{
  "example_version": "balatro-example-v1",
  "id": "discard-four-outcomes",
  "title": "Which four cards should I discard?",
  "tool": "compare_actions",
  "request": {
    "contract_version": "balatro-web-v1",
    "state": {
      "id": "worked-example",
      "hand": [
        "AH",
        "KH",
        "QH",
        "JH",
        "9H",
        "9S",
        "4C",
        "2D"
      ],
      "deck": [
        "TH",
        "9D",
        "AS",
        "KC",
        "2S"
      ],
      "hands_left": 1,
      "discards_left": 1,
      "chips_needed": 600,
      "jokers": [],
      "levels": {}
    },
    "explain_actions": [
      {
        "kind": "discard",
        "cards": [
          "2D",
          "4C",
          "9S",
          "9H"
        ]
      }
    ]
  },
  "response": {
    "analysis_mode": "exact_blind_survival",
    "analysis_objective": "Maximize mathematical single-blind action value under optimal continuation in the supported model.",
    "assumptions": [
      "Uniform draws without replacement from the complete specified draw pile, with multiplicity.",
      "Optimal continuation under the same rules and transitions.",
      "No boss effects, consumables, shop, economy, scaling or future-blind objective."
    ],
    "build_target": "aarch64-apple-darwin",
    "complete": true,
    "computation_budget": {
      "score_calls": 1000000,
      "wall_time_ms": 15000
    },
    "contract_version": "balatro-web-v1",
    "engine_version": "0.1.0",
    "error": null,
    "limits": {
      "active_jobs": 2,
      "budget_score_calls": 1000000,
      "exact_deck": 12,
      "exact_discards": 2,
      "exact_hands": 2,
      "hand": 8,
      "memory_enforcement": "Linux address-space limit; macOS RSS watchdog sampled every 10 ms (transient overshoot possible).",
      "score_deck": 52,
      "wall_time_ms": 15000,
      "worker_memory_bytes": 1073741824
    },
    "ordering": "Engine optimizes played and held arrangements; displayed card order is not evaluated literally.",
    "probability_semantics": "Mathematical action value within the supported single-blind model, not an estimated real-game success probability.",
    "request_id": "anonymous",
    "result": {
      "best_discard": {
        "cards": [
          "2D",
          "4C",
          "9S",
          "9H"
        ],
        "kind": "discard",
        "model_action_value": 0.8,
        "q": 0.8
      },
      "best_play": {
        "cards": [
          "2D"
        ],
        "clears_now": false,
        "hand_type": "high_card",
        "kind": "play",
        "model_action_value": 0,
        "q": 0,
        "score": 7
      },
      "clearing_plays": [],
      "complete": true,
      "exact_ms": 0,
      "explanations": [
        {
          "action": {
            "cards": [
              "2D",
              "4C",
              "9S",
              "9H"
            ],
            "kind": "discard",
            "model_action_value": 0.8,
            "q": 0.8
          },
          "branches": [
            {
              "best_immediate_score": 1208,
              "conditional_value": 1,
              "continuation": "optimal_under_same_model",
              "continuation_example": {
                "cards": [
                  "TH",
                  "JH",
                  "QH",
                  "KH",
                  "AH"
                ],
                "kind": "play",
                "model_action_value": 1
              },
              "draw": [
                "9D",
                "TH",
                "KC",
                "AS"
              ],
              "draw_probability": 0.2,
              "next_state": {
                "chips_needed": 600,
                "deck": [
                  "2S"
                ],
                "discards_left": 0,
                "hand": [
                  "9D",
                  "TH",
                  "JH",
                  "QH",
                  "KH",
                  "KC",
                  "AS",
                  "AH"
                ],
                "hands_left": 1,
                "jokers": [],
                "levels": {}
              },
              "physical_draw_ways": 1,
              "terminal": false,
              "weighted_value": 0.2
            },
            {
              "best_immediate_score": 1208,
              "conditional_value": 1,
              "continuation": "optimal_under_same_model",
              "continuation_example": {
                "cards": [
                  "TH",
                  "JH",
                  "QH",
                  "KH",
                  "AH"
                ],
                "kind": "play",
                "model_action_value": 1
              },
              "draw": [
                "2S",
                "TH",
                "KC",
                "AS"
              ],
              "draw_probability": 0.2,
              "next_state": {
                "chips_needed": 600,
                "deck": [
                  "9D"
                ],
                "discards_left": 0,
                "hand": [
                  "2S",
                  "TH",
                  "JH",
                  "QH",
                  "KH",
                  "KC",
                  "AS",
                  "AH"
                ],
                "hands_left": 1,
                "jokers": [],
                "levels": {}
              },
              "physical_draw_ways": 1,
              "terminal": false,
              "weighted_value": 0.2
            },
            {
              "best_immediate_score": 124,
              "conditional_value": 0,
              "continuation": "optimal_under_same_model",
              "continuation_example": {
                "cards": [
                  "AH"
                ],
                "kind": "play",
                "model_action_value": 0
              },
              "draw": [
                "2S",
                "9D",
                "KC",
                "AS"
              ],
              "draw_probability": 0.2,
              "next_state": {
                "chips_needed": 600,
