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Topic: Measure stereotyped openings (Read 16115 times) |
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Fritzlein
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Re: Measure stereotyped openings
« Reply #60 on: Mar 25th, 2014, 4:51pm » |
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Super, thanks for doing this again! It is telling that the entropy in the Gold setup has decreased for the first time. If anyone asks whether Arimaa has opening theory yet we can now say, "Yes it does: use the 99of9 setup as Gold." After that, however, we're still pretty much at sea, as demonstrated by how quickly we approach maximum entropy.
One of the more dramatic jumps in the numbers from last time to this time was the most common position after 3g (17 -> 81) and after 3s (6 -> 26). The absolute numbers are small, but the more than 300% increase is huge given that the total number of games increased only 30%. This most-popular line is nowhere near a standard opening, but it is perhaps the first inkling of one.
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woh
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Re: Measure stereotyped openings
« Reply #61 on: Mar 25th, 2014, 4:57pm » |
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The share of setups with both horses on the same half of the board stopped increasing. It is now 9.2% or 1053 games.
16. (20) 85 (+36)
RHCHECMR
RRRDDRRR
27. (35) 40 (+17)
RHDHEDMR
RRRCCRRR
29. (32) 36 (+10)
RMRDERHH
RCRCDRRR
37. (30) 27 (+0)
RMRDECHH
RCRRDRRR
39. (34) 27 (+3)
DHCHECMD
RRRRRRRR
40. (45) 23 (+7)
DMCDECHH
RRRRRRRR
45. (38 ) 20 (+1)
RMCDDEHH
RRRRRCRR
48. (37) 19 (+0)
DMRCEDHH
RRRCRRRR
54. (46) 17 (+1)
RHDHECMR
RRRCDRRR
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Fritzlein
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Re: Measure stereotyped openings
« Reply #62 on: Mar 25th, 2014, 5:40pm » |
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on Mar 25th, 2014, 4:57pm, woh wrote:| The share of setups with both horses on the same half of the board stopped increasing. It is now 9.2% or 1053 games. |
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But sure the share of openings with a decentralized camel has increased? It seems the new trend in imbalance isn't HH on one side and M on the other, but rather MH on one side and H on the other, with a rather more aggressive intent.
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Fritzlein
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Re: Measure stereotyped openings
« Reply #63 on: Apr 9th, 2014, 12:13pm » |
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By the way, I find that a number of people who want to fix chess think that Chess960, by shuffling the setup of the pieces behind the pawns, does away with opening theory for chess without creating any problems. This isn't quite true, but as a fan of Arimaa it isn't my task to convince Chess960 fans that their variant fails to fix chess. Rather, I can piggyback on their preference to extol the virtues of Arimaa, because Arimaa has even more opening variety. Converting the opening entropy into a number, 2^10.8053 = 1789, so we can say Arimaa is like "chess one thousand seven hundred and eighty nine". (Say it that way unless you want it to sound like the year of the French Revolution.) Our number is bigger than your number, in fact we are almost double Chess960. 
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chessandgo
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Re: Measure stereotyped openings
« Reply #64 on: Apr 10th, 2014, 7:28am » |
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Just like Chess960 is an improvement over chess, I believe some EEE-style-ish variant would be an improvement over arimaa (randomly choosing material to be used at setup, or even randomly choosing a random starting setup position with that random material).
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Fritzlein
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Re: Measure stereotyped openings
« Reply #65 on: Apr 10th, 2014, 10:58am » |
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on Apr 10th, 2014, 7:28am, chessandgo wrote:| Just like Chess960 is an improvement over chess [...] |
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Ah, I am surprised. Apart from the inelegance of taking control away from players who otherwise determine everything between them, isn't it fairly well accepted that some of the 960 setups give white a big opening advantage, even bigger than the traditional chess setup? Or is the first-player advantage not a big flaw of chess in your estimation, such that potentially increasing it is no big deal? By the way, there was at least one EEE setup that was overwhelmingly in favor of one player.
Quote:| [...] I believe some EEE-style-ish variant would be an improvement over arimaa (randomly choosing material to be used at setup, or even randomly choosing a random starting setup position with that random material). |
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For my part, I would not add external randomness to an otherwise pure strategy game unless there were too little variety and novelty produced by the players themselves trying to win. I don't think the repetition in Arimaa is anywhere close to being a big enough problem to warrant adding randomizers. As just a taste of the downside, imagine the loser of a championship match being able to say, with justice, "My opponent got lucky because the randomized setup kept favoring his playing strengths over mine."
To me it is important to have the variations in who wins come from inside the players themselves. Also I value the fact that removing external noise makes it easier (albeit not trivial) to know which of two players is better. But I guess I'm not going to get far with my bias against randomization when talking to a professional poker player. The fact that it is extraordinarily difficulty to tell which of two poker players is better is an essential feature of the game. If the suckers weren't able to think, "I only lost because I got unlucky," then they would quit playing and poker would die off.
