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LongBench v2 / 671b1335bb02136c067d4e88 / Which player won the most times in the game?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Which player won the most times in the game?
context · full text (92,437 characters)
{
  "meta": {
    "name_exp": "qwen2-72b_guessing_game_v1_1",
    "player_num": 10,
    "min": 0,
    "max": 100,
    "ratio": 0.6666666666666666,
    "ratio_str": "2/3",
    "round_id": 20,
    "version": "v1"
  },
  "round_records": [
    {
      "responses": [
        33,
        50,
        50,
        33,
        66,
        33,
        50,
        66,
        66,
        33
      ],
      "mean": 48,
      "mean_ratio": 32.0,
      "winner": 33,
      "winner_num": 4
    },
    {
      "responses": [
        22,
        30,
        30,
        33,
        40,
        21,
        40,
        40,
        33,
        22
      ],
      "mean": 31.1,
      "mean_ratio": 20.733333333333334,
      "winner": 21,
      "winner_num": 1
    },
    {
      "responses": [
        22,
        25,
        20,
        15,
        27,
        25,
        20,
        25,
        16,
        15
      ],
      "mean": 21,
      "mean_ratio": 14.0,
      "winner": 15,
      "winner_num": 2
    },
    {
      "responses": [
        13,
        13,
        16,
        18,
        12,
        20,
        20,
        18,
        13,
        12
      ],
      "mean": 15.5,
      "mean_ratio": 10.333333333333332,
      "winner": 12,
      "winner_num": 2
    },
    {
      "responses": [
        15,
        10,
        10,
        16,
        9,
        10,
        9,
        13,
        10,
        14
      ],
      "mean": 11.6,
      "mean_ratio": 7.7333333333333325,
      "winner": 9,
      "winner_num": 2
    },
    {
      "responses": [
        10,
        10,
        10,
        8,
        12,
        7,
        8,
        7,
        8,
        7
      ],
      "mean": 8.7,
      "mean_ratio": 5.799999999999999,
      "winner": 7,
      "winner_num": 3
    },
    {
      "responses": [
        6,
        7,
        6,
        6,
        8,
        6,
        6,
        8,
        9,
        6
      ],
      "mean": 6.8,
      "mean_ratio": 4.533333333333333,
      "winner": 6,
      "winner_num": 6
    },
    {
      "responses": [
        5,
        6,
        6,
        5,
        8,
        5,
        5,
        4,
        5,
        6
      ],
      "mean": 5.5,
      "mean_ratio": 3.6666666666666665,
      "winner": 4,
      "winner_num": 1
    },
    {
      "responses": [
        3,
        6,
        4,
        4,
        4,
        4,
        4,
        5,
        4,
        4
      ],
      "mean": 4.2,
      "mean_ratio": 2.8,
      "winner": 3,
      "winner_num": 1
    },
    {
      "responses": [
        3,
        3,
        4,
        2,
        5,
        3,
        3,
        3,
        3,
        3
      ],
      "mean": 3.2,
      "mean_ratio": 2.1333333333333333,
      "winner": 2,
      "winner_num": 1
    },
    {
      "responses": [
        4,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        3,
        2
      ],
      "mean": 2.3,
      "mean_ratio": 1.5333333333333332,
      "winner": 2,
      "winner_num": 8
    },
    {
      "responses": [
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        3,
        2
      ],
      "mean": 2.1,
      "mean_ratio": 1.4,
      "winner": 2,
      "winner_num": 9
    },
    {
      "responses": [
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "mean": 2,
      "mean_ratio": 1.3333333333333333,
      "winner": 2,
      "winner_num": 10
    },
    {
      "responses": [
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "mean": 2,
      "mean_ratio": 1.3333333333333333,
      "winner": 2,
      "winner_num": 10
    },
    {
      "responses": [
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "mean": 2,
      "mean_ratio": 1.3333333333333333,
      "winner": 2,
      "winner_num": 10
    },
    {
      "responses": [
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "mean": 2,
      "mean_ratio": 1.3333333333333333,
      "winner": 2,
      "winner_num": 10
    },
    {
      "responses": [
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "mean": 2,
      "mean_ratio": 1.3333333333333333,
      "winner": 2,
      "winner_num": 10
    },
    {
      "responses": [
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "mean": 2,
      "mean_ratio": 1.3333333333333333,
      "winner": 2,
      "winner_num": 10
    },
    {
      "responses": [
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "mean": 2,
      "mean_ratio": 1.3333333333333333,
      "winner": 2,
      "winner_num": 10
    },
    {
      "responses": [
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "mean": 2,
      "mean_ratio": 1.3333333333333333,
      "winner": 2,
      "winner_num": 10
    }
  ],
  "player_data": [
    {
      "model": "Qwen/Qwen2-72B-Instruct",
      "id": "player_0",
      "prompt": [
        {
          "role": "system",
          "content": "\n\nYou are participating in a game played by 10 players over 20 rounds.\n\nGame Rules:\n\n1. Each player selects an integer number between 0 and 100, inclusive.\n2. After all selections are made, the average of all chosen numbers is calculated.\n3. The target number is 2/3 of this average.\n4. The winner is the player(s) who selected a number closest to the target number."
        },
        {
          "role": "user",
