This paper introduces a systematic method for evaluating the strength of customizable trading card game (TCG) cards using a Calculated Power (CP) system. The CP metric provides a quantitative approach to card balance, accounting for attack, defense, health, mana cost, and special abilities. The system also integrates mana complexity to balance mono-color, multi-color, and colorless cards. We apply the CP framework to real-world examples, including powerful creatures such as Ulamog and Emrakul, and contrast them with weaker cards to demonstrate the effectiveness of the model.

Introduction

The balance of power in TCGs like Magic: The Gathering (MTG) is a crucial factor in game design. Overpowered cards can destabilize a format, while underpowered cards may never see play. This study introduces a CP-based evaluation system that provides a structured, numerical approach to assessing card strength. The CP calculation accounts for raw stats, ability modifiers, and mana complexity, ensuring an equitable representation of a card’s impact on gameplay.

Methodology: The CP Calculation Model

The CP system evaluates a card using the formula:

CP = (ATK + DEF + (HP / 2) + MANA_VALUE) + \sum ABILITY_VALUE

Where:

  • ATK (Attack Power): Direct damage dealt.
  • DEF (Defense/Block Power): Reduction of incoming damage.
  • HP (Health Points): Half of HP contributes to CP.
  • MANA_VALUE: Adjusted based on mana complexity:
    • Mono-Color: ×1.7 multiplier.
    • Dual-Color: ×1.3 multiplier.
    • Three-Color: ×1.1 multiplier.
    • Four/Five-Color: ×1.0 multiplier.
    • Colorless: ×2.0 multiplier.
  • ABILITY_VALUE: Numerical adjustments for card abilities.

The CP value is then mapped to rarity levels:

CP Range Rarity
1 - 5 Common
6 - 10 Uncommon
11 - 15 Rare
16 - 20 Epic
21+ Legendary

Case Study: Evaluating Strong and Weak Cards

Case 1: Ulamog, the Ceaseless Hunger

Ulamog is a well-known powerhouse in MTG, with the following stats:

  • ATK: 10
  • DEF: 10
  • HP: N/A (Assume 0 for CP purposes)
  • Mana Cost: 10 (Colorless)
  • Abilities:
    • Indestructible (+8 CP)
    • Exile two permanents on cast (+6 CP)
    • Mill 20 on attack (+6 CP)

CP Calculation for Ulamog

CP = (10 + 10 + (0/2) + (10 \times 2.0)) + (8 + 6 + 6)
CP = (10 + 10 + 20) + 20
CP = 60  \Rightarrow \textbf{Mythic/Overpowered}

Ulamog vastly exceeds the CP system’s scale, confirming its role as a game-altering powerhouse.

Case 2: Emrakul, the Promised End

  • ATK: 13
  • DEF: 13
  • HP: N/A
  • Mana Cost: 13 (Colorless, reduced based on opponent’s types)
  • Abilities:
    • Protection from Instants (+4 CP)
    • Control opponent’s turn (+12 CP)
    • Flying (+3 CP)
    • Trample (+3 CP)

CP Calculation for Emrakul

CP = (13 + 13 + (0/2) + (13 \times 2.0)) + (4 + 12 + 3 + 3)
CP = (13 + 13 + 26) + 22
CP = 74  \Rightarrow \textbf{Mythic/Overpowered}

Emrakul exceeds even Ulamog’s CP, reflecting its historically oppressive nature in MTG formats.

Case 3: Humorously Weak Card – Chimney Imp

  • ATK: 1
  • DEF: 2
  • HP: N/A
  • Mana Cost: 5 (Mono-Black)
  • Abilities:
    • Opponent puts a card on top of their library on death (+1 CP)
    • Flying (+3 CP)

CP Calculation for Chimney Imp

CP = (1 + 2 + (0/2) + (5 \times 1.7)) + (1 + 3)
CP = (1 + 2 + 8.5) + 4
CP = 15.5  \Rightarrow \textbf{Rare (but ironically bad)}

Case 4: Humorously Weak Card – Mudhole

  • ATK: 0
  • DEF: 0
  • Mana Cost: 3 (Mono-Red)
  • Abilities:
    • Exile all lands from a graveyard (+1 CP)

CP Calculation for Mudhole

CP = (0 + 0 + (0/2) + (3 \times 1.7)) + 1
CP = (0 + 0 + 5.1) + 1
CP = 6.1  \Rightarrow \textbf{Uncommon}

Conclusion

The CP system provides a structured, numerical method for balancing TCG cards. By applying it to existing cards, we see that it successfully differentiates between game-breaking threats and weak, meme-worthy cards. The mana complexity adjustment ensures fairness between mono-color and colorless strategies, preventing unintended advantages. Future research could refine this model by introducing interaction-based modifiers or playtesting results.