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99of9
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Superstrategies for Arimaa
« on: Jul 18th, 2005, 2:25am » |
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This thread is intended to collect ideas for superstrategies for winning arimaa. Some methods may only work against bots, but I think it would be nice to be able to somehow categorize arimaa wins. It would be even better if we could get sample games for each category, as Arimanator has started elsewhere, and I will quote below.
Here are some superstrategies I can think of, which might give you an idea of what I mean by this:
1) Attrition: Gradually erode opponents pieces (faster than s/he erodes yours), eventually you have dominance so can just send a rabbit in. This is usually characterised by keeping most pieces back, except for forays into enemy territory with elephants and sometimes horses or camels.
2) Race: Gain total control of one of the opponent's traps, usually ceding one of your own. Then try to kill enough material to punch your rabbit through before your own defences fail. Every step matters in a race.
3) Smothering: Press forward with all your pieces but keep the opponent's pieces in front of you - eventually taking over both his/her traps, and confining him/her so much that s/he either has no move, or has to give away pieces for free. Ryan_Cable gave a great demonstration of this against Bomb_2005_P2 in game 16992.
4) Asymmetric Dominant Pieces (anybody got a better name for this?) This method tries to ensure that the most powerful free piece the opponent has is weaker than the most powerful free piece that you have. Once this is achieved, it is easy to win. Examples include elephant blockades or taking a camel hostage. This superstrategy is a bit of a continuum however because sometimes pieces can be "partially free".
Any others?
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| « Last Edit: Jul 18th, 2005, 2:29am by 99of9 » |
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99of9
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Re: Superstrategies for Arimaa
« Reply #1 on: Jul 18th, 2005, 2:27am » |
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Arimanator provided a few examples of the race superstrategy which were tried in handicap games against bomb. I'm quoting him here for convenience:
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| « Last Edit: Jul 18th, 2005, 2:28am by 99of9 » |
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omar
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Re: Superstrategies for Arimaa
« Reply #2 on: Jul 18th, 2005, 7:18pm » |
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Great idea Toby.
I can think of some games that I've seen for all these, but I'll have to dig up the game ids.
One other strategy that comes to mind is the one which Frank (Belbo) likes to use on the bots (and even humans). Basically just driving a rabbit through a complicated mess. He did this against Bomb in the postal tournament.
It would probably also be good to make a wiki page for this topic to collect the main ideas from this discussion along with links to the games.
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Fritzlein
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Re: Superstrategies for Arimaa
« Reply #3 on: Jul 18th, 2005, 9:31pm » |
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Interesting thread, this. I like the idea of having game collections where similar themes are present. I had earlier thought of the less grand idea of enumerating how many different strategies we collectively know for beating Bomb. (I say "collectively" because Belbo's ability to shove a rabbit home through a mess is something I have never comprehended myself.)
One thing I get hung up on is that the strategies overlap so much that it is hard to keep them separate. For example, suppose I make a strong attack on an opposing trap. If my opponent defends one way, then I will get his camel hostage. If he defends another way, then I will get clear with a rabbit I can capture for nothing. If he counter-attacks instead of defending, then it becomes a race that I am trying to win. So which strategy was I using? Perhaps I didn't prefer any particular way of winning when I made my attack; I just knew that the other guy would be in trouble in some way.
My postal game with RonWeasley is full of this sort of thing. On move 11w he could have defended with his elephant and I would have pulled a rabbit, but when he counter-attacked my horse, I felt I had to capture his horse. You might have said I had a rabbit-pulling strategy at that phase of the game, but he didn't let the game go down that path.
Then on move 15b I launched an E+H attack on RonWeasley's c6 trap. My strategic thought was that he would need his elephant to take my horse hostage, after which my elephant would be more mobile than his. (With a pair of horses gone, I didn't think he could frame my horse to good effect.) But again he didn't let me execute my strategy, as he fended off my horse with his camel on 16w. Suddenly I had a "camel hostage" strategy, which wasn't what I intended, but that's what he gave me in return for blocking my intended strategy.
(For the record, I totally overlooked the possibility of 19w, so my move 18b can't well be analyzed strategically.  )
And just now, on move 22w, I got another surprise. My strategy was to win the war of lone elephant attack vs. lone elephant attack by virtue of having extra tempi. But RonWeasley denied me my extra tempi and instead offered me a dog capture for freeing his camel. I would never choose to play an unbalanced game because it seems I could lose by accident. My strategy is always to keep everything under control and eke out a tiny advantage which I try to increase without conceding any weaknesses in my own position. But RonWeasley essentially forced me into the unbalanced game by taking away the strategy I had intended to play.
In short, it reminds me of what the offensive coordinator often says before a football game: "Their defense can't stop everything. We'll take what they give us." Or more simply, "If they put eight men in the box, we'll pass, and if they put seven men in the box, we'll run." What do you call that strategy?