          "content": "Game Results for Round 1:\n\nAverage Number Chosen: 48\nTarget Number (2/3 of Average): 32.00\nWinning Number: 33.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"66\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 2:\n\nAverage Number Chosen: 31.1\nTarget Number (2/3 of Average): 20.73\nWinning Number: 21.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"40\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 3:\n\nAverage Number Chosen: 21\nTarget Number (2/3 of Average): 14.00\nWinning Number: 15.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"25\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 4:\n\nAverage Number Chosen: 15.5\nTarget Number (2/3 of Average): 10.33\nWinning Number: 12.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"16\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 5:\n\nAverage Number Chosen: 11.6\nTarget Number (2/3 of Average): 7.73\nWinning Number: 9.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"10\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 6:\n\nAverage Number Chosen: 8.7\nTarget Number (2/3 of Average): 5.80\nWinning Number: 7.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"8\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 7:\n\nAverage Number Chosen: 6.8\nTarget Number (2/3 of Average): 4.53\nWinning Number: 6.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"6\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 8:\n\nAverage Number Chosen: 5.5\nTarget Number (2/3 of Average): 3.67\nWinning Number: 4.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"5\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 9:\n\nAverage Number Chosen: 4.2\nTarget Number (2/3 of Average): 2.80\nWinning Number: 3.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"4\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 10:\n\nAverage Number Chosen: 3.2\nTarget Number (2/3 of Average): 2.13\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"3\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 11:\n\nAverage Number Chosen: 2.3\nTarget Number (2/3 of Average): 1.53\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 12:\n\nAverage Number Chosen: 2.1\nTarget Number (2/3 of Average): 1.40\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 13:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 14:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 15:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 16:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 17:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 18:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 19:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 20:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        }
      ],
      "records": [
        66,
        40,
        25,
        16,
        10,
        8,
        6,
        5,
        4,
        3,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "utility": []
    },
    {
      "model": "Qwen/Qwen2-72B-Instruct",
      "id": "player_1",
      "prompt": [
        {
          "role": "system",
          "content": "\n\nYou are participating in a game played by 10 players over 20 rounds.\n\nGame Rules:\n\n1. Each player selects an integer number between 0 and 100, inclusive.\n2. After all selections are made, the average of all chosen numbers is calculated.\n3. The target number is 2/3 of this average.\n4. The winner is the player(s) who selected a number closest to the target number."
        },
        {
          "role": "user",
          "content": "Game Results for Round 1:\n\nAverage Number Chosen: 48\nTarget Number (2/3 of Average): 32.00\nWinning Number: 33.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"50\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 2:\n\nAverage Number Chosen: 31.1\nTarget Number (2/3 of Average): 20.73\nWinning Number: 21.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"33\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 3:\n\nAverage Number Chosen: 21\nTarget Number (2/3 of Average): 14.00\nWinning Number: 15.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"20\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 4:\n\nAverage Number Chosen: 15.5\nTarget Number (2/3 of Average): 10.33\nWinning Number: 12.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"13\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 5:\n\nAverage Number Chosen: 11.6\nTarget Number (2/3 of Average): 7.73\nWinning Number: 9.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"9\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 6:\n\nAverage Number Chosen: 8.7\nTarget Number (2/3 of Average): 5.80\nWinning Number: 7.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"7\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 7:\n\nAverage Number Chosen: 6.8\nTarget Number (2/3 of Average): 4.53\nWinning Number: 6.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"6\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 8:\n\nAverage Number Chosen: 5.5\nTarget Number (2/3 of Average): 3.67\nWinning Number: 4.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"5\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 9:\n\nAverage Number Chosen: 4.2\nTarget Number (2/3 of Average): 2.80\nWinning Number: 3.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"4\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 10:\n\nAverage Number Chosen: 3.2\nTarget Number (2/3 of Average): 2.13\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"3\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 11:\n\nAverage Number Chosen: 2.3\nTarget Number (2/3 of Average): 1.53\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 12:\n\nAverage Number Chosen: 2.1\nTarget Number (2/3 of Average): 1.40\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 13:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 14:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 15:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 16:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 17:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 18:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 19:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 20:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        }
