitions of strong players. If I pitted two random steppers against each other, I wouldn't be surprised if the game results favored R over E when the two players start with those respective handicaps. (Actually, that experiment wouldn't be too hard to run. 99of9 could tell us in an afternoon whether E or R is worth more to a random stepper.) But if R happens to be favored over E in that set of games, who cares? The strength of the players invalidates the data. I argued in a different thread that an M handicap is only a moderate advantage between beginners, but is decisive among experts. The value of the extra piece increases with playing strength. I fully expect that the same is true of the value of M versus HR: the stronger the players are, the more the full force of the M will be felt. Of course, it wouldn't have to be this way; in theory it could be that the stronger the players are, the more effectively they are able to use an advantage in numbers. But I think in reality the control game is generally more subtle and difficult than the race game, and understood later in one's Arimaa career. This is just my $0.02 that the "reverse causality" argument is not the only argument that undermines the game database. The "data" that will really convince me is when chessandgo uses his HR to beat my M. :) |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 22nd, 2008, 8:39pm on 04/22/08 at 20:28:47, Janzert wrote:
What I propose is that handicap A is bigger than handicap B if and only if the pieces in A can be set against the pieces in B so that every piece in B is "covered" by at least an equal piece in A, plus 1) A has at least one piece left over or 2) A has the stronger piece in at least one pair. DRR can't cover both cats in CCR, and CCR can't cover a D at all, so the two are incommensurable, and both would have to be listed in the Hall of Fame. However, DCR can cover each of them while meeting criterion (2), so it would bump both of the previous handicaps out. |
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Title: Re: Handicap Order - what beats what? Post by Janzert on Apr 22nd, 2008, 8:59pm So ER=MRR or any handicap leaving 3+ pieces but without an E? Janzert |
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Title: Re: Handicap Order - what beats what? Post by Fritzlein on Apr 22nd, 2008, 10:09pm on 04/22/08 at 20:59:48, Janzert wrote:
Yep. But don't use the equal sign. MCR beats one of those and not the other. EC beats the other but not the one. So they aren't equal, just unordered compared to each other. It takes ERR to beat them both. |
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Title: Re: Handicap Order - what beats what? Post by Janzert on Apr 22nd, 2008, 11:32pm I find it hard to believe botbasher's will be satisfied unable to distinguish between ER on the board and MHHDDCCRRRRRRRR on the board for a handicap. If the botbasher's are willing to agree to it though, I suppose I won't fight against it. Since what it does rank I think it probably ranks correctly I just think it leaves too much unranked. [Edit: or maybe I'm being confused about which pieces are left on the board and which are taken off] [Edit2: actually I think maybe it doesn't matter which way around you look at it, it works out the same] Janzert |
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Title: Re: Handicap Order - what beats what? Post by 99of9 on Apr 23rd, 2008, 12:44am on 04/22/08 at 23:32:32, Janzert wrote:
You're right that one of those is clearly harder than the other. But that just means the easier one will be attacked first. Sooner or later, those two records will be broken up into (on the board):
The big question for me is how many unranked records will there be per bot in the long term, and is this unacceptably high? |
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Title: Re: Handicap Order - what beats what? Post by 99of9 on Apr 23rd, 2008, 2:42am on 04/22/08 at 13:05:06, Janzert wrote:
I'm sure that this is possible in principle, but I have not seen it yet. Quote:
No, Fritz is right that random will give us misguided results. It will favor rabbits over anything. Quote:
I only see three viable choices:
The last one needs clarification. Say we are comparing handicap X with handicap Y. If handicap X (or self-evidently better) has been achieved against more bots than handicap Y (or self-evidently better) has been, then handicap Y is the better handicap (for the moment). In the case of a tie, both records remain. This list would be slightly dynamic, and would require a fair bit of overhead in terms of keeping it up to date. But it would (almost by definition) be a good way of ordering the handicaps fairly. |