                "deck": [
                  "TH"
                ],
                "discards_left": 0,
                "hand": [
                  "2S",
                  "9D",
                  "JH",
                  "QH",
                  "KH",
                  "KC",
                  "AS",
                  "AH"
                ],
                "hands_left": 1,
                "jokers": [],
                "levels": {}
              },
              "physical_draw_ways": 1,
              "terminal": false,
              "weighted_value": 0
            },
            {
              "best_immediate_score": 1208,
              "conditional_value": 1,
              "continuation": "optimal_under_same_model",
              "continuation_example": {
                "cards": [
                  "TH",
                  "JH",
                  "QH",
                  "KH",
                  "AH"
                ],
                "kind": "play",
                "model_action_value": 1
              },
              "draw": [
                "2S",
                "9D",
                "TH",
                "AS"
              ],
              "draw_probability": 0.2,
              "next_state": {
                "chips_needed": 600,
                "deck": [
                  "KC"
                ],
                "discards_left": 0,
                "hand": [
                  "2S",
                  "9D",
                  "TH",
                  "JH",
                  "QH",
                  "KH",
                  "AS",
                  "AH"
                ],
                "hands_left": 1,
                "jokers": [],
                "levels": {}
              },
              "physical_draw_ways": 1,
              "terminal": false,
              "weighted_value": 0.2
            },
            {
              "best_immediate_score": 1208,
              "conditional_value": 1,
              "continuation": "optimal_under_same_model",
              "continuation_example": {
                "cards": [
                  "TH",
                  "JH",
                  "QH",
                  "KH",
                  "AH"
                ],
                "kind": "play",
                "model_action_value": 1
              },
              "draw": [
                "2S",
                "9D",
                "TH",
                "KC"
              ],
              "draw_probability": 0.2,
              "next_state": {
                "chips_needed": 600,
                "deck": [
                  "AS"
                ],
                "discards_left": 0,
                "hand": [
                  "2S",
                  "9D",
                  "TH",
                  "JH",
                  "QH",
                  "KH",
                  "KC",
                  "AH"
                ],
                "hands_left": 1,
                "jokers": [],
                "levels": {}
              },
              "physical_draw_ways": 1,
              "terminal": false,
              "weighted_value": 0.2
            }
          ],
          "complete": true,
          "continuation": "optimal_under_same_model",
          "draw_probability_sum": 1,
          "formula": "Q(s,a) = sum_draw P(draw|a) V(s_after_action_and_draw)",
          "model_action_value": 0.8,
          "replacement_count": 4,
          "residual": 0,
          "retained_cards": [
            "JH",
            "QH",
            "KH",
            "AH"
          ],
          "score_calls": 2180,
          "specified_pile_size": 5,
          "tolerance": 1e-10,
          "weighted_value": 0.8
        }
      ],
      "mode": "exact_blind_survival",
      "n_actions": 436,
      "nodes": 1287,
      "objective": "Maximize mathematical blind-clear action value under optimal continuation in the supported model",
      "optimal_action_count": 2,
      "optimal_actions": [
        {
          "cards": [
            "2D",
            "4C",
            "9S",
            "9H"
          ],
          "kind": "discard",
          "model_action_value": 0.8,
          "q": 0.8
        },
        {
          "cards": [
            "2D",
            "4C",
            "9S",
            "AH"
          ],
          "kind": "discard",
          "model_action_value": 0.8,
          "q": 0.8
        }
      ],
      "q": [
        {
          "cards": [
            "2D",
            "4C",
            "9S",
            "9H"
          ],
          "kind": "discard",
          "model_action_value": 0.8,
          "q": 0.8
        },
        {
          "cards": [
            "2D",
            "4C",
            "9S",
            "AH"
          ],
          "kind": "discard",
          "model_action_value": 0.8,
          "q": 0.8
        },
        {
          "cards": [
            "2D",
            "4C",
            "9H"
          ],
          "kind": "discard",
          "model_action_value": 0.6,
          "q": 0.6
        },
        {
          "cards": [
            "2D",
            "4C",
            "9S"
          ],
          "kind": "discard",
          "model_action_value": 0.6,
          "q": 0.6
        },
        {
          "cards": [
            "2D",
            "4C",
            "AH"
          ],
          "kind": "discard",
          "model_action_value": 0.6,
          "q": 0.6
        },
        {
          "cards": [
            "2D",
            "9S",
            "9H"
          ],
          "kind": "discard",
          "model_action_value": 0.6,
          "q": 0.6
        },
        {
          "cards": [
            "2D",
            "9S",
            "AH"
          ],
          "kind": "discard",
          "model_action_value": 0.6,
          "q": 0.6
        },
        {
          "cards": [
            "4C",
            "9S",
            "9H"
          ],
          "kind": "discard",
          "model_action_value": 0.6,
          "q": 0.6
        },
        {
          "cards": [
            "4C",
            "9S",
            "AH"
          ],
          "kind": "discard",
          "model_action_value": 0.6,