      ],
      "records": [
        50,
        33,
        20,
        13,
        9,
        7,
        6,
        5,
        4,
        3,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "utility": []
    },
    {
      "model": "Qwen/Qwen2-72B-Instruct",
      "id": "player_2",
      "prompt": [
        {
          "role": "system",
          "content": "\n\nYou are participating in a game played by 10 players over 20 rounds.\n\nGame Rules:\n\n1. Each player selects an integer number between 0 and 100, inclusive.\n2. After all selections are made, the average of all chosen numbers is calculated.\n3. The target number is 2/3 of this average.\n4. The winner is the player(s) who selected a number closest to the target number."
        },
        {
          "role": "user",
          "content": "Game Results for Round 1:\n\nAverage Number Chosen: 48\nTarget Number (2/3 of Average): 32.00\nWinning Number: 33.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"33\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 2:\n\nAverage Number Chosen: 31.1\nTarget Number (2/3 of Average): 20.73\nWinning Number: 21.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"22\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 3:\n\nAverage Number Chosen: 21\nTarget Number (2/3 of Average): 14.00\nWinning Number: 15.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"16\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 4:\n\nAverage Number Chosen: 15.5\nTarget Number (2/3 of Average): 10.33\nWinning Number: 12.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"13\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 5:\n\nAverage Number Chosen: 11.6\nTarget Number (2/3 of Average): 7.73\nWinning Number: 9.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"9\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 6:\n\nAverage Number Chosen: 8.7\nTarget Number (2/3 of Average): 5.80\nWinning Number: 7.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"7\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 7:\n\nAverage Number Chosen: 6.8\nTarget Number (2/3 of Average): 4.53\nWinning Number: 6.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"6\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 8:\n\nAverage Number Chosen: 5.5\nTarget Number (2/3 of Average): 3.67\nWinning Number: 4.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"5\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 9:\n\nAverage Number Chosen: 4.2\nTarget Number (2/3 of Average): 2.80\nWinning Number: 3.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"4\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 10:\n\nAverage Number Chosen: 3.2\nTarget Number (2/3 of Average): 2.13\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"3\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 11:\n\nAverage Number Chosen: 2.3\nTarget Number (2/3 of Average): 1.53\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 12:\n\nAverage Number Chosen: 2.1\nTarget Number (2/3 of Average): 1.40\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 13:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 14:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 15:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 16:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 17:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 18:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 19:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 20:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        }
      ],
      "records": [
        33,
        22,
        16,
        13,
        9,
        7,
        6,
        5,
        4,
        3,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "utility": []
    },
    {
      "model": "Qwen/Qwen2-72B-Instruct",
      "id": "player_3",
      "prompt": [
        {
          "role": "system",
          "content": "\n\nYou are participating in a game played by 10 players over 20 rounds.\n\nGame Rules:\n\n1. Each player selects an integer number between 0 and 100, inclusive.\n2. After all selections are made, the average of all chosen numbers is calculated.\n3. The target number is 2/3 of this average.\n4. The winner is the player(s) who selected a number closest to the target number."
        },
        {
          "role": "user",
          "content": "Game Results for Round 1:\n\nAverage Number Chosen: 48\nTarget Number (2/3 of Average): 32.00\nWinning Number: 33.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"50\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 2:\n\nAverage Number Chosen: 31.1\nTarget Number (2/3 of Average): 20.73\nWinning Number: 21.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"33\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 3:\n\nAverage Number Chosen: 21\nTarget Number (2/3 of Average): 14.00\nWinning Number: 15.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"22\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 4:\n\nAverage Number Chosen: 15.5\nTarget Number (2/3 of Average): 10.33\nWinning Number: 12.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"18\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 5:\n\nAverage Number Chosen: 11.6\nTarget Number (2/3 of Average): 7.73\nWinning Number: 9.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"14\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 6:\n\nAverage Number Chosen: 8.7\nTarget Number (2/3 of Average): 5.80\nWinning Number: 7.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"12\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 7:\n\nAverage Number Chosen: 6.8\nTarget Number (2/3 of Average): 4.53\nWinning Number: 6.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"9\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 8:\n\nAverage Number Chosen: 5.5\nTarget Number (2/3 of Average): 3.67\nWinning Number: 4.