Arimaa/Trap Control
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Silver's long-term threat to c3 is strong. |
Trap control is related to ownership. A trap might be fully controlled by one side, or might be shared. At the outset, each player essentially has full control of his two home traps. Trap control depends on the key squares, especially the decentralized ones (e.g. b6 and c7 in the northwest, b3 and c2 in the southwest). Getting a non-elephant safely onto a decentralized key square of an away trap is usually an important step toward wresting control of that trap. Even if one doesn't take full control of an away trap, strong shared control can impact the rest of the board.
On 5s of this game, a horse procured a long-term trap control advantage for Silver. With a silver horse already behind the c3 trap, Silver would likely win an EMH attack race, so Gold needs to defend that trap. It is not clear whether Gold has any good way to do so, however. If the gold camel comes west to defend, Silver can still attack that trap and threaten the camel and other pieces with quick capture. If the gold elephant defends, Gold will have a poor alignment, as his elephant will be fighting a horse; furthermore, Silver could still advance more pieces in the west and perhaps rotate his own elephant out of that fight.
Deadlocked Traps
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There is an elephant deadlock at f6 and a camel deadlock at c3. (Game) |
A trap is deadlocked when its strongest gold defender and strongest silver defender are equal. In the event of an elephant deadlock, no capture can happen in the deadlocked trap until an elephant chooses to leave. If both elephants stay beside the same trap, it is usually because both sides have a large stake there. Remember that a hostage position can tie down both sides, as a hostage might become an attacker if the hostage-holder simply leaves. Here, the silver elephant is not holding a hostage, but is defending against an attack which more gold pieces might soon join.
A camel deadlock will hold only so long as neither elephant can be bothered to break it. Despite Silver's material advantage, she has more to lose than does Gold, as a threat to the silver camel would by extension threaten the horse which it defends. Gold's attack on f6 is well ahead of any possible trap attack by Silver, who would need to get the gold camel off of b3 in order to make any capture in c3. Gold can now move his horse to f7, setting up a potential attack on c6 or swarm of f6, either of which could allow the gold elephant to go west and create a strong second threat. Even though there are currently multiple deadlocks, this game is likely to move quickly.
Since no capture is possible in a trap defended by both elephants, the player whose home trap is deadlocked is often at a space disadvantage. Enemy pieces can safely advance toward such a deadlock, whereas the home elephant would have to leave if it wanted to ensure safe advances of its own pieces. One unprepared to make a strong threat elsewhere on the board should avoid getting into a home elephant deadlock, as the opponent can work such a deadlock to his advantage if he has time. Here, Silver could have kept a horse in the east and defended f6 without her elephant.
Stronger vs. weaker pieces
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At each trap, the strongest local piece faces multiple weaker pieces which protect each other. |
Shared trap control also occurs when one side has the strongest local piece, but the other has multiple weaker pieces which protect one another from capture. After 23s of this game, all four traps were contested in such a manner. A capture can happen only when one side gains full control of a trap. When a strong piece moves from one fight to another, the area it leaves could be affected; here, Gold would face at least a horse loss in f6 if he moved his elephant away from that trap. A position with multiple trap control fights may become a race if each side prioritizes offense.
Losing control
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As long as Gold owns no trap, Silver has nothing to fear. (Game) |
Silver currently defends all four traps, and will face no capture threat until Gold can change that. The gold elephant can't take a strong hostage, and can't afford to leave c3. Even if one can take a seemingly strong hostage, it won't ultimately be effective without a second threat. To have any chance here, Gold must advance his camel and reassert full control of f3; if that draws the silver elephant east, Gold can then own c3 instead of f3. Once Gold owns a home trap, he might then attack the away trap on that wing. It is crucial to own at least one trap, so that the opponent is somewhat limited by capture threats.
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To gain ownership of a trap, Silver must attack one of Gold's home traps. |
After 15g of this game, Gold had strong shared control of f6 even without his elephant directly beside it. Consequently, Silver owned no trap and was close to being overloaded. Silver's only chance is to attack c3 or f3, perhaps advancing her eastern horse, which is of no use around f6. The silver elephant should defend f6 for now, but might eventually join an attack. Even if the gold elephant leaves c6, Silver may not have time to pull pieces toward it.