Arimaa/Frames
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The gold elephant is pinned to the horse framed on c6. |
A piece held on a trap square, securely surrounded on three sides, has been framed. In this game, Silver framed a gold horse on c6; a phalanx stops the framed horse from pushing onto c7. The gold elephant is pinned: if it takes one step, the framed horse will disappear.
A pinned piece is more stuck than a hostage defender, which can at least move between key squares or otherwise step away during a turn. Here, it would be pointless for the pinned gold elephant to break the phalanx; even flipping the d7 rabbit would instantly lose the framed horse. If a pinned piece abandons a framed piece, the framer won't even use up a turn making the capture, since the piece is already gone. This strength of frames is balanced by the high material cost of maintaining them.
When possible, a framer should rotate out strong pieces, replacing them with the weakest ones which can reliably hold the frame. If the a5 horse moves to c5, the silver elephant will be the strongest free piece, although it may not be totally free if Silver wants to avoid an even horse trade.
Even if elephant rotation is not feasible, a framer will often have a mobility advantage. Gold would instantly lose the framed horse if he moved his elephant, whereas Silver could move his elephant at no cost other than giving up the frame. It would thus be risky for the gold camel to advance, whereas the silver camel is already in Gold's home territory.
A frame is broken when a framing piece is dislodged. A frame might be broken from the side or from behind, but here Silver can likely prevent either maneuver. With the gold elephant pinned, the gold camel is the only piece that could dislodge a silver horse, but Silver could likely stop such an intrusion in the west. Gold might instead aim to break the c7 phalanx; with the gold elephant immobile, this would require a gold piece to advance and begin a turn active on e7 or d8. If this piece could pull away a rabbit, the c6 horse could then push its way out. Silver can strengthen the phalanx by sliding the d7, c7, b7, and a7 pieces east.
A frame's value depends on each side's free pieces. This frame should be very strong once the silver elephant rotates out. By contrast, a breakable frame may backfire on the framer, since the formerly framed piece could become an attacker. On a depleted board, a horse frame may not be worth the material it uses, as the framer could become thin on the other wing. A dog or cat frame could be wasteful at any juncture; a framer must always weigh the cost of keeping material tied up in the frame.
Elephant position
[edit | edit source]When a frame is already in place, it is too late for the pinned piece to choose its square. In general, however, d6 is a strong square for an advanced gold elephant, and this often holds true when that elephant is pinned:
- With the pinned gold elephant on d6, the frame requires a silver piece on c5 (except in the case of rabbit frames). If the silver elephant goes east, the c5 piece may be vulnerable to capture in c3.
- The pinned gold elephant on d6 stops Silver from moving the framed piece onto d6 or e6 for a fork.
- For the gold elephant, d6 is a better attacking square than c5. If the frame can be broken, Gold may then have a strong attack on the c6 trap.
If the framed piece is not at imminent risk of capture in f6, however, c5 is an acceptable square for the pinned gold elephant. In fact, this may make it easier for a gold piece to break the frame along the b-file.
Camel frames
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Gold combines a camel frame with a horse hostage. (Game) |
When an elephant is pinned to a camel framed by the enemy camel and elephant, the four strongest pieces are all tied up. If the framer cannot rotate out his elephant or camel, the horses may decide the game. Due to elephant mobility, the framer's horses might be freer than their enemy counterparts, but the framed side might counter this by partially blockading the framing elephant and/or setting up a strong attack should it leave.
If the framing elephant or camel can be replaced by a phalanx of weaker pieces, the framer will have the strongest free piece while still rendering the two strongest enemy pieces completely immobile. The diagram shows another strong type of camel frame, in which a horse is held hostage by the framing camel. There is no single strongest free piece, but Gold has two free horses against Silver's one. Gold's progress may be slow, but Silver has little counterplay, having so much to lose if she abandons f3. A hybrid frame-hostage can be very strong, if balance is maintained.
Away frames
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An away horse frame. |
In the course of a trap attack, it is sometimes possible to frame an enemy piece in its own home trap. On 13g of this game, Gold used a pull-and-replace to frame a silver horse in f6. If the pinned silver elephant were to move, the horse would be lost instantly, and more silver pieces could quickly follow.
The one potential threat to the frame is the silver camel. If the silver camel went east, however, the gold camel could dominate the west. Gold might get a strong attack on c6 before Silver could break the f6 frame and free his elephant.
Gold should not attempt to directly rotate anything out of this frame; a phalanx would not be viable, and replacing the gold elephant with the camel might allow Silver to get a horse-for-camel trade if the gold elephant didn't stand guard. However, Gold can advance more pieces in the east and perhaps eventually give up the frame but keep shared control of f6 even with his elephant elsewhere.
Non-elephant pins
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The silver camel is pinned to the c3 cat, and both pieces will be at risk if the gold elephant can step to d4. |
A dog or cat frame which ties up the framer's elephant is usually not worthwhile. In this game, however, Gold's cat frame was strong, pinning down both the silver elephant and camel. With the silver camel pinned to the c3 cat, the silver elephant must stay on d4 to defend both the cat and camel. This leaves the gold camel as the strongest free piece; if this will remain so, the silver camel should abandon the cat.
