Arimaa/Elephant and Horse Attacks
Objectives and Risks
The Elephant and Horse Attack (commonly known as the “EH Attack” or “E+H Attack”) is a very popular system and is seen much more frequently than the Elephant and Camel Attack due to the high risks involved with the latter. The important distinction is that the attacker’s Camel remains safe during an Elephant and Horse Attack and can be used to counterbalance the defender’s Camel. In the Elephant and Camel Attack, by contrast, the defender’s Camel becomes quite powerful if the attacking Camel is taken hostage and the cost for abandoning the hostage is more severe for the attacker. The Elephant and Horse Attack is currently very effective against the best computer programs but there is not yet a consensus in the Arimaa community as to whether the E+H Attack is the best system to use against a strong human defender.
Note: For simplicity, many examples below will assume that the Gold player is attacking the c6 trap. Naturally, the same theories can apply equally to attacks on all 4 traps.
Reasons to use the Elephant and Horse Attack:
- to trap enemy pieces when the enemy Elephant is too far away, or unable, to defend the trap
- to create a wall with two strong pieces so that a Rabbit may be advanced along the outside
- to distract the enemy Elephant from the opposite wing
- to encourage a Horse hostage in order to decentralize the enemy Elephant
- to encourage a Horse hostage in order to attempt an Elephant blockade
- to encourage a Horse hostage with the intention of swarming the trap with small pieces and releasing the attacking Elephant
Summary of risks (assuming Gold attacks the c6 trap):
- the Horse may be taken hostage
- the Horse may be framed – this is a major disadvantage if the attacking Elephant is pinned to the c5, b6 or c7 square
- the opposing player may be able to begin an attack on the trap just vacated by the Horse and/or Elephant
Ideal Placement of Pieces
The attacker should employ the Elephant and Horse attack against a trap that does not have a defending Camel. It is often disastrous if the Horse is taken hostage by the Camel and the attacking Elephant becomes decentralized during a rescue operation.
When attacking an enemy trap, a very effective plan is to place the Horse on b6 and the Elephant on d6. The advantages are:
- if the enemy Elephant cannot reach c5, it is usually difficult for the defender to place a piece on c5, making it problematic to defend the trap – even if a defender can reach c5 it may still be in danger of being pushed towards the c3 trap
- if the Horse is taken hostage it will be safe from the f6 trap
- if the Horse is framed, the Elephant is ideally placed on d6 – it can be quite disadvantageous for the attacker if the Gold Elephant is pinned to c5, b6 or c7
- the Horse cannot become forked on the d6 square while the Elephant is standing there!
- the Horse is located as far as possible from the enemy Elephant and Camel while still maintaining a convenient escape route along the ‘a’ or ‘b’ file – this becomes especially important if the Gold Elephant ever moves away from the c6 trap
- the Horse can effectively assist an advancing Rabbit on the ‘a’ file
- if the Gold Horse occupies b6, then the Silver Horse is denied its ideal defensive square
- the defensive position becomes highly cramped
If there is a Silver Rabbit on d8, it is usually a good idea to pull it to d7 with the Elephant:
- it will become an obstacle for a Silver Camel that is located behind the f6 trap
- the Rabbit may be captured after Gold controls the c6 trap
- a Silver defender is removed from the back rank for the benefit of any advanced Gold Rabbits
The attacking Horse can also occupy the c7 square rather than the b6 square in order to capture an enemy piece on c8, just as a Camel often does during an Elephant and Camel Attack. However, this is sometimes dangerous for the attacking Horse and some players prefer to simply leave the Horse at b6. The major problem is that during an Elephant and Horse Attack on c6, the enemy Camel often lurks at a nearby square, such as f7. And that Camel would love nothing more than to hold the Horse hostage behind the c6 trap in order to either paralyze the Elephant, or lure it behind the trap. Before the Gold Horse is moved to c7, it is prudent to ensure that the Silver Elephant cannot create any threats that will distract the Gold Elephant from the c6 trap.
If the defender has many pieces near the trap, it may be necessary to advance a third attacker in order to quickly seize control of the trap. If possible, the third attacker should be a Dog, or weaker, so that the other Horse and the Camel can be used defensively.
Defensive Systems and Counter-Attacks
There are a few simple and effective prophylactic measures that the defender can use to prevent or delay the Elephant and Horse Attack. By placing defending Horses on the outside of both traps (on the ‘b’ and ‘g’ files), the enemy will need to devote some extra moves to first pull the Horse away from the square, then occupy it with the attacking Horse. The defending Elephant will usually arrive on the scene long before the attacker can accomplish his/her objectives. A second possibility is to guard the trap with both a Camel and a Horse – of course, the opposing player may simply attack the other trap in that case! A third preventative measure commonly used is to threaten an Elephant and Horse Attack on the same wing. For example, if Horses are defending traps at b3 and b6 and then Gold Elephant moves to the b5 square, the Silver Elephant can simply move to the b4 square and neither player will successfully carry out the Elephant and Horse Attack – not yet.
