How many sticker packages should I open to fully complete Panini's World Cup Album?

In this repo, I simulate 1000 times the opening of packages with Panini's World Cup Album 2022.

Methodology and considerations

I considered the following:

• Each sticker is randomly assigned to a package.
• The sampling is with replacement. So that, we have duplicates.
• Basically, this is a bootstrapping approach.

Album and packages features:

• To complete the album, you should collect 638 different stickers.
• There are other 80 additional stickers. They are not part of the main collection. So I didn't considered them here.
• Each package comes with 5 stickers inside.
• The price of each package varies from country to country. In my case (Ecuador) it's 0.80 USD.

Results

After simulating 1000 times, we get a distribution as follows:

And the cumulative probability:

From those figures, we can summirise numerically as follows:

count 1000.000000 mean 902.181000 std 163.262828 min 572.000000 25% 792.000000 50% 873.000000 75% 984.250000 max 1693.000000

Having a CI at 95%: 659.975, 1307.300

Conclusions and recommendations

• The number of packages you should open is between 660 and 1307 (95% CI).

• You need a minimum of 572 packages, but the probability of completing the album with those is very low. Less than 1%.

• In order to get a probability of 90% of completing the album, you need at least 1108 packages.

• There may be a different and optimal approach of completing the album. We can find a number of packages where we can start buying stickers individually. Of course each sticker sold individually is more expensive, but I encourage you to figure out whether it's a better approach.

References

FIFA World Cup Qatar 2022™ - Box of 50 sticker packets |Panini

FIFA World Cup Qatar 2022™ - Hardcover Sticker Album |Panini

What the Euro 2020 Panini sticker album can teach us about probability