How PackValue Calculates Expected Value

Expected Value (EV) is a fundamental concept from probability theory used to describe the average outcome of a random process over a large number of trials. In the context of Pokémon card packs, EV represents the long-run average monetary return from opening identical packs under the same conditions.

PackValue models each booster pack as a probabilistic system. Every possible card outcome has an associated probability of appearing and an associated market price. EV combines these two quantities into a single metric that reflects both rarity and value.

1. Pull Probabilities

Each rarity tier (e.g., Rare, Ultra Rare, Hyper Rare, Mega Hyper Rare) has a known or estimated pull rate. These probabilities are derived from published pull-rate data, large-sample openings, and community-verified sources. Lower probabilities correspond to higher rarity cards.

If a card has a pull rate of 1 in 200, its probability is:
P = 1 / 200 = 0.005

2. Market Prices

Each card’s contribution to EV is weighted by its current market value. Prices are sourced from TCGPlayer and updated daily to reflect real market conditions. This ensures EV calculations respond to price spikes, declines, and newly released products.

3. Expected Value Formula

The expected value of a pack is calculated using the standard formula:

EV = Σ ( Pᵢ × Vᵢ )

where Pᵢ represents the probability of pulling card i, and Vᵢ represents that card’s market value. The summation runs across all eligible cards in the pack.

The resulting EV reflects the average value of the “hits” in a pack. It does not guarantee profit on any single opening, but it provides a statistically grounded benchmark for comparing sets and products.