Solution Editorial

1) General strategy

This is a stochastic multi-player game with hidden opponent parameters, so deterministic greedy play is weak.

The core strategy is:

• infer each opponent’s behavior parameters online from observed moves,
• keep multiple plausible parameter hypotheses per opponent,
• evaluate our moves by expected value over sampled futures,
• spend more simulation budget on promising moves via progressive pruning.

So the solver is a model-based rollout agent with online opponent inference.

2) Special handling by case

M = 2

Two-player games are more tactical and contact-driven.

• Before contact, move toward the opponent quickly.
• After contact, switch to deeper simulation.
• Use a faster, tactical move policy in rollouts for this mode.

M >= 3, U = 1

When U=1, reinforce/weaken depth disappears, and steal pressure dominates.

• Start deeper simulation earlier.
• Use stronger early-game shaping in evaluation.
• Prefer moves that keep options and avoid unnecessary exposure.

M >= 3, U >= 2

Use the default pipeline (inference + rollout + pruning + optional shallow extra lookahead).

3) How rollouts work

Each tested current-turn move is evaluated by simulating future turns up to a horizon.

Rollout policy

At each simulated turn:

• Our move:
  • in 2-player mode, use a fast tactical heuristic;
  • otherwise use a probability-aware greedy heuristic.
• Opponent move:
  • sample one parameter hypothesis for each opponent,
  • sample random values for that turn,
  • apply the statement model:
    • with probability epsilon, pick by uniform indexed choice among reachable cells,
    • otherwise pick action type by highest weighted class score, then pick among tied best cells by indexed choice.
• Apply simultaneous move resolution exactly under the game rules (occupy/reinforce/steal/weaken outcomes).

This repeats until the simulation horizon.

Rollout evaluation

The terminal simulated state is scored by a phase-aware objective:

• late game: close to true objective (our score vs strongest opponent),
• earlier turns: smoother surrogate with temperature/softmax shaping so estimates are less brittle.

For U=1, early scoring uses additional value transformation to better reflect that early control structure is different from final raw score.

4) Horizon design and length choice

The lookahead window is dynamic.

• It starts longer in early game.
• It gradually shrinks as turns progress.
• 2-player mode gets slightly longer lookahead than multi-player mode.
• The horizon is always clipped by remaining turns.

In practice this gives:

• long enough horizon early to capture setup effects,
• shorter horizon later to keep per-turn runtime stable,
• better time allocation across all 100 turns.

The solver also uses per-turn time slicing (remaining time divided by remaining turns), so simulation count adapts automatically.

5) Brief note on second-layer lookahead

A shallow extra lookahead is used only in selective situations (few top candidates left and enough budget).

It tests a small set of plausible next-turn continuations, picks the best continuation on one sample set, and evaluates it on another set to reduce selection bias.

This is intentionally limited; most strength comes from robust first-layer rollouts.

6) Speed techniques

Main performance optimizations:

• bit-mask board sets for fast set algebra and iteration,
• incremental local updates after simultaneous actions,
• cached per-player class maxima/tie sets,
• sampling mostly high-weight opponent hypotheses,
• progressive candidate elimination (sequential halving),
• lightweight state snapshot/restore for selective extra lookahead.

Overall: online opponent inference + high-throughput stochastic rollouts + adaptive horizon/time control.