Add utility-based strategic AI (ai_utility.js + ai_strategic.js)

[Copilot]

Implements a new AI strategy that scores board states by utility and selects attacks by expected value, plus a reusable BoardUtility library for graph/board analysis.

ai_utility.js — shared library (BoardUtility)

• Win-probability table: iterative bottom-up convolution of d6 sum distributions → WIN_PROB[a][d] precomputed at load time. Correctly models that the attacker rolls attack_dice − 1 dice.
• board_score(game, arm, dice, pn): four-factor utility:
  • +3.0 × my_largest_connected_region — drives dice income
  • −2.0 × max_opponent_connected_region — their income threat
  • +0.4 × frontier_dice — dice that can actually attack (locked interior dice contribute 0)
  • −0.5 × exposed_opponent_strong_dice — opponent armies ≥5 dice bordering me
• get_largest_component(game, arm, pn) and BFS helpers operate on detached arm/dice arrays so simulated states never touch the live game object.

ai_strategic.js — the AI

Each turn, for every legal attack:

EV = p_win × score(win_state) + (1 − p_win) × score(loss_state) + income_bonus

• Win/loss states are evaluated via in-place mutation + restore on local snapshots — no array copies per iteration.
• income_bonus = max(0, my_conn/opp_conn_max − 1) × 0.3: when my connected region significantly outpaces opponents', marginally negative-EV attacks become worth taking because dice income means faster recovery.
• Attack only if EV > baseline_score; return 0 (end turn) otherwise.

Integration

• index.html: loads ai_utility.js → ai_strategic.js before game.js
• game.js: player slot 4 switched from ai_default to ai_strategic

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