Mathematical Methodology

About TCG Pocket Luck Calculator

How binomial probability, official Genetic Apex drop rates, and stamina efficiency algorithms model your Pokémon TCG Pocket pull luck.

🎯 The Purpose of This Calculator

With millions of players opening packs daily in Pokémon Trading Card Game Pocket, human cognitive bias frequently causes players to believe their accounts are either unusually "lucky" or unfairly "cursed."

TCG Pocket Luck Calculator was engineered to replace subjective feelings with rigorous mathematical proof. By taking your lifetime booster pack total from your in-game medals and calculating binomial probability curves against official disclosure rates, we provide a mathematically sound global luck percentile.

📐 Probability & Mathematical Formulations

1. Cumulative Drop Rate Model

In a standard booster pack, card slots are not uniform. Slots 1 through 3 are fixed to common 1-Diamond cards, while ultra-rare cards only appear in Slot 4 and Slot 5 with tiered probabilities:

P(Crown Rare in Pack) = 1 - (1 - P_Slot4) × (1 - P_Slot5) ≈ 0.200% (1 in 500 packs)

2. God Pack (Rare Pack) Probability

A God Pack replaces the entire standard 5-card booster with an all-rare pack where every single card is an Illustration Rare (1-Star), Super Rare (2-Star), Immersive (3-Star), or Crown Rare. Its base probability is fixed at 0.050% (1 in 2,000 packs).

Cumulative God Pack Probability = 1 - (1 - 0.0005)^n

3. Wonder Pick Stamina Return-On-Investment (ROI)

Wonder Pick presents 5 face-down cards. Regardless of visual animation shuffles, selecting 1 random card out of 5 yields a flat 20.0% probability per desired target card:

Expected Stamina per Hit = (Stamina Cost) / (Target Count / 5)

Spending 3 Wonder Stamina on a pool with only 1 card you need yields an expected cost of 15 Stamina per hit. Saving stamina for pools with 2 or more desired cards drastically improves your collection velocity.

Independent Fan Project Disclaimer

Pokémon and Pokémon character names are trademarks of Nintendo, Creatures Inc., and Game Freak Inc. Pokémon Trading Card Game Pocket is published by The Pokémon Company and developed by DeNA Co., Ltd. TCG Pocket Luck Calculator is an independent, fan-made educational and statistical tool. It is not affiliated with, endorsed, sponsored, or supported by Nintendo, Game Freak, Creatures, The Pokémon Company, or DeNA.