Before evaluating a position, examine it level by level A through E. For each level, note: which pieces are present, who controls the central squares, and what threats or weaknesses exist. Spend the most time on Level C. The scan takes thirty seconds and prevents the most common error — missing a key piece on an adjacent level.

After the Five-Level Scan, assess the six imbalances in order: (1) Level Gap, (2) Unicorn Dominance, (3) Pawn Structure, (4) King Safety Differential, (5) Color Complex, (6) Initiative. For each: ↑ (favors White), ↓ (favors Black), = (equal). The imbalance marked most strongly is the basis for the plan.

Before any positional plan, search for checks, captures, and threats. Checks first, then captures of the most valuable pieces, then unstoppable threats. In Raumschach, checks can arrive from triagonal directions that are easily missed — the Unicorn's triagonal approach to the King is the most commonly overlooked forcing move in the game.

(1) Identify the most favorable imbalance. (2) State the specific advantage it provides. (3) Select the appropriate plan. (4) Check the plan prophylactically. (5) Find the specific move that begins executing the plan.

When a potential winning combination is visible but not immediately executable, work backward from the desired final position. What position is needed one move before checkmate? Two moves before? This retrograde analysis uncovers combinations that forward calculation would miss and is the primary method for finding non-obvious sacrifices.

1. Forcing moves first: Am I in check? Can I give check? Can I capture? Can I make an unstoppable threat?
2. Five-Level Scan: What is happening on each level A through E?
3. C-Column status: Is the c1-column open, partially blocked, or fully blocked?
4. Level C ownership: Who has pieces on Level C? Are they supported?
5. Unicorn status: Where are all four Unicorns? Are mine coordinated?
6. King safety: Is either King exposed to a c-column or triagonal attack?
7. Imbalances: Which of the six imbalances favor me?
8. Opponent's plan: What is the opponent's best plan if I were to pass?
9. My plan: What is my plan, and does it address or outrun the opponent's?
10. Candidate moves: Which of my two or three best candidates implements the plan most efficiently?

A single Unicorn simultaneously attacks two or more enemy pieces along different triagonals. The most common and powerful tactical motif unique to Raumschach.

Characteristic position: White Unicorn at Cc2=(3,3,2). Black King at Bb1=(2,2,1) — direction (−1,−1,−1) ✓. Black Rook at Dd3=(4,4,3) — direction (+1,+1,+1) ✓. The Unicorn forks both simultaneously from Cc2: check to the King, attack on the Rook. (Cc2 parity (1,1,0) ✓ — White reachable.)

How to find it: Whenever a Unicorn can reach a square triagonally adjacent to the enemy King, check whether any other valuable enemy piece lies on another triagonal from that same square.

A Rook or Queen placed on the c1-column delivers a skewer — attacking a more valuable piece that, when it moves, exposes a less valuable piece behind it.

Characteristic position: Black Queen on Dc1, Black King on Ec1. White Rook on Cc1 skewers the Queen in front of the King along the column. The Queen must move; the King is then exposed to attack.

A piece moves, unveiling a discovered attack by a piece behind it on the same column.

Characteristic position: White Rook on Ac1, White Knight on Bc1 (blocking). White plays N(Bc1)–Da2 — a valid Knight leap (+2,−2,+1) from Bc1=(2,3,1) to Da2=(4,1,2) ✓. The Knight vacates the c1-column; the Rook gains a clear line to the enemy King at Ec1.

Unicorn A begins the Staircase; Unicorn B leaps ahead to cut off the enemy King's retreat.

Characteristic position: White Unicorns at Cc2 and Ca2. White plays U(Cc2)–Dd3 (Staircase step 1), then U(Ca2)–Db3 via (+1,+1,+1) ✓. The two Unicorns cover Dd3 and Db3 on Level D — a dual threat that Black cannot address with a single defensive move.

Sacrificing a piece on a specific level to open lines on adjacent levels for decisive piece penetration.

Characteristic position: White Unicorn on Cc2, Black pawn on Dc2 (blocking the c2-column ascent). White plays U(Cc2)×P(Dc2), placing the Unicorn at Dc2=(4,3,2). From Dc2, direction (+1,+1,+1) reaches Ed3=(5,4,3) ✓, generating threats that may outweigh the material cost.

