Dice Chess FEN (DFEN) Specification

To fully represent the state of a Dice Chess game, standard Forsyth-Edwards Notation (FEN) is insufficient. Dice Chess introduces two major mechanics that break standard FEN assumptions:

1. Multiple En Passant Squares: Because a player can execute up to three micro-moves in a single turn, they can perform multiple double pawn pushes (e.g., a2-a4, c2-c4, e2-e4). In the subsequent turn, the opponent must be able to capture any of these pawns on the pass.
2. Mid-Turn Game State (Dice Pool): A standard turn consists of rolling three dice and performing up to three micro-moves. To support game pauses, bookmarks, and search-tree evaluations mid-turn, the FEN must encode the active player’s remaining dice pool.

To address these requirements, we specify Dice Chess FEN (DFEN).

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The DFEN Structure

DFEN extends the standard FEN to seven space-separated fields:

<pieces> <color> <castling> <en-passant> <halfmove> <fullmove> [dice-pool]

Fields 1, 2, 3, 5, and 6 remain fully compatible with standard chess. Fields 4 and 7 are modified to support Dice Chess rules.

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Field 4: Multiple En Passant Target Squares

In standard FEN, Field 4 is either a single square (e.g. e3) or -. In DFEN, Field 4 supports multiple en-passant squares through Alphabetical Concatenation:

• No Active Targets: Represented by a single dash -.
• Single Active Target: Represented by the standard algebraic notation (e.g., e3).
• Multiple Active Targets: Represented as a concatenated string of 2-character square notations, sorted alphabetically (e.g., a3c3e3 or b6f6).

Sorting & Determinism

To guarantee that logically identical positions serialize to identical DFEN strings:

• En-passant squares must be sorted alphabetically (e.g., a3 < c3 < e3).
• Only squares that are valid en-passant capture coordinates (the squares skipped by double-pushed pawns in the immediate previous turn) are included.

Example (3 Double Pawn Pushes)

If White plays a2-a4, c2-c4, and e2-e4 in one turn:

• The en-passant field becomes: a3c3e3
• Complete DFEN (Field 7 omitted or empty -): rnbqkbnr/pppppppp/8/8/P1P1P3/8/1P1P1PPP/RNBQKBNR b KQkq a3c3e3 0 1 -

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Field 7: The Dice Pool (Turn State)

Field 7 is an optional field that represents the active player’s remaining dice pool for their current turn.

The dice values are mapped to piece types:

• P or p = Pawn (♙) = 1
• N or n = Knight (♘) = 2
• B or b = Bishop (♗) = 3
• R or r = Rook (♖) = 4
• Q or q = Queen (♕) = 5
• K or k = King (♔) = 6

Representation Rules

• No Dice Rolled / Fresh Turn: Represented by a single dash -. This indicates that the active color has transitioned, and the player must roll the dice before making any moves.
• Active Dice Pool: Represented by a string of piece letters (e.g. PNB or pnb). The case must match the active color (uppercase for White, lowercase for Black). The letters must be sorted by their piece value (P < N < B < R < Q < K).

🔄 Five-Phase Turn State Progression (Example)

Here is how the active color and 7th field progress during a White turn where White rolls three pawns (P, P, P) and plays three micro-moves:

Phase	State Description	Color Field	Dice Field	Meaning
1	Turn started, waiting for roll	w	-	White’s turn, dice not rolled yet
2	White rolls P, P, P	w	PPP	White has 3 pawn moves available
3	White plays a2-a4	w	PP	White has 2 pawn moves remaining
4	White plays c2-c4	w	P	White has 1 pawn move remaining
5	White plays e2-e4 (turn ends)	b	-	Black’s turn, waiting for roll

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Impact on Engine Domain & Search

1. GameState Updates

enPassant is represented as a high-performance Bitboard instead of an Option[Square]:

opaque type Bitboard = Long // Zero-GC 64-bit mask

A new field dicePool is introduced to GameState:

case class GameState(
    ...,
    mailbox: Map[Square, Piece],
    flags: GameFlags,         // Packed 29-bit int holding activeColor, dicePool (List[Int]), etc.
    enPassant: Bitboard,      // Holds multiple target squares
    ...
)

2. Move Generation & Application

• Move Generation: Iterates through set bits in state.enPassant to yield all possible en-passant capture moves.
• Move Application: If a micro-move is applied:
  • The played die is removed from dicePool.
  • If a double pawn push occurs, its target square is added (bitwise OR) to the enPassant bitboard.
  • If a pawn is captured (via regular or en-passant capture), its associated target square is explicitly removed from the bitboard.
• Turn Boundaries: En-passant targets are NOT cleared during individual micro-moves. Instead, when a player’s turn formally starts, the engine calls state.clearEnPassant(activeColor) to wipe out their own old EP targets from previous turns, while keeping the opponent’s EP targets fully intact and available for capture.

3. Bot & Expectimax Engine Alignment

Expectimax search transitions between states using the 7th field:

• When evaluating chance nodes (dice rolls), the engine branches on the 6 possible rolls (1 to 6), populating the dicePool field in child states.
• Maximizing/Minimizing players then search through paths matching the dicePool combinations, fully aligned with multiple en-passant opportunities.