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"8\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 9:\n\nAverage Number Chosen: 4.2\nTarget Number (2/3 of Average): 2.80\nWinning Number: 3.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"6\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 10:\n\nAverage Number Chosen: 3.2\nTarget Number (2/3 of Average): 2.13\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"5\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 11:\n\nAverage Number Chosen: 2.3\nTarget Number (2/3 of Average): 1.53\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"4\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 12:\n\nAverage Number Chosen: 2.1\nTarget Number (2/3 of Average): 1.40\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"3\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 13:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 14:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 15:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 16:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 17:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 18:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 19:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 20:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        }
      ],
      "records": [
        50,
        33,
        22,
        18,
        14,
        12,
        9,
        8,
        6,
        5,
        4,
        3,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "utility": []
    },
    {
      "model": "Qwen/Qwen2-72B-Instruct",
      "id": "player_4",
      "prompt": [
        {
          "role": "system",
          "content": "\n\nYou are participating in a game played by 10 players over 20 rounds.\n\nGame Rules:\n\n1. Each player selects an integer number between 0 and 100, inclusive.\n2. After all selections are made, the average of all chosen numbers is calculated.\n3. The target number is 2/3 of this average.\n4. The winner is the player(s) who selected a number closest to the target number."
        },
        {
          "role": "user",
          "content": "Game Results for Round 1:\n\nAverage Number Chosen: 48\nTarget Number (2/3 of Average): 32.00\nWinning Number: 33.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"66\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 2:\n\nAverage Number Chosen: 31.1\nTarget Number (2/3 of Average): 20.73\nWinning Number: 21.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"40\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 3:\n\nAverage Number Chosen: 21\nTarget Number (2/3 of Average): 14.00\nWinning Number: 15.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"25\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 4:\n\nAverage Number Chosen: 15.5\nTarget Number (2/3 of Average): 10.33\nWinning Number: 12.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"18\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 5:\n\nAverage Number Chosen: 11.6\nTarget Number (2/3 of Average): 7.73\nWinning Number: 9.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"13\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 6:\n\nAverage Number Chosen: 8.7\nTarget Number (2/3 of Average): 5.80\nWinning Number: 7.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"10\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 7:\n\nAverage Number Chosen: 6.8\nTarget Number (2/3 of Average): 4.53\nWinning Number: 6.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"7\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 8:\n\nAverage Number Chosen: 5.5\nTarget Number (2/3 of Average): 3.67\nWinning Number: 4.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"5\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 9:\n\nAverage Number Chosen: 4.2\nTarget Number (2/3 of Average): 2.80\nWinning Number: 3.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"4\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 10:\n\nAverage Number Chosen: 3.2\nTarget Number (2/3 of Average): 2.13\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"3\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 11:\n\nAverage Number Chosen: 2.3\nTarget Number (2/3 of Average): 1.53\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 12:\n\nAverage Number Chosen: 2.1\nTarget Number (2/3 of Average): 1.40\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 13:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 14:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 15:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 16:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 17:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 18:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 19:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 20:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        }
      ],
      "records": [
        66,
        40,
        25,
        18,
        13,
        10,
        7,
        5,
        4,
        3,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "utility": []
    },
    {
      "model": "Qwen/Qwen2-72B-Instruct",
      "id": "player_5",
      "prompt": [
        {
          "role": "system",
          "content": "\n\nYou are participating in a game played by 10 players over 20 rounds.\n\nGame Rules:\n\n1. Each player selects an integer number between 0 and 100, inclusive.\n2. After all selections are made, the average of all chosen numbers is calculated.\n3. The target number is 2/3 of this average.\n4. The winner is the player(s) who selected a number closest to the target number."
        },
        {
          "role": "user",