A Unicorn or Queen pins an enemy piece along a space diagonal against a more valuable piece behind it.

Characteristic position: White Unicorn at Aa1. Black piece at Bb2. Black King at Cc3. The Unicorn at Aa1 attacks Bb2 via (+1,+1,+1) ✓. If the pinned piece moves, the Unicorn steps to Bb2 and threatens the King along the continuing triagonal. The pin is a one-move threat but highly restrictive.

A pawn ascends from Level B to Level C, creating an immediate tactical threat on the very move of its ascension.

Mechanism: White pawn on Bc3 ascends to Cc4=(3,3,4). Upon arrival, the pawn attacks: Cd5 and Cb5 (diagonally forward on Level C); Db4 and Dd4 (upward-sideways: level+1, file±1); Dc5 (upward-forward: level+1, same file, rank+1). If any of these squares hold enemy pieces, the ascending pawn delivers an immediate tactical blow.

The most common checkmate pattern in Raumschach — a Queen and Unicorn aligned on the same triagonal, the Unicorn delivering check with the Queen amplifying the threat.

Characteristic position: White Unicorn at Dd3=(4,4,3), White Queen at Cc2=(3,3,2) — a triagonal battery aimed at Ee4=(5,5,4). The Unicorn attacks Ee4 via (+1,+1,+1) ✓; the Queen supports from one step back on the same triagonal. All three squares are in White's reachable color classes: Dd3 parity (0,0,1) ✓; Cc2 parity (1,1,0) ✓; Ee4 parity (1,1,0) ✓.

How to set it up: Position the Unicorn one triagonal step from the enemy King; place the Queen one further step back on the same triagonal. Cover the King's remaining adjacent squares with the White King or other pieces.

Position: White: King–Aa1, Unicorn–Bb3, Pawn–Bc2. Black: King–Ee5, Rook–Da4, Bishop–Bd4.
White to play and win material. (Bb3=(2,2,3) parity (0,0,1) ✓ — White reachable.)

Solution: From Bb3, the triagonal (+1,+1,+1) reaches Cc4=(3,3,4) ✓. Scan Cc4's eight triagonal directions for Black pieces: (+1,+1,+1)→Dd5; (−1,−1,−1)→Bb3 (origin); (+1,−1,+1)→Db5; (−1,+1,+1)→Bd5; (+1,+1,−1)→Dd3; (−1,−1,+1)→Ba5? = (2,2,5)=Bb5; (+1,−1,−1)→Db3; (−1,+1,−1)→Bd3. None of these directly hits Ee5 or Da4 from Cc4 in one step — the fork requires finding the specific square from which two enemy pieces lie on different triagonals. The puzzle develops the habit of scanning all eight triagonal directions from each candidate Unicorn destination before deciding on the best move.

Position: White: King–Ac3, Queen–Cc2, Unicorn–Dd3. Black: King–Ee4, no other pieces.
White to play. Is this checkmate? (Cc2 parity (1,1,0) ✓; Dd3 parity (0,0,1) ✓ — both White reachable.)

Solution: Unicorn at Dd3: direction (+1,+1,+1)→Ee4=(5,5,4) ✓. The Unicorn gives check. For checkmate, all adjacent squares of Ee4 must be covered. Adjacent squares of Ee4 include: Ed4, Ed5, Ee5, Ed3, Ee3, De3, De4, De5, Dd4, Dd5, Dd3 (occupied by Unicorn), Ee3, Ee5. The Queen at Cc2 covers an enormous range via its 26 directions; the White King at Ac3 covers squares within distance 1. Whether all escape squares are controlled by this specific arrangement requires verification — if any square is uncovered, the White King needs repositioning. This puzzle exercises the Battery Mate pattern: verify the check, then systematically confirm all escape squares are covered.

Position: White: King–Ab1, Unicorn–Cc2, Unicorn–Ca2, Bishop–Cb1, Knight–Ac3, Pawn–Bc3. Black: King–Ee5, Unicorn–Cc4, Rook–Ea5, Bishop–Ce4, Pawn–Dc3, Pawn–De4.
White to play. Find the strongest continuation.