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99of9
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Re: Superstrategies for Arimaa
« Reply #4 on: Jul 19th, 2005, 12:05am » |
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on Jul 18th, 2005, 9:31pm, Fritzlein wrote:One thing I get hung up on is that the strategies overlap so much that it is hard to keep them separate. For example, suppose I make a strong attack on an opposing trap. If my opponent defends one way, then I will get his camel hostage. If he defends another way, then I will get clear with a rabbit I can capture for nothing. If he counter-attacks instead of defending, then it becomes a race that I am trying to win. So which strategy was I using? Perhaps I didn't prefer any particular way of winning when I made my attack; I just knew that the other guy would be in trouble in some way.
{snip}
In short, it reminds me of what the offensive coordinator often says before a football game: "Their defense can't stop everything. We'll take what they give us." Or more simply, "If they put eight men in the box, we'll pass, and if they put seven men in the box, we'll run." What do you call that strategy?
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I agree. I take a similar approach myself, and rarely have full control over which case I will eventually adopt. Perhaps it is better to call these "game-ending situations" than strategies. We might aim for one, or take advantage of one when our opponent opens an opportunity. My experience however is that once the game takes one of these paths for a reasonable number of moves, it becomes almost irrevocable if both players play well. So think of it as some kind of topological splitting of the game tree.
I also agree that it is possible to do more than one at the same time. These mixed cases wouldn't be listed on the examples page  .
Are they always "game-ending"? No, not always... so maybe that name isn't good enough either.
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99of9
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Re: Superstrategies for Arimaa
« Reply #5 on: Jul 19th, 2005, 12:12am » |
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on Jul 18th, 2005, 7:18pm, omar wrote:| It would probably also be good to make a wiki page for this topic to collect the main ideas from this discussion along with links to the games. |
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Yes, you're probably right it would be better in wiki. Anyone who'd like to copy it across is welcome to. I will try to at some stage if nobody else does.
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omar
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Re: Superstrategies for Arimaa
« Reply #6 on: Jul 19th, 2005, 8:22pm » |
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on Jul 18th, 2005, 9:31pm, Fritzlein wrote:
One thing I get hung up on is that the strategies overlap so much that it is hard to keep them separate.
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Like Toby, I also agree with you on this. In fact my last game with BombP3 started out as a "race" strategy but shifted to an "asymmetric dominant pieces" strategy and sort of ended with "attrition" (game 17005).
In some games you see just one SuperStrategy, but I think many more games tend to have a combination of them.
I still like the idea of trying to classify SuperStrategies.
The strategies listed on the Wikipedia page nicely illustrate the basic strategic positions we know about, but I view the SuperStrategies as being more dynamic and could not be illustrated with one just one board position. To understand something like Attrition or Smothering one needs to see the game in motion. The dynamic SuperStrategies will build on the concepts introduced by the "static" strategies. To understand Race you would need to know what "trap control" means; or to understand "asymmetric dominant pieces" you fist need to know the concepts of hostage and blockade.
The SuperStrategies won't be as clear cut as the static strategies, and a single game could use various combinations of them. But I have a feeling that categorizing and labeling SuperStrategies will help us acheive higher levels of play.
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Fritzlein
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Re: Superstrategies for Arimaa
« Reply #7 on: Jul 28th, 2005, 6:49pm » |
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on Jul 19th, 2005, 8:22pm, omar wrote:But I have a feeling that categorizing and labeling SuperStrategies will help us acheive higher levels of play.
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I agree. Having names for and descriptions of our long-range plans is an advantage we collectively have over the machines, as well as an advantage one human can have over another. It is easy to play Arimaa planlessly, because one might not have any idea what to do in a given position. But if one plays without a plan of some sort, one's opponent will usually gain an advantage simply by virtue of having a long-term plan at all.
Perhaps one can consider "superstrategies" as a hierarchy of threats. Each move represents one or more strategic threats. The other player decides which threats to defend against, and/or considers whether he can make a bigger threat instead of defending. For example a goal threat trumps a threat to win material.
I guess trying to make a hierarchy quickly runs into trouble, because there are different sizes of material win, different values of a hostage, and so on. Is a camel hostage worth a dog capture? Is an elephant smother worth a horse capture? It depends on so many details of the positions.
Even so, it seems that roughly speaking one pursues a lower level of threat only when the higher level isn't available. You take a hostage because you can't win material directly. You pull a rabbit because you can't get a hostage, etc. My first stab at this type of categorization would be:
1) Direct goal
2) Win material
3) Take a hostage
4) Pull rabbits
5) Rebalance pieces to gain local dominance
But this hierarchy assumes lone-elephant mentality it best, and specifically assumes that attacking an opposing trap is not worth it, because by nature that involves giving up a hostage. If the position somehow calls for assaulting an opposing trap, then rabbit advances may be good rather than bad, and smothering one or both wings may play a greater role. I still can't make up my mind whether it is disadvantageous to make an E+H attack from the opening position. If it is advantageous even in a fair number of situations (say in 25% of opening positions), then the hierarchy might change to:
1) Direct goal
2) Win material
3) Take over opposing trap
4) Take a hostage
5) Rebalance pieces to threaten trap attack
6) Push rabbits to threaten trap attack
or something completely different. I can imagine rabbit-pulling becoming extinct if we realize that advanced rabbits give one an edge in attacking. I can imagine people becoming eager to occupy the third and fourth rank (as opposed to shying back to the second rank) because it both cushions the home trap from attack and makes an attack on the opposing traps easier to launch.