          "content": "Game Results for Round 1:\n\nAverage Number Chosen: 48\nTarget Number (2/3 of Average): 32.00\nWinning Number: 33.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"66\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 2:\n\nAverage Number Chosen: 31.1\nTarget Number (2/3 of Average): 20.73\nWinning Number: 21.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"40\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 3:\n\nAverage Number Chosen: 21\nTarget Number (2/3 of Average): 14.00\nWinning Number: 15.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"27\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 4:\n\nAverage Number Chosen: 15.5\nTarget Number (2/3 of Average): 10.33\nWinning Number: 12.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"20\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 5:\n\nAverage Number Chosen: 11.6\nTarget Number (2/3 of Average): 7.73\nWinning Number: 9.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"16\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 6:\n\nAverage Number Chosen: 8.7\nTarget Number (2/3 of Average): 5.80\nWinning Number: 7.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"10\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 7:\n\nAverage Number Chosen: 6.8\nTarget Number (2/3 of Average): 4.53\nWinning Number: 6.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"8\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 8:\n\nAverage Number Chosen: 5.5\nTarget Number (2/3 of Average): 3.67\nWinning Number: 4.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"6\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 9:\n\nAverage Number Chosen: 4.2\nTarget Number (2/3 of Average): 2.80\nWinning Number: 3.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"4\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 10:\n\nAverage Number Chosen: 3.2\nTarget Number (2/3 of Average): 2.13\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"3\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 11:\n\nAverage Number Chosen: 2.3\nTarget Number (2/3 of Average): 1.53\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 12:\n\nAverage Number Chosen: 2.1\nTarget Number (2/3 of Average): 1.40\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 13:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 14:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 15:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 16:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 17:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 18:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 19:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 20:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        }
      ],
      "records": [
        66,
        40,
        27,
        20,
        16,
        10,
        8,
        6,
        4,
        3,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "utility": []
    },
    {
      "model": "Qwen/Qwen2-72B-Instruct",
      "id": "player_6",
      "prompt": [
        {
          "role": "system",
          "content": "\n\nYou are participating in a game played by 10 players over 20 rounds.\n\nGame Rules:\n\n1. Each player selects an integer number between 0 and 100, inclusive.\n2. After all selections are made, the average of all chosen numbers is calculated.\n3. The target number is 2/3 of this average.\n4. The winner is the player(s) who selected a number closest to the target number."
        },
        {
          "role": "user",
          "content": "Game Results for Round 1:\n\nAverage Number Chosen: 48\nTarget Number (2/3 of Average): 32.00\nWinning Number: 33.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"33\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 2:\n\nAverage Number Chosen: 31.1\nTarget Number (2/3 of Average): 20.73\nWinning Number: 21.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"21\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 3:\n\nAverage Number Chosen: 21\nTarget Number (2/3 of Average): 14.00\nWinning Number: 15.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"15\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 4:\n\nAverage Number Chosen: 15.5\nTarget Number (2/3 of Average): 10.33\nWinning Number: 12.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"12\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 5:\n\nAverage Number Chosen: 11.6\nTarget Number (2/3 of Average): 7.73\nWinning Number: 9.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"10\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 6:\n\nAverage Number Chosen: 8.7\nTarget Number (2/3 of Average): 5.80\nWinning Number: 7.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"7\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 7:\n\nAverage Number Chosen: 6.8\nTarget Number (2/3 of Average): 4.53\nWinning Number: 6.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"6\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 8:\n\nAverage Number Chosen: 5.5\nTarget Number (2/3 of Average): 3.67\nWinning Number: 4.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"6\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 9:\n\nAverage Number Chosen: 4.2\nTarget Number (2/3 of Average): 2.80\nWinning Number: 3.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"4\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 10:\n\nAverage Number Chosen: 3.2\nTarget Number (2/3 of Average): 2.13\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"3\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 11:\n\nAverage Number Chosen: 2.3\nTarget Number (2/3 of Average): 1.53\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 12:\n\nAverage Number Chosen: 2.1\nTarget Number (2/3 of Average): 1.40\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 13:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 14:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 15:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 16:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 17:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 18:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 19:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 20:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        }
