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I'm trying to create a program to play a card game. After a deck of cards (say a standard 52-deck) is shuffled, imagine I'm dealing 5 cards each to all 4 players. I could:

  1. Distribute one card to the first player, one card to the second player, one card to the third player, one card to the fourth player, a second card to the first player ... etc.

Or:

  1. Give five cards to the first player. Give five cards to the second player. Give five cards to the third player. Give five cards to the fourth player.

Or to be fair, even:

  1. Give one card to the first player. Give two cards to the fourth player. Give another card to the first player. Give 4 cards to the second player. Etc.

If the deck of cards is perfectly shuffled, is there any particular disadvantage to taking the second or third approach? It "feels" subjectively to me like distributing the cards equally should make it more random, but if the deck is truly randomly shuffled, shouldn't it not matter how you distribute them?

Apologies if this is the wrong site and if I've misunderstood terminology, as I'm not a mathematician. I'm not sure which tags befit the question, so would welcome an edit.

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    $\begingroup$ If the deck is well shuffled, the order in which you distribute cards is irrelevant. $\endgroup$
    – Doug M
    Commented Mar 31, 2020 at 17:13
  • $\begingroup$ Okay, thanks for confirming this for me. $\endgroup$
    – Lou
    Commented Mar 31, 2020 at 17:18

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Makes no difference whatsoever iff the deck is perfectly shuffled, so you are at liberty to distribute the cards however you like.

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  • $\begingroup$ Essentially your answer is "No." Are you able to provide a mathematical justification, which would make the answer more substantial? $\endgroup$
    – sammy gerbil
    Commented Mar 31, 2020 at 18:49

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