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Topic: Arimaa Strategy: Camel Hostage (Read 3767 times) |
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tharkun
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Arimaa player #7288
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Arimaa Strategy: Camel Hostage
« on: Mar 8th, 2012, 6:46pm » |
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Greetings! I've been looking to hone my strategic skills and decided to start by tackling camel hostage situations. I gathered quite a few positions and wrote down my impressions about the plans for both sides and a tenative assessment of the position. I would love to learn the feelings/thoughts of other Arimaa players, especially when it differs from my own, so that I can correct my misconceptions and improve my intuition in these kind of positions. I may do something similar for other strategic concepts in the near future, so feedback on my concept is very much welcome as well. Do you think something like this (a large number of positions with a specific strategic theme) can be a useful resource in general, possibly as an extension of the wikibook?
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#1
Position after 14s
Seems pretty good for silver. His horse on h3 means that it will be difficult for gold to swarm the f6-trap, and he seems to have good chances to create a second threat on the other wing. Silver should leave his camel on the defence in the west and go forward with his horse there; his goal is to either drag some small piece back to the c6-trap or to take over control of the c3-trap in order to overload the gold elephant. I'm not sure what gold should do. Maybe his best bet is to prevent te creation of weaknesses in the west as much as possible and try to exchange his camel for the h3-horse at an appropriate moment, for example if silver overreaches in the west.
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#2
Position after 13s
Silver has achieved a camel hostage, but he has no bailout option. His rabbit and dog in the east prevent a swarm, but they can also become weak. In the west it is not easy for silver to make progress either. There is no easy plan to pull rabbits available, since silver's advanced rabbit on a5 is weak as well. A general advance is double-edged as well, since the advanced position of the silver pieces means that the gold elephant has good chances to get enough material for his camel if he gives it up at the right moment. Silver wants his camel in the west and a controlled advance towards c3 with multiple pieces. Gold wants to move his horse to the east to threaten the silver rabbit and dog. I think the position is very double-edged and it may be slightly in gold's favour.
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#3
Position after 16s in the same game
Silver has made good progress here because of the horse hostage on g7. It has become much more difficult for gold to give up his camel. Therefore silver can act in the west more easily. Gold's highest priority is to improve the situation in the east. He can try to swarm f6 in order to free his elephant; Maybe move the elephant to e6 and move a dog to f5 and try to push into f7. I think that silver can probably counter this plan pretty effectively here and remain on top.
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#4
Position after 17s
Material is unbalanced with a horse against two rabbits. The gold cats are not strong enough to free the elephant from the defence of f6 effectively. The gold dog on a5 and the silver rabbit on g4 are both in danger. Gold's west wing is depleted. The position is probably going to become a race in which gold tries to free his elephant by swarming f6 and silver creates threats in the west. My hunch is that the position favours silver.
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#5
Position after 9g
It's hard to believe that silver can create anything worthwhile out of this hostage situation without risking being overrun by gold pieces. On the other hand, silver is a rabbit up and has no real weaknesses. He should probably play for control and not try to maintain the camel hostage against all costs. Gold should probably try to make use of his advanced pieces in the east and try to use them to restrict the mobility of the silver elephant and fight for control of f6. Nevertheless, I'd guess that gold does not have enough compensation for the rabbit deficit.
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#6
Position after 20s
Gold has a horse for dog and rabbit, but his camel is hostaged. It will be difficult for gold to swarm c6 effectively here because of the silver horse on b3. Most probably the c3-rabbit will not survive in the long run, but it does complicate life for gold at the moment. Gold could retreat his horse and try to capture the b3-horse and the c3-rabbit for the hostaged camel at some point. Silver ought to try and create a second threat in the east, but it's not so easy without making his camel vulnerable. Pulling some piece to f6 will probably be difficult; maybe silver should advance with camel + dog + rabbits. I'd say that silver is slightly better here.