Even supposing we do start randomizing setups, I strongly feel we should continue to use the full set of pieces. Admittedly, the Endless Endgame Event is great for training in an area where we don't have enough opportunities to train, and also it leads to positions which are immediately sharp and therefore exciting. If, however, EEE were the entirety of Arimaa it would probably considerably reduce the strategic depth. Using the full set of pieces brings a broader array of strategic ideas into play. The full piece set allows for many types of elephant blockades (full or partial) and frames that can't happen in an endgame. Also it makes it so that the question of whether to pull rabbits or advance them yourself is the most subtle point of strategy, and the most enduring advantage humans have over computers. A reduced piece set like the EEE uses would mostly eliminate what is currently the strategy of the opening, and leave us only with the strategy of the endgame, a smaller set and more in favor of the computers.
I can see the benefit of a reduced piece set as a teaching tool, and I have proposed removing HDC from each side as a possible to solution to the hypothetical problem of drawn games, but in the absence of draws, I would strongly advocate for using all sixteen pieces on each side for "real" Arimaa, whether randomized or no.
I know I always come out as critical or at least skeptical of any change to the rules of Arimaa, but that is because I feel that Arimaa is something very rare. It is easy to identify some imperfection in any game and propose new rules to fix it, but the cost of any such changes is hidden. We don't know what we will lose. If awesome abstract strategy games were more abundant, I would probably jump on the bandwagon of "improving" Arimaa myself. The reality, however, is that almost every abstract strategy game eventually breaks in some serious way, and as long as Arimaa shows no signs of breaking in any of these ways, I'm going to be unenthusiastic about trying to fix anything cosmetic.
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| « Last Edit: Apr 10th, 2014, 11:01am by Fritzlein » |
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Fritzlein
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Re: Measure stereotyped openings
« Reply #66 on: Apr 10th, 2014, 11:14am » |
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Furthermore, I don't even think the variation in Gold setups is necessarily destined to decline further from here. The dominance 99of9 setup may just be a passing fad. For example, I don't think we have seen the last of setups with the gold elephant behind a trap. Browni's opening attacking idea would be most powerful with the horse on the a-file, camel on the b-file, and elephant on the c-file. Silver surely isn't going to come up with a faster attack in the east, so what is the Silver defense of the west that would deter this Gold setup? My meager opening knowledge would say that the silver elephant wants to be on b4 in this case, but does it then start on d7 and move there with a loss of time? I'm not saying there is no defense, just that it isn't obvious what Silver should do, and that we are far from having "settled" that the 99of9 setup is best. The theory of even just the setup, never mind of the whole opening, has a long way to evolve before we need dice to keep it interesting.
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| « Last Edit: Apr 10th, 2014, 11:18am by Fritzlein » |
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chessandgo
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Re: Measure stereotyped openings
« Reply #67 on: Apr 10th, 2014, 3:26pm » |
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I was not aware that some 960 setups give a significantly different white advantage. That would indeed be a problem.
When I say EEE style, I mean essentially playing with one or two (or three?) fewer pieces than all 16.
The current opening trend seems to be for each player to go all-in with a horse on opposite wings, which means the opening proceeds at a good pace. A few years ago, horse dances (or heaven forbid facing camels) were a lot more common, and I was worried that 20 moves dancing-for-nothing situations might become the norm. Hopefully that won't happen, but if it does, and long openings start boring players, I think taking one or two pieces off would re-make a game of arimaa exciting from start to finish.
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browni3141
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Re: Measure stereotyped openings
« Reply #68 on: Apr 10th, 2014, 5:31pm » |
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on Apr 10th, 2014, 3:26pm, chessandgo wrote:I was not aware that some 960 setups give a significantly different white advantage. That would indeed be a problem.
When I say EEE style, I mean essentially playing with one or two (or three?) fewer pieces than all 16.
The current opening trend seems to be for each player to go all-in with a horse on opposite wings, which means the opening proceeds at a good pace. A few years ago, horse dances (or heaven forbid facing camels) were a lot more common, and I was worried that 20 moves dancing-for-nothing situations might become the norm. Hopefully that won't happen, but if it does, and long openings start boring players, I think taking one or two pieces off would re-make a game of arimaa exciting from start to finish. |
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I agree about this current trend. It seems players have started to think it is an error to move a camel to face the opponent's  . What I don't agree with is your opinion that it leads to a boring opening. The opening may be longer on average, but why does it have to be boring? Often I see games with symmetrical camels where both sides can think of nothing but trying to pull pieces out, and neither side makes any progress until the opponent makes a mistake. I find such games very boring, but they happen because the involved players have limited understanding of the opening, and perhaps not enough creativity to make something happen. I don't think opposing camels are intrinsically boring in any way.
