Sports Card case break odds

I've about given myself an aneurysm trying to figure this out, so I'm hoping an expert can answer this for me.

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: exavatar

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?

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: exavatar

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?

The probability that it happens exactly twice is (59/1200)² x (1141/1200)⁸ x 45 = about 1 in 13.75.

Quote: exavatar

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?

0: 4.90%
1: 14.86%
2: 22.44%
3: 22.52%
4: 16.89%
5: 10.10%

I've often considered posing some case break related items on this board, but I thought I might be the only one interested.

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

I used to buy boxes for autographs and you're looking at this the wrong way.

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.

I am stuck with cases of Pro-set 1990 football along with Pacific football that was "rare"

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.

I 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

Quote: Buzzard

I 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.

Does that mean my 1928 Babe Ruth ball, autographed by a ball point pen, might not be worth $8,000 ? OMG

Selling packs of cards like lottery tickets started in 1989 with Lud Denny and proset pushing one Pete Rozell card in every 200 packs and then moving on to autographed cards as a way to get people to buy more packs. Facts were they printed and had thousands more signed that they sold behind the backs of customers to increase profits. No one policed them until they got greedy.

Worse ye,t there was no bubble gum in the card paks either.

But look how many kids teeth it saved!

I 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

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Quote: Buzzard

I 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?

"Pack Searching" is still a real problem. There are videos all over the youtube showing it. People will take digital scales into a big store like Target and sit there and weigh the packs to find the ones that contain relics and/or auto's. Only buy your packs from a card shop you trust. Plus generally the 'hobby' boxes that card shops sell have better premium card selection (and higher price point)