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#7
Position after 30g
Gold is a rabbit down, but the hostage of both camel and horse seems to form ample compensation. A slight complication is that gold momentarily does not have the strongest free piece in the west, and it is complicated to get the camel there. Gold could move the silver horse to g2 in order to get his horse out. As silver I probably wouldn't try to swarm f3 since gold has many defenders there. I'd rather try to move towards c3; the horses are the strongest pieces locally at the moment, and the silver elephant is exerting more influence on the west compared to his gold counterpart. This game will probably be about time: will gold have enough time to rearrange his pieces effectively? I'm not so sure about that.
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#8
Position after 45g
Gold's horse in the east will make it difficult for silver to rotate his elephant out of the defence of f3. Gold can move his camel to the west, but the absence of a pair of horses means that is it difficult for gold to create anything special in the west without exposing his camel. Silver will probably move pieces forward in the east, while gold tries to prevent being smothered. Double-edged position without a clear advantage to either side.
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#9
Position after 12s
Very safe hostage position for silver without huge risks of being swarmed. Some advantage to silver. Silver should rotate his camel out of f7 and move it to the west. Then try to start pulling rabbits. Gold can send a horse to the east towards the silver dog; two horses in the west are not much use when silver's camel is heading there.
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#10
Position after 6s
Nice hostage position for silver. His horse on a5 can fight against a gold swarm, his camel defends in the east and his horse is ready to jump into h3 to start pulling rabbits. I'm not sure what gold can do apart from trying to swarm c6, but I do not see this plan succeeding.
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#11
Position after 12s
Gold can put his elephant on d6 and try to swarm c6. Silver will soon have a real threat in f6 by pulling the h2-rabbit north. I'd guess the position is somewhat better for silver.
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#12
Position after 12s
The gold elephant will move to c5, and silver should reply by moving his horse out of the immediate range of the silver elephant (maybe to a3). Silver can probably start pulling rabbits in the east relatively quickly, but on the other hand gold is a rabbit up at the moment. The position seems reasonably well balanced, maybe a tad better for silver.
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#13
Position after 10g
I don't think gold has any real chances to create a favourable camel hostage situation. Silver should advance some pieces in the east in order to be able to swarm quickly if gold decides to set up Eg3, mh3. Maybe gold should retreat his cat and start pulling rabbits in the west. It somewhat difficult for silver to match this plan due to the presence of the gold camel on c2.
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#14
Position after 13s in the same game
Gold has made more progress than silver. His cat is safe and the hostage situation has improved.
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#15
Position after 36g
This position belongs to the class of camel hostage positions due to the fact that the camels have been exchanged. Gold is better, he is a rabbit up. He does not have real chances to create a goal attack with his cat, since silver can easily slide a dog east to strengthen the defence. Gold can move his horse to the west and start to advance there. Silver seems to be in dire straits; I do not know what his best options are. Move a dog to the east and try to threaten the gold cat?
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#16
Position after 58g
Gold has a horse and a rabbit for a camel. He has hostaged the silver camel, but his rabbit on h4 is weak and it seems difficult for him to create a second threat. Silver can try to pull the h4-rabbit towards f6. Gold could move his dog to f2 and his horse to the west so that he has two horses against one there.
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#17
Position after 109g
Gold has taken the silver camel hostage, but this does not compensate fully for the fact that he is a horse down against a dog. Moreover, the silver horse on e6 is ideally placed to start harassing the gold dog on h7. Gold should probably try to get something going in the west with the help of his camel, but it seems that silver has sufficient resources to defend. The silver elephant is ideally placed on e3 to threaten the gold camel if it exposes itself too much.
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#18
Position after 38s
Gold's rabbits in the east are in the way, and the silver rabbit on h2 is a huge annoyance. Silver can probably combine attacking in the east effectively with maintaining a solid position in the west quite effectively. Maybe move some piece to f4 and harass the advanced rabbits. What should gold do? He has to find counterplay somewhere and hope for a mistake by silver, his position looks quite bad.