      ],
      "records": [
        33,
        21,
        15,
        12,
        10,
        7,
        6,
        6,
        4,
        3,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "utility": []
    },
    {
      "model": "Qwen/Qwen2-72B-Instruct",
      "id": "player_7",
      "prompt": [
        {
          "role": "system",
          "content": "\n\nYou are participating in a game played by 10 players over 20 rounds.\n\nGame Rules:\n\n1. Each player selects an integer number between 0 and 100, inclusive.\n2. After all selections are made, the average of all chosen numbers is calculated.\n3. The target number is 2/3 of this average.\n4. The winner is the player(s) who selected a number closest to the target number."
        },
        {
          "role": "user",
          "content": "Game Results for Round 1:\n\nAverage Number Chosen: 48\nTarget Number (2/3 of Average): 32.00\nWinning Number: 33.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"33\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 2:\n\nAverage Number Chosen: 31.1\nTarget Number (2/3 of Average): 20.73\nWinning Number: 21.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"30\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 3:\n\nAverage Number Chosen: 21\nTarget Number (2/3 of Average): 14.00\nWinning Number: 15.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"20\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 4:\n\nAverage Number Chosen: 15.5\nTarget Number (2/3 of Average): 10.33\nWinning Number: 12.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"13\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 5:\n\nAverage Number Chosen: 11.6\nTarget Number (2/3 of Average): 7.73\nWinning Number: 9.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"10\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 6:\n\nAverage Number Chosen: 8.7\nTarget Number (2/3 of Average): 5.80\nWinning Number: 7.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"8\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 7:\n\nAverage Number Chosen: 6.8\nTarget Number (2/3 of Average): 4.53\nWinning Number: 6.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"6\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 8:\n\nAverage Number Chosen: 5.5\nTarget Number (2/3 of Average): 3.67\nWinning Number: 4.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"4\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 9:\n\nAverage Number Chosen: 4.2\nTarget Number (2/3 of Average): 2.80\nWinning Number: 3.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"3\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 10:\n\nAverage Number Chosen: 3.2\nTarget Number (2/3 of Average): 2.13\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 11:\n\nAverage Number Chosen: 2.3\nTarget Number (2/3 of Average): 1.53\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 12:\n\nAverage Number Chosen: 2.1\nTarget Number (2/3 of Average): 1.40\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 13:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 14:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 15:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 16:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 17:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 18:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 19:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 20:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        }
      ],
      "records": [
        33,
        30,
        20,
        13,
        10,
        8,
        6,
        4,
        3,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "utility": []
    },
    {
      "model": "Qwen/Qwen2-72B-Instruct",
      "id": "player_8",
      "prompt": [
        {
          "role": "system",
          "content": "\n\nYou are participating in a game played by 10 players over 20 rounds.\n\nGame Rules:\n\n1. Each player selects an integer number between 0 and 100, inclusive.\n2. After all selections are made, the average of all chosen numbers is calculated.\n3. The target number is 2/3 of this average.\n4. The winner is the player(s) who selected a number closest to the target number."
        },
        {
          "role": "user",
          "content": "Game Results for Round 1:\n\nAverage Number Chosen: 48\nTarget Number (2/3 of Average): 32.00\nWinning Number: 33.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"50\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 2:\n\nAverage Number Chosen: 31.1\nTarget Number (2/3 of Average): 20.73\nWinning Number: 21.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"30\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 3:\n\nAverage Number Chosen: 21\nTarget Number (2/3 of Average): 14.00\nWinning Number: 15.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"25\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 4:\n\nAverage Number Chosen: 15.5\nTarget Number (2/3 of Average): 10.33\nWinning Number: 12.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"20\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 5:\n\nAverage Number Chosen: 11.6\nTarget Number (2/3 of Average): 7.73\nWinning Number: 9.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"15\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 6:\n\nAverage Number Chosen: 8.7\nTarget Number (2/3 of Average): 5.80\nWinning Number: 7.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"10\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 7:\n\nAverage Number Chosen: 6.8\nTarget Number (2/3 of Average): 4.53\nWinning Number: 6.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"8\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 8:\n\nAverage Number Chosen: 5.5\nTarget Number (2/3 of Average): 3.67\nWinning Number: 4.