However, Silver might hope to replace the elephant with a phalanx; this might also require a piece on c5 or b4 to prevent a flip. A d4 phalanx would divide up the board; the gold elephant might be forced to give up the frame and make its way east, but then the position would be unclear. If the silver camel were instead pinned on b3 while protected by a b4 phalanx and a piece on c5 or d4, Silver's shared trap control could be fairly solid. See, for instance, the blockade on 29s of this game.
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Gold to move can frame and then capture the e3 horse. |
On 28g of this game, Gold played a pull-and-replace to create a frame which then forced a horse capture, as Silver could not keep the pinned dog in place or add a defender.
Elephant frame
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If the gold camel can dislodge the pinned silver horse while the silver elephant is still on f3, the elephant will be captured. |
An elephant frame is occasionally possible, if an elephant has chosen to occupy a trap square. If the pinned piece can be dislodged, the framed elephant will be captured. On 12s of this game, Silver did not see the risk to his elephant. It is not always bad to place one's elephant on a trap square, but extreme caution is needed; an elephant should never be left in a trap that is not adequately defended.
Horse baskets
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The gold horse cannot escape, and might soon be framed. |
In this position, the gold horse is in a basket: it is blocked on three sides, so that no escape is possible even if it is unfrozen from the fourth side. Silver to move could flip the gold horse into the trap, creating a frame which the silver elephant might soon rotate out of. Gold to move might possibly prevent a frame via congestion, if he can occupy both f4 and e5 while still defending the trap. Alternatively, Gold could delay the frame by flipping the e7 dog, although this might lose time if Silver plays correctly. With e7 empty, Silver should not flip the gold horse into the defended trap, as the horse could then push onto f7, where it would be well placed. Instead, Silver might pull the gold horse to f5 and move the h5 horse to g5, fencing the gold horse next to the trap. On Silver's next turn, the gold horse could be pushed into the trap in two steps, leaving another two steps to reestablish the phalanx.
Since rabbits can't retreat, a silver rabbit on the wrong square could end up blocking the intended frame. A silver rabbit on e7 could be flipped into the trap. A rabbit on f7 would make a fence less effective; with the gold horse on f5, the gold elephant could pull an f7 rabbit into the trap.
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Gold to move can prevent a frame. |
To force a frame, a basket-holding elephant must usually be next to a trap. With f5 open, the gold elephant could take two steps and prevent a horse frame. The silver elephant might then have to move west to avoid a blockade.
Frame-breaking tactics
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A breakable frame may end badly for the framer. With Silver to move in the diagram at left, the silver horse can reach b3 via the pull-and-replace mb5sn Hb3n hc3w. Gold could restore the frame with a pull-and-replace of his own, but this would recreate a position which Gold has already created once. Silver could then repeat her previous move and force Gold to do something different. With the frame broken, Silver will have a good position: the formerly framed horse will be a strong attacker, and the camel might pull the gold horse to c6.
Gold to move could delay the frame-break with Ec4ns mb5e. If there is a silver piece on d5 or c6, however, the camel could return to b5 in a single step, thus undoing in one step what Gold did in three. Instead of wasting steps and letting Silver strengthen her position, Gold to move might flip the silver horse to b4; the horse might escape, but at least it wouldn't take b3. The advanced silver rabbits might then be vulnerable.
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The second diagram shows a similar position, but with the silver camel on b4 rather than b5. Now, the frame can be broken in three steps (mb4n Hb3n hc3w), but there is a complication: Gold could restore the frame with a pull-and-replace (Ec4sn hb3e Hb4s), and this time Gold would create a new position, since the silver camel would not be where it was after Gold's last turn. For this same reason, Silver would then need four steps for her own pull-and-replace, and thus would create the exact position she created the first time she broke the frame: the silver camel on b5, the gold horse on b4, the silver horse on b3, and nothing else different since she had no extra step. Gold could thus restore the frame and win the repetition fight, unless Silver found a different way to break this frame:
- mb4n Hb3n hc3w Cc2n pulls the gold cat into the trap to prevent Gold's pull-and-replace. This is the simplest, and thus most common, maneuver to break such a frame.
- mb4n Hb3n hc3w ed3w: The silver elephant occupies the c3 trap, and the silver horse cannot be dislodged from b3. An elephant occupying a trap must be very careful not to get captured.
- mb4n Hb3n ra3e ra4s: Silver rabbits block the gold horse out of b3.
- mb4n Hb3n mb5e Hb4n: By moving her camel to c5 and pulling the gold horse to b5, Silver establishes a phalanx which stops the gold elephant from stepping forward and unfreezing its horse. Gold could unfreeze the horse from below, but then the horse couldn't return to b3.
If a camel flip were possible, it would at least buy Gold some time. The d4 cat prevents a camel flip; a silver piece on c5 would do the same job.
In both diagrams, Silver's a4 rabbit keeps the camel unfrozen on b4. If instead a gold piece were on a4, the frame would be stronger.
Another way to break a frame is to take an additional key square while the framed piece is still in the trap. If a3 or b2 were empty, the silver camel could itself occupy b3, pushing the gold horse away. The camel might then be taken hostage, but the formerly pinned elephant might quickly rotate out of hostage defense.