Arimaa/Introduction to Strategy

From Wikibooks, open books for an open world
Jump to navigation Jump to search

Strategy is focused on long-term positions. If no capture or goal can be forced, a tactic may become a strategy. A goal threat's value may lie in the space advantage it creates; enemy pieces forced to defend goal will not be a problem elsewhere. A capture threat may likewise tie enemy pieces to defense, if the opponent is unwilling to give up the threatened piece. By tying up enemy forces, one can build a whole-board advantage.

Direct goal[edit]

The ultimate object of Arimaa is to get a friendly rabbit to goal. This requires that space be cleared, but how? Should one immediately try to rip a hole in the goal line and then march a rabbit through? If one side attempts this, how should the other side respond?

It is best not to treat the whole game as a race. Until a fair amount of space has been cleared, forcing a goal is much harder than stopping a goal. Even if a goal path is opened, the defender can often close it easily. One might get a quick goal against a weak opponent, but a skilled opponent is usually attentive to home defense.

As long as there is no real opening in the goal line, it is futile to advance a rabbit for the purpose of reaching goal. A quick rabbit advance may be costly, since an advanced rabbit can never retreat. Defending a rabbit from capture is often untenable, as an elephant has more important things to do, and any other defender could be captured itself.

In short, going for an early goal is a poor strategy which can quickly set one back. Nevertheless, a goal path must eventually be cleared somehow.

Capture[edit]

a b c d e f g h
8 Arimaa rs.svg Arimaa rs.svg Arimaa rs.svg 8
7 Arimaa rs.svg Arimaa ds.svg Arimaa es.svg Arimaa eg.svg Arimaa ds.svg Arimaa rs.svg 7
6 Arimaa rs.svg Arimaa dg.svg Arimaa rs.svg Arimaa rs.svg Arimaa rg.svg 6
5 Arimaa hs.svg 5
4 Arimaa ms.svg Arimaa rg.svg Arimaa rg.svg 4
3 Arimaa mg.svg Arimaa hg.svg Arimaa rg.svg 3
2 Arimaa rg.svg Arimaa dg.svg Arimaa cg.svg 2
1 Arimaa rg.svg Arimaa rg.svg Arimaa rg.svg 1
a b c d e f g h

Because the gold elephant was decentralized, Silver was able to fork a gold dog. (Game)

While a game can finish with minimal captures or even no captures, capture threats are important. A piece is captured only when it is on a trap square with no friendly piece beside it; there are many ways to prevent a capture. If nothing else, the defending elephant can camp out beside a trap where there is a capture threat; since nothing can dislodge an elephant, its friendly pieces can never be captured in a trap it stays next to.

The key to progress is to make strong threats around two different traps. The enemy elephant can only defend one trap, and any other defender or rescuer could itself be at risk.

The simplest double threat is a fork between one's home traps. If a piece can be flipped in the center, it may be doomed to such a fork. This is one of many reasons both elephants might stay near the center. Although any piece can unfreeze a friend, an elephant can do so without putting itself at risk.

A rabbit near the center could be an easy target for a fork, since rabbits can't retreat homeward. This is one reason rabbits often do not begin in the middle. A piece might be dragged up a flank, but this would not in itself force a capture, as it would create a threat in only one trap. Many flank pulls are not worth the time they use up, though certain threats can be game-changing; if an elephant is stuck defending its camel, neither piece can counter the enemy camel elsewhere.

Hostages[edit]

a b c d e f g h
8 Arimaa rs.svg Arimaa rs.svg Arimaa rs.svg 8
7 Arimaa rs.svg Arimaa rs.svg Arimaa rs.svg Arimaa cs.svg Arimaa hg.svg Arimaa rs.svg 7
6 Arimaa ds.svg Arimaa hs.svg Arimaa rs.svg 6
5 Arimaa ds.svg 5
4 Arimaa hs.svg Arimaa cs.svg Arimaa mg.svg 4
3 Arimaa rg.svg Arimaa eg.svg Arimaa es.svg Arimaa dg.svg 3
2 Arimaa rg.svg Arimaa ms.svg Arimaa hg.svg Arimaa dg.svg Arimaa cg.svg Arimaa rg.svg 2
1 Arimaa rg.svg Arimaa rg.svg Arimaa rg.svg Arimaa rg.svg Arimaa rg.svg 1
a b c d e f g h

In this game, the silver camel has been taken hostage.

In the diagram, Gold has taken the silver camel hostage, threatening to capture it in c3 if the silver elephant leaves. The c4 cat could not defend the hostage alone, as the cat could itself be captured if the trap had no other silver defender. Since an elephant on b3 could normally pull a non-elephant defender into the c3 trap, this type of hostage can only be defended by an elephant or by a team of well-placed weaker pieces. A solid camel hostage will make the forces asymmetrical: with the gold elephant holding the silver camel hostage and the silver elephant defending it, the gold camel is the strongest free piece. Until something changes, there is not even a threat to a gold horse. With the gold camel and horse both active in the east, Gold might soon overload Silver's defenses. Having the strongest free piece is a large advantage, if that piece is well-positioned and supported by other pieces.