If the prophylactic measures fail, and the opposing player does carry out an Elephant and Horse Attack there are several defensive options:
- occupy the c5 square with the Elephant in order to neutralize the attack
- take the Horse hostage with the Elephant – current Arimaa theory considers this to be a dubious decision
- use the Camel, possibly with supporting pieces, to counter-attack on the opposite wing – there is a risk involved because the Gold Elephant may decide to abandon the Horse in order to pursue the Silver Camel
- launch an Elephant and Horse Attack on the same wing – if both armies can maintain 2 defenders on the traps then a curious, but temporary, stalemate sometimes occurs
- launch an Elephant and Horse Attack on the opposite wing – this is much riskier than an attack on the same wing because mutual attrition followed by a Rabbit race on opposite wings becomes a distinct possibility
- create a distraction for the Gold Elephant so that the c6 trap will be abandoned
Another tactic that the defender can use with the Silver Elephant on c5, Silver Horse on b7 and Gold Horse on b6 is to pull the attacking Horse down to b5 (returning the Elephant to c5) and then move the defending horse onto b6. From the d6 square, the Gold Elephant cannot assist the Gold Horse in returning to b6. Similarly, if there was a defending piece on c7, the Silver Elephant could pull the Gold Horse to c6 and then occupy b6 with the Silver Horse. This would force the Gold Horse to escape through the c7 square (if possible) in order to avoid being framed.
Ideas for Setup
An Elephant and Horse Attack can be commenced with the first moves of the game, and for this reason nearly all players setup either Horses or the Camel on the b2, g2, b7 and g7 squares. The Horses on these files have the dual purpose of threatening, and defending against, an Elephant and Horse Attack. A balanced distribution of forces is essential for defending against an attack; if one home trap is defended with 2 Horses and a Camel, the opposing player is likely to attack the opposite trap.
Most players like to assign their Camels in a defensive role during the opening of the game. For those players, the Camel is an ideal defender against the Elephant and Horse Attack and is often setup in the middle or behind a trap and, more importantly, the Camel’s mobility should be maintained during the game so that it can easily move from one home trap to the other. Players that do not use the Camel defensively against the Elephant and Horse Attack may setup with it located on the ‘a’, ‘b’, ‘g’ or ‘h’ file for possible offensive action.
Dogs and Cats are very often setup behind the home traps. They are very effective in those positions but they will require three supporting pieces to maintain a Horse frame on the trap. Another possibility is to setup Dogs and Cats on a2, a7, h2, or h7 for the job of unfreezing the trap defenders that are attacked by the enemy Elephant on the ‘b’ and ‘g’ files. This is sometimes preferable to advancing Rabbits for the same purpose.
At the current time, most players like to setup four Rabbits on the ‘a’ and ‘h’ files and no Rabbits on the ‘d’ and ‘e’ files. There are several ideas behind this setup related to this chapter:
- Rabbits in the middle of the home territory may become obstacles for defensive pieces that desire to move between traps, especially on the 2nd and 3rd ranks
- if the enemy Elephant attempts to pull a stronger piece from the 'b' or 'g' file then the 2nd rank 'a' or 'h' file Rabbit can be advanced to unfreeze the stronger piece with one fewer step than a 1st rank ‘a’ or ‘h’ file Rabbit
- Rabbits can be advanced on the perimeter more safely than in the middle
- outside, 2nd rank Rabbits are one step closer towards participating in an Elephant blockade on the ‘b’ file
- Rabbits advanced up the middle of the board may be exploited by the enemy to blockade the friendly Elephant in the 6th rank middle
- players that prefer to generate goal threats on the outside, rather than the middle of the board, like to stack extra Rabbits on the 'a' and 'h' files
Against an opponent that enjoys using the Elephant and Horse Attack, it is not recommended to place Rabbits behind a home trap on c2, f2, c7 or f7. They are awkward and vulnerable defenders against the E+H Attack.
If Both Camels Have Been Trapped
If each player traps the enemy Camel plus one Horse, the strategic situation will be identical to the one that arises after all four Horses are trapped and the Camels remain on the board (because the relative strengths and distribution of pieces are equivalent). Therefore, if each side has no Camel and one Horse, the Elephant and Horse Attack contains all of the risks that would be associated with an Elephant and Camel Attack with four pieces removed from the board. As such, both players should consider alternative strategies that do not expose the second strongest remaining piece to a hostage situation.
If Attacker’s Camel Has Been Trapped
If the attacker has already lost the Camel (hopefully some compensatory enemy piece(s) were captured), then the Elephant and Horse Attack is usually a strategic mistake. It involves all of the same risks that were discussed in the Elephant and Camel Attack chapter due to the power of the unopposed enemy Camel; only in exceptional circumstances would the attack be beneficial.
A player that has lost the Camel but gained smaller piece(s) as compensation should instead consider strategies that involve goal threats, blockades, obtaining a Camel hostage, or creating an open tactical game in which the enemy Camel cannot effectively participate.
If Defender’s Camel Has Been Trapped
If the opposing player has already lost the Camel in exchange for a couple of weaker pieces, there are differences of opinion amongst Arimaa experts about whether the side with the Camel should use the Lone Elephant Attack or the Elephant and Horse Attack. The ideal strategy can vary considerably from one situation to the next, so both players will need to rely upon judgement and experience rather than relying upon rules carved in stone.
Horse Frame Theories