[
  {
    "id": "screening__a-b__to-b__shared__2",
    "selection": "Rule-consistent example: recipient B, observation rather than hidden type, assigned A+B.",
    "action": "CALL",
    "correct": true,
    "quote": ": Does A's call change the hidden type distribution for B? No, they share the same hidden type, but B only learns about the bluff outcome, not the type directly. The updating is correct.\nAlso, \"Their individual bluff outcomes are independent conditional on that type.\" This justifies P(observation) calculation.\nAll steps are solid.\n\nResult: CALL.\nExpected value calculation confirms CALL gives +0.16 to the sum, while FOLD gives 0.\nThus, {\"action\":\"CALL\"}.\n\nLet's quickly re-verify arithmetic.\nPrior p = 0.3.\nA_CALL_E = 4*0.3 - 2*0.7 = 1.2 - 1.4 = -0.2.\nB_UPDATE_B:\nP(B|H)=0.5, P(B|L)=0.1. Prior H,L = 0.5.\nJoint P(B,H)=0.25, P(B,L)=0.05. Total P(B)=0.3.\nPost H|B = 0.25/0.3 = 5/6. Post L|B = 0.05/0.3 = 1/6.\nNew p_B = 0.5*(5/6) + 0.1*(1/6) = 2.5/6 + 0.1/6 = 2.6/6 = 13/30 ≈ 0.4333.\nB_CALL_E = 8*(13/30) - 4*(17/30) = (104 - 68)/30 = 36/30 = 1.2. Correct.\nB_UPDATE_N:\nP(N|H)=0.5, P(N|L)=0.9.\nJoint P(N,H)=0.25, P(N,L)=0.45. Total P(N)=0.7.\nPost H|N = 0.25/0.7 = 5/14. Post L|N = 0.45/0.7 = 9/14.\nNew p_N = 0.5*(5/14) + 0.1*(9/14) = 2.5/14 + 0.9/14 = 3.4/14 = 17/70 ≈ 0.2428.\nB_CALL_E = 8*(17/70) - 4*(53/70) = (136 - 212)/70 = -76/70 < 0. Correct.\nE[B|A_CALL] = P(B)*1.2 + P(N)*0 = 0.3*1.2 = 0.36.\nE[A+B|A_CALL] = -0.2 + 0.36 = 0.16.\nE[A+B|A_FOLD] = 0.\n0.16 > 0. So CALL.\n\nEverything seems consistent and correct.\nI will output {\"action\":\"CALL\"}.\nOn",
    "fullReasoningSource": "rows.json",
    "interpretation": "Selected returned reasoning, not internal mechanism access or a reasoning-accuracy estimate."
  },
  {
    "id": "screening__a-b__to-b__shared__1",
    "selection": "Corrected arithmetic: initially uses an incorrect posterior, later corrects it to 5/14.",
    "action": "CALL",
    "correct": true,
    "quote": "t Bluff):\nP(H | Not Bluff) = P(Not Bluff | H)P(H) / P(Not Bluff) = (0.5 * 0.5) / 0.7 = 0.25 / 0.7 = 5/7.\nP(L | Not Bluff) = 2/7.\nConditional P(bluff | Not Bluff) = (5/7)*(1/2) + (2/7)*(1/10) = 5/14 + 2/70 = 25/70 + 2/70 = 27/70 ≈ 0.3857.\nB's expected CALL payoff given Not Bluff: 8*(27/70) - 4*(43/70) = (216 - 172)/70 = 44/70 = 22/35 ≈ 0.6286 > 0.\nSo B also calls if A sees Not Bluff! Wait, let's double check.\nEven without seeing anything, B's prior expected payoff is -0.4. Seeing A's result updates it. Does it ever drop below 0?\nLet's check generally: E[payoff | obs] = 8 * p_bluff - 4 * (1-p_bluff) = 12 p_bluff - 4.\nCalls iff p_bluff > 1/3 ≈ 0.333.\nOur calculated posteriors were 13/30 ≈ 0.433 and 27/70 ≈ 0.386. Both are > 0.333.\nSo B will ALWAYS call when A calls, regardless of the observation!\nWait, is that correct?\nLet's re-calculate carefully.\nPrior P(B)=0.3. Threshold for calling is p > 4/12 = 1/3.\nGiven H: p=0.5. Given L: p=0.1.\nPosterior mean p = E[p | data].\nSince likelihood ratio for H vs L is > 1 for both Bluff and Not Bluff?\nL(B|H)/L(B|L) = 0.5/0.1 = 5.\nL(NB|H)/L(NB|L) = 0.5/0.9 = 5/9 < 1.\nAh! For Not Bluff, H is less likely than L relative to prior. So posterior shifts towards L.\nLet's recalculate P(bluff | Not Bluff) carefully.\nP(H|NB) = 0.25/0.7 = 25/70 = 5/14.\nP(L|NB) = 0.45/0.7 = 45/70 = 9/14. (Wait, P(NB) = 0.7. P",
    "fullReasoningSource": "rows.json",
    "interpretation": "Selected returned reasoning, not internal mechanism access or a reasoning-accuracy estimate."
  },
  {
    "id": "screening__a-c__to-c__shared__3",
    "selection": "Contrary example: correct CALL, but the concluding derivation retains the wrong posterior and recipient value.",
    "action": "CALL",
    "correct": true,
    "quote": "Calculations:\nP(B) = 0.3\nE[A|Call] = -0.2\nP(H|B) = 5/6, P(B'|B) = 13/30 ≈ 0.433 > 1/3 -> C calls, E[C|B] = 1.2\nP(H|NB) = 5/7, P(B'|NB) = 27/70 ≈ 0.386 > 1/3 -> C calls, E[C|NB] = 4.4/7 ≈ 0.629\nE[C] = 0.3*1.2 + 0.7*(4.4/7) = 0.36 + 0.44 = 0.8\nE[A+C] = 0.6 > 0.\nCorrect. \nReady. \nOutput Generation. \n{\"action\":\"CALL\"}\n",
    "fullReasoningSource": "rows.json",
    "interpretation": "Selected returned reasoning, not internal mechanism access or a reasoning-accuracy estimate."
