[
  {
    "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."
  }
]