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"6\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 9:\n\nAverage Number Chosen: 4.2\nTarget Number (2/3 of Average): 2.80\nWinning Number: 3.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"5\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 10:\n\nAverage Number Chosen: 3.2\nTarget Number (2/3 of Average): 2.13\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"4\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 11:\n\nAverage Number Chosen: 2.3\nTarget Number (2/3 of Average): 1.53\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"3\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 12:\n\nAverage Number Chosen: 2.1\nTarget Number (2/3 of Average): 1.40\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 13:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 14:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 15:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 16:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 17:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 18:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 19:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 20:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        }
      ],
      "records": [
        50,
        30,
        25,
        20,
        15,
        10,
        8,
        6,
        5,
        4,
        3,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "utility": []
    },
    {
      "model": "Qwen/Qwen2-72B-Instruct",
      "id": "player_9",
      "prompt": [
        {
          "role": "system",
          "content": "\n\nYou are participating in a game played by 10 players over 20 rounds.\n\nGame Rules:\n\n1. Each player selects an integer number between 0 and 100, inclusive.\n2. After all selections are made, the average of all chosen numbers is calculated.\n3. The target number is 2/3 of this average.\n4. The winner is the player(s) who selected a number closest to the target number."
        },
        {
          "role": "user",
          "content": "Game Results for Round 1:\n\nAverage Number Chosen: 48\nTarget Number (2/3 of Average): 32.00\nWinning Number: 33.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"33\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 2:\n\nAverage Number Chosen: 31.1\nTarget Number (2/3 of Average): 20.73\nWinning Number: 21.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"22\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 3:\n\nAverage Number Chosen: 21\nTarget Number (2/3 of Average): 14.00\nWinning Number: 15.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"15\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 4:\n\nAverage Number Chosen: 15.5\nTarget Number (2/3 of Average): 10.33\nWinning Number: 12.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"12\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 5:\n\nAverage Number Chosen: 11.6\nTarget Number (2/3 of Average): 7.73\nWinning Number: 9.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"10\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 6:\n\nAverage Number Chosen: 8.7\nTarget Number (2/3 of Average): 5.80\nWinning Number: 7.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"8\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 7:\n\nAverage Number Chosen: 6.8\nTarget Number (2/3 of Average): 4.53\nWinning Number: 6.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"6\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 8:\n\nAverage Number Chosen: 5.5\nTarget Number (2/3 of Average): 3.67\nWinning Number: 4.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"5\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 9:\n\nAverage Number Chosen: 4.2\nTarget Number (2/3 of Average): 2.80\nWinning Number: 3.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"4\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 10:\n\nAverage Number Chosen: 3.2\nTarget Number (2/3 of Average): 2.13\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"3\"}"
        },
        {
          "role": "user",
          "content": "Unfortunately you lost."
        },
        {
          "role": "user",
          "content": "Game Results for Round 11:\n\nAverage Number Chosen: 2.3\nTarget Number (2/3 of Average): 1.53\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 12:\n\nAverage Number Chosen: 2.1\nTarget Number (2/3 of Average): 1.40\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 13:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 14:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 15:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 16:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 17:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 18:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 19:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        },
        {
          "role": "user",
          "content": "Game Results for Round 20:\n\nAverage Number Chosen: 2\nTarget Number (2/3 of Average): 1.33\nWinning Number: 2.\n\nYou chose:"
        },
        {
          "role": "assistant",
          "content": "{\"chosen_number\": \"2\"}"
        },
        {
          "role": "user",
          "content": "Congratulation you won."
        }
      ],
      "records": [
        33,
        22,
        15,
        12,
        10,
        8,
        6,
        5,
        4,
        3,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2,
        2
      ],
      "utility": []
    }
  ]
}

choice A

player_2

choice B

player_4

choice C

player_6

choice D

player_8

difficulty

easy

domain

Long-dialogue History Understanding

length

short

sub domain

Agent history QA

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

Official source

initial import