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#19
Position after 16g
Gold has a camel plus rabbit against horse plus dog, but his camel is hostaged. The silver a4-rabbit is exposed, but his horse can probably safeguard it quite effectively. Silver should probably bring horse plus dog to the east and start to create play on that wing. In the long run silver seems to be better off, but regrouping takes time. Maybe gold should up the ante by moving pieces to c6, especially rabbits. I'd say that silver has slightly better chances in the position.
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#20
Position after 36g
Silver is a rabbit down, but he has framed a rabbit in c6 and taken the gold camel hostage. The gold rabbits on d3 and e3 look out of place, but is does not seem easy for silver to exploit this. On the other hand, gold can quickly bring a horse to c5 and try to free up this elephant. Silver could try to threaten the advanced gold pieces in the east. I'd prefer gold here.
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#21
Position after 6s
It seems quite possible for gold to swarm f6 successfully. On the other hand, gold's western wing looks a bit depleted at the moment. Silver could mount a quick attack against the c3-trap, when it is doubtful that gold will be able to complete a smother in the east before silver creates strong threats. Silver seems to be just a bit better.
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#22
Position after 16s
Gold is a rabbit up and his elephant is doing really well on d6. He has some advanced pieces in the west already to start a swarm against c6. Silver can try to pull the h2-rabbit, but it seems that gold is on top anyway.
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#23
Position after 21g
On its own the camel hostage does not nearly suffice to compensate for a two rabbit deficit. However, the silver rabbit on h5 may become weak. Gold can try to threaten this rabbit in f3. Moreover, gold is much better developed at the moment. The position seems not far from equal. Silver should develop. Gold could move a cat to the west and retreat his dog to balance his forces.
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| « Last Edit: Mar 8th, 2012, 6:46pm by tharkun » |
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clyring
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Arimaa player #6218
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GoldRe: Arimaa Strategy: Camel Hostage
« Reply #1 on: Mar 8th, 2012, 10:01pm » |
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I'll offer my opinions on these positions as well.
#1: While the hostage situation itself is fairly solid, gold to move can shut the silver horse out of g3 with 15g Hf2n Rf1n Dg3s Hf3e and silver will have a hard time both stopping gold's swarm and preventing gold from dragging minor pieces to f3. The game is far from over.
#2: Silver's dog and rabbit are ill-prepared to fight against a horse and the silver camel is not very useful on f7. Further, silver's western clump of pieces is far enough advanced to make a nice target if the gold elephant switches wings, but not far enough forward to protect one another effectively. However, at the same time, gold's horses are far away and more gold pieces need to be advanced to support the attack. Neither player has any fast options and it seems the game will take a slow manoeuvring course. The position's value is very unclear; I don't honestly have a clue who should win here.
#3: Gold's position has worsened considerably despite winning the rabbit. Gold's only free horse simply cannot offer enough power to handle silver's attack and too much material for both sides is concentrated around f6 for either abandoning it or attacking to be feasible. Silver should have a significant advantage here.
#4: Silver's lack of a seconds horse would significantly reduce the value of the hostage, but silver's own advanced pieces in the east are in the way of any attempts by gold to make progress by pulling out small pieces. Both of gold's dogs are poorly placed and gold's goal defense is dangerously thin across the board. The rabbit on g4 is vulnerable, but perfectly positioned to delay a silver attack. If silver can get an attack going in the west fast enough, they should have an appreciable advantage. However, gold will always have the threat of leaving f6 with their elephant and silver can do little to prevent gold from eventually switching the elephant out without losses, making the position rather double-edged.
#5: In my opinion, gold has more than sufficient positional compensation for the lost rabbit. Taking the gold camel hostage here seems unlikely to yield good results with the silver horse buried and an encroaching mass of pieces. Silver's best hope is probably to play for profit elsewhere, as gold simply has too many pieces there for silver to make progress.