Without a strong alignment, holding a hostage can be costly. An elephant deadlock at one's home trap is a potential space disadvantage, since the opponent can safely advance pieces toward the deadlocked trap, but the home elephant is not available to ensure safe advances of its own friendly pieces. A home hostage-holder often can't easily leave, as the former hostage might then team up with its elephant to force captures in the trap, clearing space for a goal. In fact, the defending elephant often has better prospects for leaving; its friendly pieces might swarm the trap and soon defend it independently. That could be a devastating turn of events for a hostage-holder, as the enemy elephant would become the strongest free piece. To prevent an easy rotation by the defender, a hostage-holder should usually have an additional strong piece standing guard.

Given such costs, one must be selective about hostage-taking. In general, a long-term hostage should only be held by a just-stronger piece; while the silver camel remains, the gold elephant must always be somewhat prepared to confront it, and thus should not be stuck in a corner while that camel is elsewhere. Conversely, it is usually fine for one's own elephant to defend a horse hostage held by the enemy elephant; if the elephants are deadlocked and both camels are elsewhere, the side with the more centralized elephant will have a freer camel, as that camel will face little danger from an elephant in a corner.

A camel could take a horse hostage, but a hostage-holding camel might be vulnerable to the "defending" elephant. To maintain a hostage position, a non-elephant hostage-holder may need supporting pieces. A solid horse-by-camel hostage can be quite effective, however, if the hostage-holder's own elephant is free.

Attacking[edit]

a b c d e f g h
8 Arimaa rs.svg Arimaa rs.svg Arimaa rs.svg Arimaa rs.svg 8
7 Arimaa rs.svg Arimaa rs.svg Arimaa rs.svg Arimaa cs.svg Arimaa ds.svg Arimaa rs.svg 7
6 Arimaa dg.svg 6
5 Arimaa hs.svg Arimaa ds.svg Arimaa eg.svg Arimaa ms.svg 5
4 Arimaa rg.svg Arimaa mg.svg Arimaa dg.svg 4
3 Arimaa rg.svg Arimaa cs.svg Arimaa es.svg Arimaa rg.svg Arimaa hg.svg Arimaa cg.svg Arimaa rg.svg 3
2 Arimaa rg.svg Arimaa hs.svg Arimaa hg.svg Arimaa rg.svg Arimaa rg.svg 2
1 Arimaa cg.svg Arimaa rg.svg 1
a b c d e f g h

In this game, Silver is making threats in c3 and c6.

If a piece cannot be taken as a strong hostage, it can safely advance along with its elephant. When the enemy camel is decentralized, a horse might advance on the other wing. In the game shown, the silver horses advanced with impunity because the gold camel was far away; Gold could have decentralized his elephant to hostage a silver horse, but that would have been a bad move overall.

Trap control concerns one's ability to make capture threats and defend against capture threats in a particular trap. A trap attack entails an attempt to control an away trap and thereby overload the opponent's defenses. If nothing else, an elephant could defend its home trap, but that would often give the attacker opportunities elsewhere. Here, Silver has a strong attack on c3, where he can make multiple captures unless the gold elephant moves to c4, which would leave the a6 dog to be captured in c6.

Seeing his overall weakness in the west, Gold looked east and counterattacked f6, but this was too late; Silver captured two gold pieces in c3 and then forced a rabbit through to goal. Even had the gold elephant defended c3, Gold's long-term prospects would have been bleak; more silver pieces could have advanced in the west, and the silver elephant likely could have gone elsewhere while a team of weaker silver pieces kept shared control of c3. Away trap control creates a space advantage, capture threats, and potential goal threats. Had Gold attacked f6 sooner, there might have been a capture race.

Home and away games[edit]

There are two basic plans: try to take control of an away trap, or aim to create capture threats at home. Since rabbits can't retreat, they can be pulled out gradually. Rabbit pulling was once routine, but fell out of favor as trap attacks caught on. One who simply chases and drags pieces may quickly find a home trap under siege. Homeward pulling has its place, but should perhaps not be one's main strategy.

Instead of thinking in terms of home and away play, one should think about the whole board. For a while, any possible move could be met with a solid defense or counterattack. The object is to attain the stronger overall position.

Elephant mobility[edit]

The elephants are extremely important, but cannot do everything at once. A recurring theme in Arimaa strategy is elephant mobility. Sometimes an elephant gets blockaded, but more often it is restricted by the cost of leaving a particular trap. Before getting into a position that will require one's elephant to stay put, one must consider the opposing elephant's situation. If one elephant is even slightly more free than the other, this can snowball, since it affects how free other pieces are.

Strategy vs. tactics[edit]

a b c d e f g h
8 Arimaa rs.svg Arimaa rs.svg Arimaa cs.svg Arimaa rs.svg Arimaa rs.svg Arimaa rs.svg 8
7 Arimaa rs.svg Arimaa rg.svg Arimaa cs.svg Arimaa rs.svg 7
6 Arimaa eg.svg 6
5 Arimaa rg.svg Arimaa cg.svg 5
4 4
3 Arimaa rg.svg Arimaa dg.svg Arimaa hg.svg 3
2 Arimaa rs.svg Arimaa rg.svg 2
1 Arimaa dg.svg Arimaa es.svg Arimaa cg.svg Arimaa rg.svg Arimaa rg.svg 1
a b c d e f g h

Gold has a far superior board, but will lose the game unless he immediately occupies b2. (Game)

Though strategy is vital, tactics should not be overlooked. A goal wins the game regardless of the rest of the board; a strong position may mean nothing if one forgets to defend goal. Beyond that, one must watch for hanging pieces and false protection. If a player is careless in this regard, the opponent might quickly gain ground.