Arimaa theory has drastically changed and expanded since I learned to play last summer. How will it change and expand in the coming year?
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99of9
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Re: Superstrategies for Arimaa
« Reply #8 on: Jul 28th, 2005, 9:52pm » |
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on Jul 28th, 2005, 6:49pm, Fritzlein wrote:| Perhaps one can consider "superstrategies" as a hierarchy of threats. |
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So each superstrategy might be characterised by a different hierarchy of threats? Yes, I think I like this. I'll give an example later.
Quote:| I guess trying to make a hierarchy quickly runs into trouble, because there are different sizes of material win, different values of a hostage, and so on. Is a camel hostage worth a dog capture? |
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They do overlap somewhat, but that doesn't mean we can't say which is higher on average. Clearly a camel hostage is worth less than a camel capture, so when we compare apples with apples, capture is higher on the hierarchy than hostage taking. I agree that figuring out the exact ordering in the overlap regime can sometimes distinguish a good arimaa player from a great one, but here I guess we're searching for superstrategies which have entirely different hierarchies from each other - which makes them categorically different.
Quote:My first stab at this type of categorization would be:
1) Direct goal
2) Win material
3) Take a hostage
4) Pull rabbits
5) Rebalance pieces to gain local dominance
But this hierarchy assumes lone-elephant mentality is best
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This is the hierarchy I try to use when playing Attrition against someone also playing Attrition.
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If the position somehow calls for assaulting an opposing trap, then rabbit advances may be good rather than bad, and smothering one or both wings may play a greater role. {snip} then the hierarchy might change to:
1) Direct goal
2) Win material
3) Take over opposing trap
4) Take a hostage
5) Rebalance pieces to threaten trap attack
6) Push rabbits to threaten trap attack
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I view the E-H attack as a precursor to entering either Race, Smother, or Asymmetric-Dominance. The difficulty is that the opponent usually choses which of these paths you have to go down by his/her response to your attack.
[If the opp chooses to take the H hostage with their elephant, you can try to smother the elephant, achieving Asymm-Dom, or even full Smother.]
[If the opp chooses to counterattack with his/her own E-H attack on the diagonally opposite corner, they have chosen to enter a Race.]
[Or finally, if the E-H has been mismanaged (eg my 1st round game against naveed in the 2005WC), the opp can sometimes choose to maintain the Attrition superstrategy by defending the trap with the elephant, and bringing the camel across to take the H hostage. If this works and not too many pieces are lost in the process, the E-H attacker can end up a horse down in the Attrition-Attrition game.]
Nevertheless, I agree that the hierarchy you have proposed is good for this middlegame trap-control strategy.
Quote:
I can imagine rabbit-pulling becoming extinct if we realize that advanced rabbits give one an edge in attacking. I can imagine people becoming eager to occupy the third and fourth rank (as opposed to shying back to the second rank) because it both cushions the home trap from attack and makes an attack on the opposing traps easier to launch.
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All of these are certainly possible, but for the moment I'd prefer to try to slightly codify current conventional wisdom for each superstrategy. If we can manage that then later generations of ourselves can look back and laugh heartily.
So unless people come up with other superstrategies, now we need to try to associate a hierarchy with each one. It looks like Arimanator and Paul can help us out by providing highly successful hierarchies for the Smother superstrategy.
Here's a preliminary go at one for a game which has descended into Race superstrategy. I'll use the tags (A) and (D) to denote the two different wings of the board, A for attacking wing, and D for defending wing (the one your opponent is attacking, usually opposite to the one you are attacking).
1) Direct Goal
2) Take over opposing trap (A)
3) Win material (A)
4) Advance one rabbit (A)
5) Insert piece into opp backrow (A)
6) Shuffle your backrow pieces toward (D)
7) Extract rabbits from opp backrow (A)
 Freeze opp pieces near trap (A)
9) Win material (D)
10) Advance another rabbit (A)
[Feel free to suggest changes to this order, I'm not claiming it's totally correct - for example 4 could well be higher than 3]
Out of interest, I think the reason that bots are so susceptible to Races is that they confuse 3 with 9 (they happily give away small material or rabbit advancement in the corner they should be defending in exchange for big material in areas they are not really attacking), and they confuse 4 with 7 (they hold back all rabbits, and thus can never mount a Race of their own.) Perhaps they think they are still playing Attrition when their human opponent has turned it into a race.
Am I right that Jeff has been toying with the idea of making Clueless Race-aware? Some of the opening setups he tried seemed to suggest that.
Anyone want to have a go at an Asymmetric-Dominant Piece hierarchy? This would need to include concepts like hostage or blockade rescue-attempts.
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| « Last Edit: Jul 28th, 2005, 9:53pm by 99of9 » |
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