          "q": 0.6
        },
        {
          "cards": [
            "2D",
            "4C"
          ],
          "kind": "discard",
          "model_action_value": 0.4,
          "q": 0.4
        },
        {
          "cards": [
            "2D",
            "9H"
          ],
          "kind": "discard",
          "model_action_value": 0.4,
          "q": 0.4
        },
        {
          "cards": [
            "2D",
            "9S"
          ],
          "kind": "discard",
          "model_action_value": 0.4,
          "q": 0.4
        },
        {
          "cards": [
            "2D",
            "AH"
          ],
          "kind": "discard",
          "model_action_value": 0.4,
          "q": 0.4
        },
        {
          "cards": [
            "4C",
            "9H"
          ],
          "kind": "discard",
          "model_action_value": 0.4,
          "q": 0.4
        },
        {
          "cards": [
            "4C",
            "9S"
          ],
          "kind": "discard",
          "model_action_value": 0.4,
          "q": 0.4
        },
        {
          "cards": [
            "4C",
            "AH"
          ],
          "kind": "discard",
          "model_action_value": 0.4,
          "q": 0.4
        },
        {
          "cards": [
            "9S",
            "9H"
          ],
          "kind": "discard",
          "model_action_value": 0.4,
          "q": 0.4
        },
        {
          "cards": [
            "9S",
            "AH"
          ],
          "kind": "discard",
          "model_action_value": 0.4,
          "q": 0.4
        },
        {
          "cards": [
            "2D"
          ],
          "kind": "discard",
          "model_action_value": 0.2,
          "q": 0.2
        },
        {
          "cards": [
            "4C"
          ],
          "kind": "discard",
          "model_action_value": 0.2,
          "q": 0.2
        },
        {
          "cards": [
            "9H"
          ],
          "kind": "discard",
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          "q": 0.2
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        {
          "cards": [
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          ],
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          "q": 0.2
        },
        {
          "cards": [
            "AH"
          ],
          "kind": "discard",
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          "q": 0.2
        },
        {
          "cards": [
            "JH"
          ],
          "kind": "discard",
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          "q": 0
        },
        {
          "cards": [
            "KH"
          ],
          "kind": "discard",
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        {
          "cards": [
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          ],
          "kind": "discard",
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        {
          "cards": [
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        {
          "cards": [
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        {
          "cards": [
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          "cards": [
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          "cards": [
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        {
          "cards": [
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          ],
          "clears_now": false,
          "hand_type": "high_card",
          "kind": "play",
          "model_action_value": 0,
          "q": 0,
          "score": 16
        },
        {
          "cards": [
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            "QH",
            "KH",
            "AH"
          ],
          "clears_now": false,
          "hand_type": "flush",
          "kind": "play",
          "model_action_value": 0,
          "q": 0,
          "score": 340
        },
        {
          "cards": [
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            "JH",
            "KH",
            "AH"
          ],
          "clears_now": false,
          "hand_type": "pair",
          "kind": "play",
          "model_action_value": 0,
          "q": 0,
          "score": 56
        },
        {
          "cards": [
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            "JH",
            "QH",
            "AH"
          ],
          "clears_now": false,
          "hand_type": "pair",
          "kind": "play",
          "model_action_value": 0,
          "q": 0,
          "score": 56
        },
        {
          "cards": [
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            "JH",
            "QH",
            "KH"
          ],
          "clears_now": false,
          "hand_type": "pair",
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          "model_action_value": 0,
          "q": 0,
          "score": 56
        },
        {
          "cards": [
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            "9H",
            "QH",
            "KH",
            "AH"
          ],
          "clears_now": false,
          "hand_type": "pair",
          "kind": "play",
          "model_action_value": 0,
          "q": 0,
          "score": 56
        },
        {
          "cards": [
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            "JH",
            "QH",
            "KH",
            "AH"
          ],
          "clears_now": false,
          "hand_type": "high_card",
          "kind": "play",
          "model_action_value": 0,
          "q": 0,
          "score": 16
        }
      ],
      "recommendation": null,
      "sampling": null,
      "score_calls": 282964,
      "v_star": 0.8
    },
    "rules_version": "balatro-001a-rules-v0.1",
    "rustc": "rustc 1.98.0 (88d9e12ae 2026-08-18)",
    "status": "completed",
    "uncertainty": {
      "kind": "model_scope",
      "note": "No Monte Carlo estimates or confidence intervals are returned.",
      "sampling_interval": null
    }
  }
}