How set size changes the math

Set size is the number of unique cards in a release. It affects the math behind every pack you open. A larger set spreads the same pack slots across more cards, so each individual card is harder to pull. That changes your odds of finishing a set, your duplicate rate, and your trade list.

You do not need advanced math to use this. You need a count of the set, a count of cards per pack, and a simple estimate. The goal is to plan purchases and trades, not to predict exactly what will be in any pack.

Count the set and the pack

Start with two numbers: total unique cards in the set (N) and cards per pack (k). Write them down. If the set has subsets or parallels, decide whether you are collecting the base set only or everything. Mixing those goals makes the math useless.

For a specific card, a rough chance per pack is k divided by N, assuming cards are evenly distributed. That is an estimate, not a promise. Expected packs to see that one card once is about N divided by k. This is the first place set size shows up: doubling N roughly doubles the packs needed for one specific card.

Estimate duplicates with a simple model

Duplicates come from opening more packs than there are unique cards. A common planning formula for collecting all N cards is (N/k) times the harmonic number H_N. H_N is 1 + 1/2 + 1/3 + ... + 1/N. You can calculate it in a spreadsheet. The formula assumes even distribution and independent packs, so treat it as a baseline.

Use it to compare set sizes. If one set has more cards, the same number of packs produces more duplicates of the cards you already have and fewer new cards. That is why large sets often need more trading or buying singles, not just more packs.

Adjust buying and trading

Set a target: complete the base set, collect one of each common, or chase a few cards. For a large set, buy fewer random packs and trade duplicates sooner. Keep a checklist sorted by card number. After each opening, mark new cards and set aside duplicates. Trade duplicates for missing cards within the same set size group.

When trading, compare set sizes. A duplicate from a large set is usually easier to replace than a duplicate from a small set. Use that to balance trades. Do not rely on pack odds alone; use your checklist and the formula as a planning tool.

Does a bigger set always mean more packs?

For a specific card or a full set, yes, the estimate rises with set size when pack size stays the same. The exact number depends on distribution and collation.

What is the harmonic number for?

It adjusts the coupon-collector estimate for the fact that late missing cards take longer to find. You can compute H_N in a spreadsheet as the sum of 1/1 through 1/N.

Should I collect every parallel too?

That changes N. Count only the cards you actually want. If parallels are included, N is larger and the math shifts toward more packs or more singles.