#6: Silver is clearly down materially, h for R. Gold is also not far from switching his elephant out, but since c3 is temporarily safe, it may be possible for silver to intervene with the process using her camel. There is also the possibility that gold, in manoeuvring around c6 will create a long enough window during which the gold elephant is tied down further by the pieces to replace it but not yet able to leave wherein silver may be able to attack f3. I consider gold to be better off, but the position is admittedly rather unclear to me.
(tbc)
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| « Last Edit: Mar 8th, 2012, 10:51pm by clyring » |
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chessandgo
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Re: Arimaa Strategy: Camel Hostage
« Reply #2 on: Mar 12th, 2012, 7:26am » |
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Interesting Tharkun!
As a meta-remark, this is a lot of material, and I fear discussing so many positions might dilute the discussion quality. Maybe another idea would be to have slightly fewer positions, but regrouped by a theme (for example a camel hostage for a rabbit), and compare position #12 with some other position with different strategic features.
All positions where silver [edit: by silver I mean the hostaging side, although sometimes it's gold] has a good camel hostage, material is equal and army advancement is about par should be massively favourable to silver (1,2,4 [assuming H~=rr],5 to some extent,9 to some extent,10,11,13 etc). Normally silver should have had to work to establish a good camel hostage position, which means Gold's development should be way ahead of Silver's. In all these positions it feels like Gold voluntarily gave up the caMel hostage, so that the number of effective development steps that each army has taken is about the same, and so silver should have a very clear advantage.
In almost all these positions, I think pulling a rabbit would be a bad plan, especially the positions where captures have occured already. Advancing rabbits, and advancing pieces towards the enmy trap when that looks plausible is generally a better plan as far as I can tell (for example #16 the Rh4 is better on h4 than on g2 for Gold, silver pulling it towards f6 would just let Gold move his horse to g6 through g4 and get a strong attack. Likewise, #11 silver shouldn't drag a Rabbit to f6, but put a horse on g3, camel on f4 (possibly dog on e3), with rabbits following and attack around f3, that would be crushing.)
#6 is fun, I think trading the M for hr on the next move should be best for Gold. md for HH is pretty balanced material.
#7 is interesting as well, I'm not positive that the two hostages in the east are better than just one (I would actually guess it's worse). Silver should probably avoid the horse flip to g2 you mention, after which Gold would replace the Mg3 with a Horse and probably be fine. So moving a dog to g4 first looks good. If silver can keep all three EMH sealed in around f3, I'm not even sure Gold is ahead.
#8 If Gold were to play and get his Horse out (to g4 for example) he'd be clearly ahead, so silver has to put pieces on h5 and g4 on this move. Then I agree the position is unclear.
Like clyring I can't make it though the whole list in one pass, I'll try to come back to it later)
PS: as for #5, there is no rabbit deficit, is there?
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| « Last Edit: Mar 12th, 2012, 7:26am by chessandgo » |
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tharkun
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Arimaa player #7288
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Re: Arimaa Strategy: Camel Hostage
« Reply #3 on: Mar 12th, 2012, 12:33pm » |
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Thanks for the comments! I think that both of you are right that I posted too many positions at once. On itself knowledge of strategic features like hostages or frames seems very useful but ultimately incomplete. As mentioned in the Wikibook, judging when they are favourable and determining how to proceed is the main area where humans can make use of their strategic intuition. That's why I thought such a discussion would be interesting. However, the length of my post may well have been too imposing to facilitate a high quality discussion.
What would be a suitable format in general? About 8 positions at maximum, or is that still too imposing? I think it is beneficial to be able to compare positions, so too few of them isn't good either.
Maybe I could post a set of positions and observe the run of the discussion for 1 or 2 weeks before possibly moving on to the next theme? First I want to make sure that the idea is useful for others and I'm not just clogging the forum 
I have collected positions on 8 different strategic features so far, but I expect that I'll have to split up some of them to limit the number of positions.
