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Admiral_H_Nelson

Wargaming's Deck of Playing Cards must have 5 Aces in it

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I want to win the special French Commander "Jean-Jacques Honoré", but I'm having a hard time doing it.


The problem is the number of duplicate items that I am getting from the special French containers. It seems remarkably high.
(BTW five of them are the picture of "Battleship Richelieu in Indian Ocean" - there is your ace!)

 

I have collected 11 out of the 18 items. However in my last 14 containers, no less than 11 have been duplicates, including my last 8 straight.

 

I calculate that the odds of getting 8 straight duplicates in this situation at only 1.9%. (Not a mathematician so please correct my errors)

 

Either I am very unlucky, or we have a situation where certain items are deliberately rare. This used to happen in my youth when I collected bubble gum cards. There were always some which were in short supply.

 

To calculate the odds I used the general approach of the "Birthday Problem".

Spoiler

With 11 out of 18 collected, the odds on the next container (#1) being a duplicate are 11/18 (or 61.1%)
If container #1 is a duplicate, then the odds of container #2 also being a duplicate are 11/18 multiplied by 11/18
If container #2 is a duplicate, then the odds of container #3 also being a duplicate are 11/18 multiplied by 11/18 multiplied by 11/18
...and so on.

 

"Birthday problem"     (From Wikipedia (yes...I know)  https://en.wikipedia.org/wiki/Birthday_problem)

 

In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.

 

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Beta Tester
4,481 posts
7,976 battles

I got 15/18, then traded in 9 duplicates (had 10) to complete the collection.

Didn't seem that bad.

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