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Prize Blocks #2

Description

@benson0402

不知道這樣 tag 有沒有通知
@Bill-Huangz @gainsborouo

blocks = [
{"name": "Dirt", "enabled": False, "prize_chance": 10, "garbage_chance": 20, "prize_name": None, "quantity": 0, "health": 1},
{"name": "Stone", "enabled": False, "prize_chance": 10, "garbage_chance": 15, "prize_name": None, "quantity": 0, "health": 3},
{"name": "Coal", "enabled": False, "prize_chance": 15, "garbage_chance": 10, "prize_name": None, "quantity": 0, "health": 5},
{"name": "Iron", "enabled": False, "prize_chance": 20, "garbage_chance": 5, "prize_name": None, "quantity": 0, "health": 7},
{"name": "Sand", "enabled": False, "prize_chance": 10, "garbage_chance": 30, "prize_name": None, "quantity": 0, "health": 2},
{"name": "Diamond", "enabled": False, "prize_chance": 5, "garbage_chance": 0, "prize_name": "Diamond Prize", "quantity": 10, "health": 10},
{"name": "Emerald", "enabled": False, "prize_chance": 10, "garbage_chance": 0, "prize_name": "Emerald Prize", "quantity": 20, "health": 8},
{"name": "Gold", "enabled": False, "prize_chance": 15, "garbage_chance": 0, "prize_name": "Gold Prize", "quantity": 30, "health": 6},
{"name": "Ruby", "enabled": False, "prize_chance": 20, "garbage_chance": 0, "prize_name": "Ruby Prize", "quantity": 5, "health": 12},
]

假設

  • 玩家數:100
  • 速度:5 clicks/sec
  • 時長:2 hrs(7,200 secs)
  • Block types:6

估計

$TotalClicks = 5 \times 100 \times 7{,}200 = 3{,}600{,}000$

$ClicksPerType = \displaystyle\frac{3{,}600{,}000}{6} = 600{,}000$

假設每次摧毀時掉落機率為 $10 \times 0.0001 = 0.1 趴$

$$ E[\text{掉落數}] = \frac{ClicksPerType}{health} \times 0.001 = \frac{600{,}000}{health} \times 0.001 = \frac{600}{health} $$

$$ \frac{600}{health} \approx quantity \quad\Longrightarrow\quad health \approx \frac{600}{quantity} $$

結果

Quantity Health ($\approx 600/quantity$)
10 60
2 300
1 600

blocks.json

[
  {
    "name": "Dirt",
    "enabled": false,
    "prize_chance": 10,
    "garbage_chance": 10,
    "prize_name": "Miku Brunch Voucher (NT$150)",
    "quantity": 10,
    "health": 60
  },
  {
    "name": "Stone",
    "enabled": false,
    "prize_chance": 10,
    "garbage_chance": 10,
    "prize_name": "Lala Kitchen Voucher (NT$100)",
    "quantity": 1,
    "health": 600
  },
  {
    "name": "Coal",
    "enabled": false,
    "prize_chance": 10,
    "garbage_chance": 10,
    "prize_name": "Escapeholic Single Ticket (NT$550)",
    "quantity": 1,
    "health": 600
  },
  {
    "name": "Iron",
    "enabled": false,
    "prize_chance": 10,
    "garbage_chance": 10,
    "prize_name": "Jumping Grid Free Ticket (NT$499)",
    "quantity": 1,
    "health": 600
  },
  {
    "name": "Gold",
    "enabled": false,
    "prize_chance": 10,
    "garbage_chance": 10,
    "prize_name": "Golden Triangle Beer Voucher",
    "quantity": 2,
    "health": 300
  },
  {
    "name": "Diamond",
    "enabled": false,
    "prize_chance": 10,
    "garbage_chance": 10,
    "prize_name": "Tetsu Gyoza NT$100 Voucher",
    "quantity": 10,
    "health": 60
  }
]

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