I have no idea what you mean by horse dances. Perhaps you could provide an example game.
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chessandgo
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Re: Measure stereotyped openings
« Reply #69 on: Apr 12th, 2014, 5:24am » |
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A can't really find relevant game. I mentioned the The Jeh ga,e in my book to supersamu in the chatroom, not exactly what I'm looking for.
For example, I believe the following opening would be reasonable:
1g Ra1 Rb1 Rc1 Dd1 De1 Rf1 Rg1 Rh1 Ra2 Hb2 Cc2 Ed2 Me2 Cf2 Hg2 Rh2
1s ra7 hb7 cc7 md7 ee7 cf7 hg7 rh7 ra8 rb8 rc8 dd8 de8 rf8 rg8 rh8
2g Ed2n Ed3n Ed4n Hb2n
2s ee7s ee6s hg7s hb7s
3g Me2n Hg2n De1n Dd1n
3s md7s dd8s de8s ee5s
4g Hg3e Hh3n Me3e Hh4n
4s md6e hg6e me6e hb6s
5g Hh5s Hh4s Mf3w Me3w
By horse dance I mean a Horse avances on one wing, the enemy camel gets closer, the Horse retreats, a horse advances on the other wing, the caMel gets closer, the horse withdraws, rince and repeat.
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Fritzlein
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Re: Measure stereotyped openings
« Reply #70 on: Apr 12th, 2014, 8:47am » |
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In my 2013 Postal Mixer game with mistre, nothing happened for the first 30 moves of the opening, except one square of rabbit pulling by me and one square of voluntary rabbit advancing by mistre. I didn't mind because I had some more involved games eating up my thinking time and because I was the one who made all two squares of progress; I'm not sure why mistre didn't mind.
If it were commonplace for Arimaa openings to just shuffle and reshuffle pieces without any commitment by either player, it would be a problem. On the other hand, it isn't necessarily right to blame the game when both players are being tentative. Just because the players aren't willing to commit to an away game and they aren't interested in pulling rabbits doesn't mean the inherent risk/reward balance prevents the players from committing to anything.
When the dual lone-elephant attack was the dominant opening, I was afraid of a "shuffling stalemate" becoming the dominant mode of play for Arimaa, because it might be too risky for an elephant to decentralize itself enough pull a 99of9 flank rabbit. Now that we know that horses can profitably advance in the opening, I am no longer afraid. The horse-dance shuffling stalemate seems unlikely because there are too many types of threats; someone will be able to at least pull a rabbit even if all swarming opportunities are blocked.
To repeat, the players can always conspire not to make progress for either a home game or an away game (and then they can complain that they want to agree to a draw), but as long as that kind of shuffling doesn't represent best play, I won't be be worried.
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Boo
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Re: Measure stereotyped openings
« Reply #71 on: May 19th, 2014, 9:30am » |
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Quote:| isn't it fairly well accepted that some of the 960 setups give white a big opening advantage, even bigger than the traditional chess setup? |
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I don't think there are such setups. All setups give the same advantage - the 1st move.
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Fritzlein
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Re: Measure stereotyped openings
« Reply #72 on: Sep 26th, 2014, 4:07pm » |
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on May 19th, 2014, 9:30am, Boo wrote:| I don't think there are such setups. All setups give the same advantage - the 1st move. |
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Really? If that were true, then I would think Chess960 World Cup would randomize the pieces before every game, rather than playing with the same setup twice and colors reversed between each pair of opponents. Why be concerned with giving each player the same first-move advantage if the first-move advantage is the same regardless of setup?
"All sections will be with double round robin (players will have the same position with Black and White but all positions will defer from one opponent to another)."
[EDIT]
Oops, after further reading I want to backpedal. Here are some statistics from someone who is worried about the problem: http://chess960frc.blogspot.be/2012/11/waving-yellow-flag.html
He has collected about 120 game results for each of the 960 starting positions, and it appears that the some favor white more than others. But he isn't careful about his statistics. I did a little experiment where I simulated the same data set, but under the assumption that every starting position would have a 45% chance of white winning, a 35% chance of black winning, and a 20% of a draw, similar to the results this fellow is quoting, and consistent with an expected score of 0.55 for white in every game. Just by random variation, the five best and five worst positions for white in my simulation had scores of
0.691
0.662
0.658
0.654
0.650
...
0.450
0.425
0.421
0.417
0.412
In other words, under the assumption that every Chess960 position has exactly the same first-move advantage, by natural variation I get results just as extreme as the ones our blogger has compiled. So perhaps some positions have just been lucky for white so far, and others unlucky, with no inherent bias. At a minimum, if these are the most conclusive stats available, we have to say there is so far no statistical evidence that some positions favor white more than others.
I therefore withdraw my statement that Chess960 is flawed in this way.
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| « Last Edit: Sep 26th, 2014, 4:52pm by Fritzlein » |
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