Optimal Pack Calculation Tool: Algorithm and Methodology for Maximizing Collection Completion

The Optimal Pack Calculation Tool uses a two-step statistical engine that computes per-pack pull probabilities for missing cards and selects the pack with the highest percentage chance of yielding a needed card.

The Optimal Pack Calculation Tool in the marcelpanse/tcg-pocket-collection-tracker repository helps players determine which booster packs offer the best statistical odds for completing their card collection. By analyzing pull rates against a user's current inventory, the tool transforms raw probability data into actionable pack-opening recommendations. This guide explains the complete algorithm and implementation behind this collection optimization engine.

The Two-Step Statistical Engine

The methodology follows a precise statistical pipeline. First, the system calculates the exact probability of obtaining any missing card from each available pack type. Second, it compares these probabilities across all expansions to identify the single pack offering the highest chance of collection advancement. This approach ensures recommendations are grounded in the actual rarity distributions and special mechanics defined in the game's data files.

Step 1: Computing Per-Pack Pull Rates

The pullRate Function in stats.ts

The core calculation resides in frontend/src/lib/stats.ts within the pullRate function (lines 20-30). This function evaluates the probability of pulling any card from a user's "wanted" list—the cards they still need to complete their collection.

The function first filters the expansion's card database to identify which cards belong to the specific pack being analyzed, including cards marked as available in 'everypack'. It then delegates the probability calculation to pullRateForCardSubset (lines 174-250), which iterates over each missing card and aggregates the chance of appearance across all five card slots in a pack.

Handling Special Pack Mechanics

The algorithm accounts for several TCG Pocket-specific pack variants through specialized probability adjustments:

• Rare-pack bonus: The abilityByRarityToBeInRarePack modifier adjusts probabilities for 5-card rare packs
• Baby-pack bonus: Uses probabilityPerRarityBaby to calculate odds for baby-themed packs
• Shiny-pack presence: Checks structure.containsShinies to factor in shiny card availability

These mechanics ensure the tool reflects the actual in-game pack structures rather than assuming uniform distributions.

Rarity Probability Tables

The calculation relies on two primary probability tables defined in stats.ts:

• standardPackProbabilities (lines 23-66): Defines base pull rates for each rarity slot in standard packs
• deluxePackProbabilities (lines 68-83): Contains adjusted rates for deluxe/gold packs

pullRateForCardSubset maps each card's rarity against these tables to determine the exact probability of appearing in each of the five card positions, then sums these probabilities to produce the overall "new-card" chance returned as a percentage.

Step 2: Selecting the Highest-Probability Pack

The Overview.tsx Selection Logic

The UI implementation in frontend/src/pages/overview/Overview.tsx (lines 68-76) executes the selection algorithm. For each openable expansion, the component maps over available packs (excluding the generic 'everypack' category) and constructs a comparison array:

const pullRates = expansion.packs
  .filter(p => p.name !== 'everypack')
  .map(pack => ({
    packName: pack.name,
    percentage: pullRate(wantedCards, expansion, pack, filters.deckbuildingMode),
    fill: pack.color,
  }));
const highestProbabilityPackCandidate = pullRates.sort((a, b) => b.percentage - a.percentage)[0];

The candidate with the highest percentage value across all expansions becomes the recommended "optimal pack" displayed in the GradientCard component.

Filtering Wanted Cards

Before calculation, the system determines "wanted" cards based on the user's collection state and filter settings. In deckbuilding mode, the algorithm targets cards needed for deck construction; in collection mode, it identifies any card where the user owns fewer copies than the target completion level. This filtered subset feeds into pullRate to ensure calculations reflect only relevant missing inventory.

Implementation Code Examples

Directly compute the best pack for a set of wanted cards:

import { pullRate } from '@/lib/stats';
import { expansions } from '@/lib/CardsDB';

// Assume `wantedCards` is an array of Card objects you still need
// and `deckbuildingMode` is a boolean flag from the UI
function getBestPack(wantedCards: Card[], deckbuildingMode: boolean) {
  let best = { packName: '', percentage: 0, fill: '' };

  for (const expansion of expansions.filter(e => e.openable)) {
    for (const pack of expansion.packs) {
      if (pack.name === 'everypack') continue;
      const pct = pullRate(wantedCards, expansion, pack, deckbuildingMode);
      if (pct > best.percentage) {
        best = { packName: pack.name, percentage: pct, fill: pack.color };
      }
    }
  }
  return best; // → { packName, percentage, fill }
}

