Mobility and Passed Pawn Contracts

The playground evaluation model ablation (fortemate/dicechess-training#12, #14) tests position-evaluation models against the baseline KcpFeatures (kcp-13). Strategy research highlights three position properties that no previous feature schema exposed: expected wasted rolls (dice faces whose piece type has no move), pawn blockage, and tempo as separate own and opponent mobility counts rather than a single signed difference.

In addition, the endgame motivates a passed-pawn block: pawn promotion in Dice Chess depends on rolling a pawn face, and a passed pawn’s value increases sharply as it nears the back rank.

Following the principle of train == serve, training enrichment and serving inference share the exact engine implementation to prevent drift.

Shared-Core Primitives

Two primitives in dicechess.engine.search compute the underlying positional features:

PieceMobility

Exposes pseudo-legal move counts per moving piece type in dice order (Pawn, Knight, Bishop, Rook, Queen, King):

package dicechess.engine.search

object PieceMobility:
  def counts(state: GameState, color: Color): Array[Int]
  def count(state: GameState, color: Color, pieceType: PieceType): Int
  def total(state: GameState, color: Color): Int

Moves are computed on state.withActiveColor(color) with castling dice present (King and Rook dice in pool), exactly matching how RichFeatures.mobility_diff computes its operands. For every position and color:

$\sum \text{own\_moves\_*} - \sum \text{opp\_moves\_*} = \text{mobility\_diff}$

PassedPawns

Exposes passed-pawn detection and rank advancement:

package dicechess.engine.search

object PassedPawns:
  def count(state: GameState, color: Color): Int
  def maxRank(state: GameState, color: Color): Int
  def countAndMaxRank(state: GameState, color: Color): (Int, Int)
  def bitboard(state: GameState, color: Color): Bitboard

• Definition: Uses the standard chess definition: a pawn is passed if there are no opposing pawns on the same file or on adjacent files ahead of the pawn along its direction of advance.
• Max rank advancement: Counted from that side’s own back rank as 0:
  • White pawn on rank $r \in [2, 7]$: advancement is $r - 1 \in [1, 6]$.
  • Black pawn on rank $r \in [2, 7]$: advancement is $8 - r \in [1, 6]$.
  • When a side has no passed pawn, the value is $0$.
• Perspective: Evaluated from the explicit color argument, independent of active color and dice pool.

Versioned Feature Contracts

1. kcp-mobility-27-v1

Extends KcpFeatures (13 columns) with per-piece move counts and normalized PDI:

Index	Column Name	Source / Definition	Range
0–12	p_diff … queen_capture_danger	Identical to KcpFeatures.extract	float32
13	own_moves_p	Own pseudo-legal pawn moves	$\ge 0$
14	own_moves_n	Own pseudo-legal knight moves	$\ge 0$
15	own_moves_b	Own pseudo-legal bishop moves	$\ge 0$
16	own_moves_r	Own pseudo-legal rook moves	$\ge 0$
17	own_moves_q	Own pseudo-legal queen moves	$\ge 0$
18	own_moves_k	Own pseudo-legal king moves	$\ge 0$
19–24	opp_moves_p … opp_moves_k	Opponent pseudo-legal move counts	$\ge 0$
25	own_pdi	PieceDiversity.count(state, color) / 5f	0.0 to 1.0
26	opp_pdi	PieceDiversity.count(state, opponent) / 5f	0.0 to 1.0

2. kcp-mobility-pawns-31-v1

Extends kcp-mobility-27-v1 with the passed-pawn block:

Index	Column Name	Source / Definition	Range
0–26	Prefix (27 columns)	Identical to KcpMobilityFeatures.extract	float32
27	own_passed_pawns	Number of passed pawns for color	0 to 8
28	opp_passed_pawns	Number of passed pawns for opponent	0 to 8
29	own_passed_max_rank	Most advanced passed pawn rank from back rank	0 to 6
30	opp_passed_max_rank	Opponent most advanced passed pawn rank	0 to 6

Mover-Canonical Symmetry

Both contracts are mover-canonical: evaluating state from color perspective produces the identical vector as evaluating Symmetry.colorFlip(state) from color.opponent perspective. When evaluated for the side to move (state.activeColor), the vector matches that of the color-flipped state evaluated for its own mover.

Strategic Interpretation

Expected Wasted Rolls

In Dice Chess, a turn rolls 3 dice from a uniform 6-sided die $\{P, N, B, R, Q, K\}$. If a side has zero pseudo-legal moves for a piece type $T$ (and therefore zero legal moves), any die face showing $T$ cannot be used for that type.

For a single die roll, the probability that the rolled piece type has no move is:

$P(\text{unusable}) = \frac{\text{immobile\_types}}{6}$

Across the 3 dice rolled in a turn, by linearity of expectation, the expected number of wasted dice is:

$\mathbb{E}[\text{wasted rolls}] = 3 \times \frac{\text{immobile\_types}}{6} = \frac{1}{2} \times \text{immobile\_types}$

The per-piece move counts own_moves_* and opp_moves_* directly expose whether each piece type is mobile ($>0$) or blocked ($0$).

Pawn Blockage and Separate Tempo

• Pawn Blockage: When own_moves_p == 0, friendly pawns are completely locked or absent. In Dice Chess, rolling pawn dice when pawns are blocked forces the player to burn turns or forgo actions.
• Separate Tempo: Rather than collapsing mobility into a signed scalar (mobility_diff = own - opp), exposing own_moves_* and opp_moves_* separately allows non-linear models (neural nets) to evaluate asymmetries—for example, high mobility for both sides (tactical volatility) versus low mobility for both sides (closed deadlock).

Schema Versioning Rule

[!IMPORTANT] Any change in column order, normalization, perspective, or semantic definition requires a new schema identifier (e.g. kcp-mobility-27-v2) and a corresponding newly trained model. Existing schemas must remain immutable to preserve reproducibility and avoid silent evaluation failures.

JMH Benchmarks

Microbenchmarks on OpenJDK 25 (Temurin 25.0.4) compare extraction overhead across the 5 standard benchmark positions (initial, kiwipete, endgame, castling, promotion):

Benchmark	Position	Average Time ($\mu s$)
passedPawnsSummary	initial / kiwipete / endgame / castling / promotion	0.004 – 0.012 $\mu s$
pieceMobilityCounts	initial / kiwipete / endgame / castling / promotion	0.101 – 0.436 $\mu s$
kcp (13 cols)	promotion / endgame / castling / initial / kiwipete	79 – 17,664 $\mu s$
kcpMobility27	promotion / endgame / castling / initial / kiwipete	82 – 17,466 $\mu s$
kcpMobilityPawns31	promotion / endgame / castling / initial / kiwipete	78 – 17,149 $\mu s$

The 216-outcome DFS search for king/queen capture probabilities in kcp dominates total extraction time (hundreds of microseconds to tens of milliseconds). The additional per-type move counting ($\sim 0.10\text{–}0.44\,\mu s$) and passed-pawn bitboard probe ($\sim 0.01\,\mu s$) add under $0.01\%$ overhead on complex positions (e.g. $0.44\,\mu s$ on kiwipete’s $17.6\,\text{ms}$) and under $0.55\%$ on the fastest sparse positions ($0.44\,\mu s$ on promotion’s $79\,\mu s$).