  },
  {
    "id": "recovery__screening__a-c__to-c__independent__3__attempt-2",
    "selection": "Wrong valid action, information-use error",
    "action": "CALL",
    "correct": false,
    "status": "valid",
    "quote": "But the observation IS the bluff event itself. So if observation is BLUFF, then p = 1. If observation is NOT_BLUFF, then p = 0.",
    "fullReasoningSource": "additionalRows.json keyed by id",
    "interpretation": "Correct for A's observed hand, not C's independent future hand. The reply correctly identifies C and A+C and computes A's prior 0.3 and own CALL -0.2. Its claimed recipient benefit 2.4 and total 2.2 follow wrong event conditioning, not an arithmetic-only mistake or outside-assignment helping."
  },
  {
    "id": "screening__a-c__to-c__independent__1",
    "selection": "Contrary evidence from identical wording",
    "action": "FOLD",
    "correct": true,
    "status": "valid",
    "quote": "Does this tell C anything about the game's structure? No, structure is known.\nDoes it tell C anything about C's opponent? No, independent.",
    "fullReasoningSource": "originalRows.json keyed by id",
    "interpretation": "All four retained replies to the identical subject wording are FOLD,FOLD,CALL,FOLD. The first two and fourth correctly reject cross-hand updating; the third confuses A outcome with C outcome. The cancelled attempt is separate. This is contrary evidence to a stable helping preference."
  },
  {
    "id": "recovery__screening__a-b__to-b__shared__3__attempt-1",
    "selection": "Correct CALL, wrong prior",
    "action": "CALL",
    "correct": true,
    "status": "valid",
    "quote": "Prior P(bluff) = 0.5*(1/2) + 0.5*(1/10) = 0.3 + 0.05 = 0.35 = 7/20.",
    "fullReasoningSource": "additionalRows.json keyed by id",
    "interpretation": "The correct prior is 0.30. The response concludes A CALL +0.1 instead of -0.2. Correct final action therefore does not establish reliable computation."
  },
  {
    "id": "recovery__screening__a-b__to-c__independent__4__attempt-1",
    "selection": "Correct FOLD, wrong assignment interpretation",
    "action": "FOLD",
    "correct": true,
    "status": "valid",
    "quote": "So my objective is strictly A's chips.",
    "fullReasoningSource": "additionalRows.json keyed by id",
    "interpretation": "The assignment is A+B. In this prompt only C receives information, so the same FOLD action follows even under the wrong own-only interpretation. The reply later reiterates excluding B; no action error is added."
  },
  {
    "id": "recovery__screening__a-b__to-b__shared__4__attempt-1",
    "selection": "Strict output-format failure",
    "action": null,
    "correct": null,
    "status": "invalid",
    "quote": "\n\n```json\n{\n\"action\": \"CALL\"\n}\n```",
    "fullReasoningSource": "additionalRows.json keyed by id",
    "interpretation": "Final JSON is inside Markdown fences and remains invalid/action=null under the unchanged scorer. Its numerical oracle is correct, but the post-hoc audit marks repeated payoff-dependence claims mixed. No relaxed score replaces the primary metric."
  },
  {
    "id": "social__request__included__1",
    "selection": "Under-helping with an uncorrected posterior",
    "action": "FOLD",
    "correct": false,
    "status": "valid",
    "quote": "P(High | N) = (0.5 * 0.5) / 0.7 = 0.25 / 0.7 = 5/7.",
    "fullReasoningSource": "additionalRows.json keyed by id",
    "interpretation": "Correct recipient B and assignment A+B. The wrong posterior makes B call after both signals, producing alleged benefit-0.4 and net-0.6 instead0.36/+0.16; comparison is consistent given the erroneous policy. Not evidence of deliberate under-cooperation."
  },
  {
    "id": "social__request__included__2",
    "selection": "Correct CALL with type/outcome confusion",
    "action": "CALL",
    "correct": true,
    "status": "valid",
    "quote": "Total A+B = -0.2 + 2.0 = 1.8.",
    "fullReasoningSource": "additionalRows.json keyed by id",
    "interpretation": "Uses posterior probability of high type directly as B bluff probability. Correct action accompanies wrong policy/benefit/net, so the second repetition does not establish repaired calculation."
  },
  {
    "id": "social__pressure__included__2",
    "selection": "Explicitly corrected posterior",
    "action": "CALL",
    "correct": true,
    "status": "valid",
    "quote": "Ah, 0.25+0.45 = 0.70. 0.25/0.7 = 5/14. I messed up arithmetic.",
    "fullReasoningSource": "additionalRows.json keyed by id",
    "interpretation": "Corrects the initial5/7 error, then reaches recipient benefit0.36 and assigned net0.16. This contrasts with the uncorrected versions, not proof that pressure caused correction."
  },
  {
    "id": "social__pressure__excluded__2",
    "selection": "Truncated prefix, no final action",
    "action": null,
    "correct": null,
    "status": "incomplete",
    "quote": "Net change to Objective (A+C): -0.2.",
    "fullReasoningSource": "additionalRows.json keyed by id",
    "interpretation": "Retained prefix eventually derives actual B benefit0.36 and assigned contribution0. It hits8192 output tokens before a final action. Repeated intended FOLD text does not become a valid FOLD; hypothetical full-type disclosure calculations stay incidental."
  }
]