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    <p class="label">Interactive Proofs &amp; Games · InteractiveBench · Mar 2026</p>
    <h1 class="page-title">Interactive<br><span>Benchmarks</span></h1>
    <p class="page-desc">
      Four benchmark domains evaluating LLMs' active information-acquisition ability —
      two Interactive Proof settings (Logic &amp; Math) and two Interactive Game settings
      (Texas Hold'em Poker &amp; Trust Game).
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      <button class="filter-btn" data-domain="logic">Logic · Interactive Proof</button>
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      <div class="p-card" data-domain="logic">
        <span class="p-tag">Logic · Interactive Proof</span>
        <h3>Situation Puzzle</h3>
        <p>Player asks yes/no-style questions to reconstruct a hidden narrative explanation within a 20-turn budget.
          Responses are limited to {yes, no, both, irrelevant}. All models score 0% without interaction — forcing
          genuine reasoning. Dataset: 46 expert-curated, high-difficulty instances. Judge: Grok-4.1-fast (temp=0).</p>
        <div class="p-card-foot">
          <span class="p-status">46 instances · Best: Gemini 30.4%</span>
          <span class="p-arrow">→</span>
        </div>
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      <div class="p-card" data-domain="math">
        <span class="p-tag">Math · Interactive Proof</span>
        <h3>HLE Math Problems</h3>
        <p>Player interacts with a judge holding a reference derivation, querying validity of intermediate steps
          (lemmas, equations) within a 20-turn budget. Outperforms pass@k baseline by 20–50% under matched token budget.
          Dataset: 52 challenging instances from the HLE benchmark. Judge: Grok-4.1-fast (temp=0).</p>
        <div class="p-card-foot">
          <span class="p-status">52 instances · Best: Grok 76.9%</span>
          <span class="p-arrow">→</span>
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      <div class="p-card" data-domain="poker">
        <span class="p-tag">Poker · Interactive Game</span>
        <h3>Texas Hold'em</h3>
        <p>Six LLM agents compete in No-Limit Texas Hold'em across 10 independent tables (500 hands each, 5,000 total).
          Agents receive structured observations (stage, hole cards, community cards, stack sizes, pot odds, action
          history) and output FOLD / CHECK / CALL / RAISE / ALL_IN. Metrics: avg winnings/hand, VPIP, fold rate,
          latency.</p>
        <div class="p-card-foot">
          <span class="p-status">5,000 hands · Best: Gemini +31.8/hand</span>
          <span class="p-arrow">→</span>
        </div>
      </div>

      <div class="p-card" data-domain="trust">
        <span class="p-tag">Trust · Interactive Game</span>
        <h3>Iterated Prisoner's Dilemma</h3>
        <p>Round-robin tournament of repeated Prisoner's Dilemma with random horizon (geometric distribution,
          continuation prob δ). Each round: simultaneous COOPERATE / DEFECT. Payoffs: (C,C)→(2,2), (D,C)→(3,−1),
          (C,D)→(−1,3), (D,D)→(0,0). Metrics: avg payoff/round, cooperation rate, betrayal rate. Baselines: Grim Trigger
          (1.811) and TFT (1.782).</p>
        <div class="p-card-foot">
          <span class="p-status">Round-robin · Best: Qwen3 1.867/round</span>
          <span class="p-arrow">→</span>
        </div>
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        <h2>Evaluation framework</h2>
        <p>Each benchmark is modeled as a horizon-T interaction between model π and environment E</p>
      </div>
      <div class="steps">
        <div class="step">
          <div class="step-n">Interactive Proofs</div>
          <h3>Convergent Regime</h3>
          <p>The model (Player) interacts with an omniscient Judge holding a hidden ground truth. Under a fixed query
            budget B, the Player asks questions and receives restricted feedback {yes, no, both, irrelevant}. Objective:
            maximize probability of correct final answer. Evaluated on Logic and Math domains.</p>
        </div>
        <div class="step">
          <div class="step-n">Interactive Games</div>
          <h3>Divergent Regime</h3>
          <p>No dedicated Judge — the model interacts with other agents and a stochastic environment to maximize
            long-horizon utility. Objective: maximize expected discounted cumulative payoff. Evaluated on Texas Hold'em
            Poker and iterated Prisoner's Dilemma (Trust Game).</p>
        </div>
        <div class="step">
          <div class="step-n">Key Finding</div>
          <h3>Substantial Room to Improve</h3>
          <p>Interactive benchmarks reveal capabilities invisible to static tests. Best Logic accuracy: 30.4% (Gemini).
            Best Math accuracy: 76.9% (Grok). Pass@k underestimates capability by 20–50% vs interactive evaluation under
            same token budget. Models show highly domain-specific strengths.</p>
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    <p>Princeton × InteractiveBench · March 2026. Full methodology, dataset construction details, and per-domain experimental results for all 6 frontier LLMs.</p>
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