I've been pondering a question for a while, and I can't figure out the answer. Because it's odd and analytical, I thought I'd talk about it here. It comes from a digital card game I play a bit, but the question applies more broadly.
Suppose you have a deck of cards which has been properly shuffled and dealt from. Some effect or game mechanic instructs a player to look through the deck and pull out any one card whose suit is Spades then shuffle the deck.
Now suppose you are playing the same game on a computer. The same effect or mechanic is used. Because it is on a comuter, the game can show you the player his or her options without revealing the order of the deck. Because the player does not gain any information about the order of the deck, the game does not shuffle the deck after. The deck's order is left exactly the same, save one card has been removed.
The question I've been pondering is, are these two approaches effectively the same? In terms of effective randomness, does removing a card from a randomized deck have the same effect as removing the card then shuffling the deck? If both approaches were used many times in many games, would there be any difference in the overall effect on games and the order cards are drawn in them?