Four collector tools, free and private

Stated odds give the chance of a hit per pack, and a whole box can still miss

Enter the odds the maker prints, such as 1 in 24, and how many you open. The tool does the arithmetic. It does not know any pull rates itself, so it only works on numbers you give it.

The arithmetic

1. If a hit is 1 in N per pack, one pack misses with probability 1 minus 1/N.
2. Opening k packs, the chance of at least one hit is 1 minus (1 minus 1/N) to the power k.
3. Expected hits is k divided by N. That is an average over many openings, and any one box can land above or below it.
4. Packs needed to reach a target chance p is the smallest whole number k where that chance is at least p.

Worked example of the formula: at 1 in 10 per pack, 10 packs give 1 minus 0.9 to the power 10, which is 65.1 percent.

This assumes every pack is an independent draw at the stated odds. Some products use collation, guarantees or fixed box contents. If a box is guaranteed a hit, use the maker's statement and ignore this tool for that product.