I'm a trading card collector, and I am trying to determine if some recent case breaks I did were bad luck or poor collation on the manufacturer's side.

For ease of this exercise, I'm going to simplify a few things. There are 60 different autograph cards available with a stated ratio of 3/case (it's actually 1/96 packs, with 24 packs per box and 12 boxes per case). Let's assume there are equal numbers of all 60 autographs (not true, some are short prints, but let's ignore that otherwise I need 60 data points). Assuming they are all equal in number, what are the odds that of the 3 autographs you get per case that 2 would be the same one?

And then if it changes it, what are the odds that this event (2 of the same auto) would occur twice in ten case breaks, if all was truly random?

As you can guess it did indeed happen to me, and I want to see if the data backs my hypothesis that it's poor collation.

Also, if anyone wants a bonus follow on: if the stated odds are truly 1/96 packs with 288 packs in a case, what should be the odds of getting 2, 3 and 4 autographs in any given case?

I probably should have asked these questions BEFORE purchasing, sigh....

Quote:exavatarFor ease of this exercise, I'm going to simplify a few things. There are 60 different autograph cards available with a stated ratio of 3/case (it's actually 1/96 packs, with 24 packs per box and 12 boxes per case). Let's assume there are equal numbers of all 60 autographs (not true, some are short prints, but let's ignore that otherwise I need 60 data points). Assuming they are all equal in number, what are the odds that of the 3 autographs you get per case that 2 would be the same one?

There are 60 x 60 x 60 = 216,000 "3-tuples" of the 60 cards. Of these, there are 60 (possibilities for the duplicate) x 59 (possibilities for the non-duplicate) x 3 (ways they can be arranged) = 10,620 3-tuples that contain 2 of the same card. The probability is 10,620/216,000 = 59/1200, or about 1 in 20.

Quote:exavatarAnd then if it changes it, what are the odds that this event (2 of the same auto) would occur twice in ten case breaks, if all was truly random?

The probability that it happens exactly twice is (59/1200)

^{2}x (1141/1200)

^{8}x 45 = about 1 in 13.75.

Quote:exavatarAlso, if anyone wants a bonus follow on: if the stated odds are truly 1/96 packs with 288 packs in a case, what should be the odds of getting 2, 3 and 4 autographs in any given case?

0: 4.90%

1: 14.86%

2: 22.44%

3: 22.52%

4: 16.89%

5: 10.10%

You aren't talking about Panini Prizm World Cup Soccer are you?

Not all autograph cards are issued equally. Some are "short prints" and you know what the term means.

there might be only two Mantle signed or relic cards, but 200 Bobby Richardsons.

Topps at the end of each series lets you know which are the short prints and sometimes they release those numbers in advance.

They ruined this game years ago with greed and more power to you if you can find a card you can sell. Just don't be the last guy holding any card printed after 1980.

Quote:BuzzardI know a guy in the late 1990's who had a way of detecting which packs had winners them by a difference in the sealing process. Sorta like edge sorting. Of course he had money invested in Beany Babies too. LOL

I can beat that. I knew guys who opened old wax packs from the 60-80's, took out the good cards, replaced them with commons and then resealed them with heat melting the wax back and resold them. The sports card industry was and is filled with scum balls and any buyer should beware.

Quote:BuzzardI wonder what a fortune I might have spent in the 1950's using those baseball cards in the spokes of my Schwinn bicycle. Especially hated those damn rookies. LOL

How many Mantle cards did we flip, put in our back pocket, or lose when Mom threw out the shoe box when we went to college?