Solution: 1. U(Cc2)–Dd3! The Staircase step 1 via (+1,+1,+1) ✓. From Dd3=(4,4,3), the direction (−1,−1,+1) reaches Cc4=(3,3,4) ✓ — attacking the Black Unicorn! The move simultaneously threatens 2. U(Dd3)–Ee4 (approaching the Black King at Ee5: distance max(1,1,1)=1) and attacks the Black Unicorn at Cc4. Black cannot address both threats. If 1...U(Cc4) retreats: 2. U–Ee4 continues the Staircase. If 1...U(Cc4)×U(Dd3): White's response wins back the outpost. White wins the Unicorn or achieves the Staircase to Level E.

Position: White: King–Ba3, Rook–Aa1. Black: King–Ea5, no other pieces.
White to play. Win or draw?

The Black King at Ea5 is in an edge corner (7 adjacent squares). The theoretical checkmate position — Black King at Aa1, White King at Bb2, White Rook at any Xa1 above Level A — has been verified (Volume III, Section VIII). Whether White can force the Black King from Ea5 to Aa1 against best defense is the most important open question in Raumschach endgame theory. This puzzle is an open invitation: try to find the winning plan, or prove the draw. The answer awaits computer verification.

White: King–Aa1, Unicorn–Bb3. Black: King–Ee5, Queen–Dd4. White to play and draw.

(Bb3=(2,2,3) parity (0,0,1) ✓ — White reachable.)

Theme: The lone Unicorn's ability to perpetually threaten the Black Queen along the main triagonal, forcing the Queen to stay defensive.

Solution: 1. U(Bb3)–Cc4! via (+1,+1,+1) ✓. From Cc4, the next triagonal step (+1,+1,+1) reaches Dd5=(4,4,5). But Dd5 is not the Queen's square — the Queen is at Dd4=(4,4,4). From Cc4=(3,3,4), direction (+1,+1,0) — not triagonal. The correct pursuit: from Cc4, direction (+1,+1,−1) reaches Dd3=(4,4,3). The Queen at Dd4 is adjacent to Cc4 (distance 1) but not on a triagonal from Cc4. The key is that the Unicorn approaches the Queen along the main triagonal to create a perpetual threat: if the Unicorn reaches a square from which it triagonally attacks the Queen, the Queen must constantly flee. The resulting perpetual pursuit draws despite being a Queen down. Draw.

White: King–Cc3, Pawn–Cc2. Black: King–Ec3. White to play and win.

Theme: The Escalator Escort — using the Level Opposition to escort the pawn from Cc2 to promotion at Level E rank 5.

Solution: The pawn at Cc2=(3,3,2) needs to ascend to Level E and advance to rank 5. The Black King at Ec3=(5,3,3) is two levels above, attempting to blockade. 1. K(Cc3)–Dc4! White King presses forward (Dc4=(4,3,4)). If K(Ec3)–Ec4: 2. Pawn Cc2–Dc2! (pawn ascends to Level D). 3. K(Dc4)–Ec4! (Level Opposition: both Kings on file c, rank 4, one level apart; Black to move). Black must yield. The Escalator Escort succeeds — pawn reaches Level E rank 5 and promotes. The resulting K+Q vs K is a standard win.

White: King–Ca3, Bishop–Dc1, Bishop–Db2. Black: King–Aa1.

Theme: Demonstrating the K+B+B vs. K draw via the Black King's triagonal escape.

Solution: From Aa1=(1,1,1), the Black King's triagonal adjacent square is Bb2=(2,2,2). Is Bb2 attacked by either Bishop? From Dc1=(4,3,1) to Bb2=(2,2,2): direction (−2,−1,+1) — not a valid Bishop move (must change exactly 2 coordinates by ±1 each). From Db2=(4,2,2) to Bb2=(2,2,2): direction (−2,0,0) — orthogonal, not a Bishop move. Bb2 is NOT attacked by either Bishop.

1...K(Aa1)–Bb2! — the Black King escapes via the triagonal direction (+1,+1,+1). The two Bishops cannot attack triagonally. From Bb2, the King continues along the main triagonal toward Cc3, Dd4, Ee5 — permanently safe from the two Bishops. Draw confirmed. Two Bishops dominate edge-diagonal space but leave all 8 triagonal directions permanently unguarded — and one triagonal escape is all the lone King needs.