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Title: Re: Handicap Order - what beats what? Post by mistre on Apr 23rd, 2008, 8:43am After listening to the discussion for a while, I thought I would pop back in with my 2 cents. Since no one has come up with anything better yet, I think we should continue to use the list we have of the 3 combined material evaluators. Leaving many combinations unranked would just lead to a complete mess. I really don't foresee too much of an issue, like I said, 99% of the cases for handicap game purposes shouldn't be a problem. Someone trying for a handicap should almost always pick something obvious (for example the handicap is EMHD, so I will try EMHH instead of something like EMHCRR. As for general ordering for the sake of knowing which handicaps are better, we should continue to try to develop a method that is better than what we have now. What if we have a test bot play against itself with different handicaps? Omar would have to set up a way to have piece exclusion in the set-up, but after that, it should be possible right? |
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Title: Re: Handicap Order - what beats what? Post by 99of9 on Apr 23rd, 2008, 8:56am on 04/23/08 at 08:43:20, mistre wrote:
This won't help much with extreme handicaps, because none of the bots know how to attempt an extreme handicap, and some of the bots don't even know how to stop one! For the smaller handicaps, each bot might give you a different result. E.g. bomb may do better against itself when handicapped with HC, but clueless may do better when handicapped with DD. What would that tell us? |
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Title: Re: Handicap Order - what beats what? Post by RonWeasley on Apr 23rd, 2008, 11:27am I don't know if this has been said, but we might order these simply by the bot-bashing record result. Is the metric still number of moves? The order may not be the same for each bot, but the trend among bots should provide an indication. Anyone who thinks a handicap is rated too hard can prove otherwise by bashing it better, or challenging the bashing specialists. Such a ranking would not necessarily tell us what a certain handicap means 1) against a good muggle player or 2) in a position where there's been equal attrition. |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 23rd, 2008, 1:27pm BTW, Aamira2006P1 has just entered the CRN family, that is the bots that can be beat by a C and one or several Rs. That family now contains Gnobot2005P1 that is a CR1, ShallowBlue a CR2, ArimaaScoreP1 a CR3, Arimaalon a CR4 and our latest addition Aamira2006P1 a CR5. ;) |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 26th, 2008, 6:37am A little off topic: I beat bot_ArimaaScoreP2 with both colors with only a dog and eight rabbits. I suppose that cat and 8 rabbits is within the realm of possibilities but it seems so unlikely (instead of four pieces that can kill you, you have six and the enemy's cats become brick walls to you) that I don't expect my record to be beat within this century (7 rabbits is out of the question with only a single dog to defend the fort!). But of course you are welcome to try. |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 26th, 2008, 9:06am on 04/26/08 at 06:37:36, Arimabuff wrote:
Well, either I am a hundred years older or I was completely wrong on that one. I just cracked bot_ArimaaScoreP2 with a cat and eight rabbits with silver. It seemed even easier than with a dog. Now for gold, I am adamant cat and eight rabbits is completely utopist! ;) |
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Title: Re: Handicap Order - what beats what? Post by aaaa on Apr 27th, 2008, 5:57pm Here is a proposal: If there are handicap games such that one does not unambiguously dominate the other (i.e. it is not the case that one can get from one handicap to the other by any combination of adding pieces and promoting a piece which is stronger than a rabbit), then the record which stands is the one whose handicap against that particular bot has the slowest fastest result. In case of a tie, the earliest one stands. So if you have multiple players achieving for the first time certain incomparable handicaps against a particular bot, then in order to get or keep the record it would be in their interest to try to improve on the speed of the handicaps picked by the other contenders. That way you have an objective measurement of handicap achievement and as a bonus a nice way of keeping the contest going. |
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Title: Re: Handicap Order - what beats what? Post by 99of9 on Apr 28th, 2008, 2:08am I agree it's objective, but it's not really comparing apples with apples. The material handicap section is about material handicaps, not about time or moves. I think that we should be looking at all possible material methods before we resort to anything else. Since a few material valuation methods are on the table, and seem reasonable, I think we should go for one of them. |
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Title: Re: Handicap Order - what beats what? Post by Arimabuff on Apr 28th, 2008, 10:17am on 04/26/08 at 09:06:30, Arimabuff wrote:
Got bot_ArimaaScoreP2 with both colors with a cat and eight rabbits. I never thought it was possible but here it is. Hear, hear!!! ;D |
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