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In the contract, I would like to have cards distributed randomly to each user like so:

  • User1: A
  • User2: B
  • User3: C
  • User4: D

Each user should only be able to determine what their card is, and each card should only be distributed once per user (no duplicates).

Is it possible to create a contract that would do this?

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Yes, you can do it using a set (which prevents from duplication) and then use boost random number in range, and pop cards out when player receives them. https://www.boost.org/doc/libs/1_66_0/doc/html/boost_random/tutorial.html#boost_random.tutorial.generating_integers_in_a_range

Also to distribute anonymously you can use end to end encryption.

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