How the UI determines the recommendation (excerpt from Overview.tsx):

const getHighestProbabilityPack = () => {
  let newHighest: { packName: string; percentage: number; fill: string } | undefined;
  const filteredExpansions = expansions.filter(e => e.openable);
  for (const expansion of filteredExpansions) {
    const pullRates = expansion.packs
      .filter(p => p.name !== 'everypack')
      .map(pack => ({
        packName: pack.name,
        percentage: pullRate(wantedCards, expansion, pack, filters.deckbuildingMode),
        fill: pack.color,
      }));
    const candidate = pullRates.sort((a, b) => b.percentage - a.percentage)[0];
    if (candidate.percentage > (newHighest?.percentage ?? -1)) newHighest = candidate;
  }
  return newHighest;
};

Key Files and Architecture

File	Role
[frontend/src/lib/stats.ts](https://github.com/marcelpanse/tcg-pocket-collection-tracker/blob/main/frontend/src/lib/stats.ts)	Core probability engine, rarity tables, pullRate and pullRateForCardSubset.
[frontend/src/pages/overview/Overview.tsx](https://github.com/marcelpanse/tcg-pocket-collection-tracker/blob/main/frontend/src/pages/overview/Overview.tsx)	UI logic that iterates over expansions/packs, calls pullRate, and selects the highest‑probability pack.
[frontend/src/lib/CardsDB.ts](https://github.com/marcelpanse/tcg-pocket-collection-tracker/blob/main/frontend/src/lib/CardsDB.ts)	Defines expansions, pack metadata (packs, packStructure) that feed the probability engine.
[frontend/src/types/index.ts](https://github.com/marcelpanse/tcg-pocket-collection-tracker/blob/main/frontend/src/types/index.ts)	Type definitions for Pack, PackStructure, Rarity, etc., used throughout the calculations.

Summary

• The Optimal Pack Calculation Tool uses a two-step statistical engine to maximize collection completion efficiency.
• Step one calculates per-pack pull probabilities using pullRate in frontend/src/lib/stats.ts, which aggregates rarity-specific odds across all five card slots while accounting for special pack variants (rare, baby, and shiny packs).
• Step two compares these probabilities across all openable expansions in frontend/src/pages/overview/Overview.tsx to identify the single pack with the highest percentage chance of yielding a needed card.
• The algorithm filters for "wanted" cards—those missing from the user's collection—ensuring calculations target only relevant inventory gaps.

Frequently Asked Questions

How does the Optimal Pack Calculation Tool handle different pack types like rare or shiny packs?

The tool adjusts probabilities using pack-specific modifiers defined in frontend/src/lib/stats.ts. For rare packs (5-card variants), it applies abilityByRarityToBeInRarePack. For baby packs, it uses probabilityPerRarityBaby. For packs containing shiny cards, it checks structure.containsShinies to factor in those alternate rarity distributions. These adjustments ensure the pull rate reflects the actual in-game mechanics rather than standard probabilities.

What is the difference between pullRate and pullRateForCardSubset?

pullRate serves as the main entry point in frontend/src/lib/stats.ts (lines 20-30) that filters cards by pack availability and initiates the calculation. pullRateForCardSubset (lines 174-250) contains the core algorithm that iterates over each missing card, maps rarities to probability tables (standardPackProbabilities or deluxePackProbabilities), and sums the odds across all five card positions in a pack. The separation allows pullRate to handle data preparation while pullRateForCardSubset executes the mathematical model.

How does the tool determine which cards are "wanted" for the calculation?

The system defines "wanted" cards by comparing the user's current inventory against their collection goals. In frontend/src/pages/overview/Overview.tsx, the logic filters the card database to include only cards where the user owns fewer copies than required—either for deckbuilding purposes (when filters.deckbuildingMode is true) or for full collection completion. This filtered array is passed as the first argument to pullRate, ensuring the probability calculation considers only cards that would actually advance the user's collection progress.

Can the algorithm recommend packs from multiple expansions simultaneously?

Yes, the selection logic in frontend/src/pages/overview/Overview.tsx iterates through all expansions marked as openable in frontend/src/lib/CardsDB.ts. For each expansion, it calculates pull rates for every available pack (excluding the generic 'everypack' category), identifies the highest-probability candidate within that expansion, then compares these candidates across all expansions to find the single global optimum. This cross-expansion comparison ensures users receive the absolute best recommendation regardless of which expansion contains their missing cards.

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