Arimaa/Introduction to Strategy/Distribution of Force
|Neither gold horse can fight either silver dog. (game)|
An important element of Arimaa is the overall distribution of pieces. One basic concern is efficiency: one should use the weakest piece possible for any particular job, sparing stronger pieces for other duty. Another is activity: pieces should be kept flexible and available for duty. In the diagram, the b2 gold horse is passive, since its development is blocked and it cannot easily do anything useful. The a3 gold horse is less blocked, but still poorly placed, as it is very far from both silver dogs. In the east, the silver dogs are as strong as horses, as the gold camel and elephant are the only threats they face. Silver is thus correct to have dogs on g3 and g5, leaving the actual silver horses more centralized.
Although a common cause of passive pieces is a home deadlock preventing development, even a functional advanced piece is passive if it does not usefully fight for trap control.
The rest of this page discusses the distribution of the army as a whole.
In the study of trap control fights, it is clear that an important factor is which side has the strongest local piece. For example, a camel and a dog can take control of a trap against two horses, but not vice versa. The strongest local piece creates an advantage with goal attack, goal defense, mobility fights, etc. In each situation, a camel and a dog will tend to win a fight against two horses. Because of the importance of the strongest piece, the points on this page tend to apply more strongly to stronger pieces.
|Silver is dominating the entire board (game).|
Alignment refers to the general positioning of the army relative to the opposing army. An efficient alignment is one where each piece dominates the next-weaker opposing piece, while avoiding the next-stronger opposing piece. Elephants should attack camels, camels should attack horses while avoiding elephants, horses should attack dogs while avoiding camels, etc.
In the diagram, Silver has a large alignment advantage: the silver elephant is fighting the gold camel, the silver camel is fighting gold horses, the c2 horse is fighting a gold dog. The silver camel and horse are both strongest local pieces, while Gold does not have the strongest piece in any part of the board.
In this endgame, Silver had a camel advantage, but still let the one remaining gold horse beat her. When it went north on 36g, Silver took no notice. With nothing to stop the gold horse in the northeast, it created a one-turn goal threat on 38g. At that point, Silver had only one way to stop it, and that left her elephant on the f3 trap square. The elephant was lost.
It is generally best to split strong pieces, so as to get a strong piece into each local fight. In the position at right, from this endgame, Gold has split his horse and dog; the dog has just advanced in the west, and the horse is poised to advance in the east. The silver elephant cannot fight both at once, but would do best to confront the horse, which could dominate the east in the event of an elephant deadlock at c6. This leaves the question of what to do about the northwestern threat.
Silver has no use for two dogs in the east; a second dog is not needed to defend f6, and doesn't improve Silver's prospects for taking over f3. The e7 dog should move west, to counter the gold dog and delay any Gold takeover of c6. In the actual game, Silver left both dogs in the east, and soon got into trouble. Had Silver balanced his dogs, his elephant could have then confronted the horse instead of the dog. Had Gold then pursued a takeover of c6, Silver might have taken over f3.
|In this game, the silver elephant is stuck defending a horse and dog, but the gold elephant is stuck defending goal.|
It is also often important to balance weak pieces, which are vital to home defense and to goal threats. In this diagram, Gold holds an apparently strong frame-hostage, but is very weak on the other wing. The gold elephant appears to be the strongest free piece, but is actually stuck defending goal, and will still need at least one friendly piece to block the goal line. Defending against rabbits is an extremely inefficient use of the elephant.
|The decentralized gold elephant cannot help the gold camel if it advances, thus the silver horse is safe on g3. game|
Ideally, an elephant should be able to quickly get anywhere it might be needed. Thus it should stay fairly centralized, unless it could decidedly improve its side's overall position by going to the outskirts. Control of the center itself is also important: if enemy pieces are blocked or threatened in the center, they will have a harder time getting where they want to go.
The diagram illustrates the tactical dangers of elephant decentralisation. The gold elephant has gone far away from f3, allowing Silver to start an attack there. Usually attacking with a horse near the opponent's camel would be a bad idea, but until the gold elephant comes east, the gold camel cannot safely chase the g3 horse. If Gold played Me2n De1n Me3e De2n, Silver could push the gold camel to f4 (De3s ee4s Mf3n ee3e), where it would be doomed in f6. This would not work for Silver were the gold elephant in the centre.
The value of centralisation also applies to other pieces, but this is a trickier issue since they may be unsafe in the centre, at least at the beginning of the game. In this diagram, the blockade of the silver elephant means that the gold camel is free to take a fairly centralised position; the dogs are also ready to enforce Gold's central control. Any silver piece that goes into the centre risks being forked between c3 and f3. Gold's whole army therefore has more freedom of movement than Silver's.
Shared control of an opposing trap is also an opportunity to take central control, since if the opponent has complete control of only one trap, pieces in the centre are often safe. The diagram in Arimaa/Introduction to Strategy/Elephant Blockade#The Center is an example of this.
|In this game, Silver's advantage is partly a result of Silver's better development.|
When one army is more advanced than the other, the more advanced army, besides having more room to maneuver, gets the first chance to attack. Since the opponent must then divert resources to defence, this could result in a serious initiative.
Note that, in the diagram, some material is missing from both sides, which makes the value of advancement clear. In the opening, the value of having advanced pieces is less clear and depends on the attacking possibilities. It is usually good to have advanced pieces on a wing where one may get a strong attack—for instance on one's camel wing if camels are on opposite wings in the opening. In a slow opening the attacking potential of advanced pieces may be outweighed by the opponent's ability to threaten them in their home traps.
Of course, the need for development must be tempered by the need to defend the home traps and goal line. If direct home defense is sparse, the advanced army must stop threats from getting that far.
|Gold is blocked in the west, and vulnerable in the east. (Game)|
In the position at left, the board is still full, but Silver has developed to a point where Gold would have trouble advancing anything. Gold is severely blocked in the west, and any gold piece that advanced in the east would risk quick capture in f6. If the gold elephant went east, the silver camel could force captures and then perhaps a goal.