What shall I do with this thread? Leave it as it is? I am certainly going to try and group the positions according to subtheme as chessandgo suggested, so I could also leave just those positions belonging to a single subtheme in this thread and repost the others in a different thread later. (Of course, in that case I would copy and repost your comments as well wherever applicable). My first suggestion for dividing the positions into subthemes:- Camel hostage with equal material (1, 2, 3, 10, 11, 13, 14, 21)
- Camel hostage vs. material (7, 12, 17, 20, 22, 23)
- Camel hostage vs. development (5, 8, 9, 18 )
- Camel hostage with unbalanced material (4, 6, 8, 15, 16, 18, 19)
A small problem is that I doubt that I'm sufficiently capable to identify the salient strategic aspects in most positions apart from the glaringly obvious. In this case I borrowed my reasoning from your insights. Thus, I'm not really sure I will be able to make a sensible division into subthemes in general. I guess we will find out in due course 
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chessandgo
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Re: Arimaa Strategy: Camel Hostage
« Reply #4 on: Mar 12th, 2012, 1:48pm » |
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Continuing:
14: has Gold lost a Cat in the meantime?
15: moving a dog east looks good indeed, if both silver dogs are used in the center / west, Gold's Cat will push into h5 and follow with the h2 Rabbit for a very strong goal attack. Both sides want to advance rabbits on both wings whenever possible.
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chessandgo
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Re: Arimaa Strategy: Camel Hostage
« Reply #5 on: Mar 17th, 2012, 9:09am » |
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16: I guess I'd take Gold, but the position is very complicated. The Hf2 must remain in the east : HH vs h is not such a decisive advantage, and the two silver dgos would be able to control f3 and replace the elephant without a godl Horse to counter. To me the question is whether Gold wants to advanace his Horse to g6 through g4, and threaten a goal attack if silver's pieces move towards f3, or stay around f3 to prevent a rotation. In both cases Gold needs to advance rabbits (west and center), whenever possible.
18: I like silver too. Although Gold should be able to avoid quick captures by relocating his Horse towards f6 if silver threatens a capture there, and using the camel to avoid captures in the west. So Gold has some time. I'd start by pusing the hg3 back to g4, so that the Ch3 be unfrozen, and then push the rh2 back. When the rabbit has been pushed back once or twice, Gold should have more space to unearth his pieces (Hg1, Cg2) and get a more decent hostage than the current (terrible) position. I guess silver should try to prevent that (the de6 would obviously be able to seize f4 whenever it wants, and threaten pieces on f6 if that seems good).
19: again, the ra4 is better for silver than on a8. I guess retaking control over f6 is the most pressing, and then silver can h+r attack on either wing. I'm not sure Gold can replace the elephant by small pieces around c6, especially needing to defend against a goal attack, maybe trading the camel for a horse when the horse reaches b3 would be an option (R for d is not too big a disadvatange, although bigger now that on a full board since dogs are becoming stronger)
20: Silver actually has a dog for two Rabbits if I read the position correctly. Re3 and Rd3 are fine, silver won't be able to threaten a capture. It's going to be dificult to rotate the Elephant out of d6 though, and silver wil quickly be able to threaten captures on f6. If Gold can advance pieces quickly to c5 and d6 he'll be fine, but I think I'd take silver and try to get a quick capture on f6.
21: Silver ahead. Gold should push the he6 back to e7 and advance pieces to f5 and e6 as quicly as possible I guess, but silver's western attack is going to be painful.
22 I guess I like Gold too. Silver should try to attack f3 though, pulling Rh2 would be too long. h->g4 and m->g5 on the next move threaten a strong attack on the next move.
23 two rabbits should be more than enough, I like silver. Even if Gold somehow manages to capture the rh5 while silver activates his pieces (which hopefully won't happen), the position would be still about equal or slightly better for silver. Also Gold must not lose a Horse for the camel right away, as HRR > M.
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| « Last Edit: Mar 17th, 2012, 9:32am by chessandgo » |
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