Your quote of the Comp Rules answers your question. If the card says to shuffle, then you need to randomize the cards. The rules doesn't say "a shuffle means the cards are randomized" (which I could see allowing for no shuffle). It says "randomize the cards" which, in an English sense, means to perform the action resulting in a randomization the cards. It doesn't matter if they are already randomized. You need to randomize them again.
The MTR even says to "[bring] the deck to a state...". Being in a random state isn't good enough. You need to bring them to a state of randomization which, as I mentioned above, means to take an action that results in a random order of cards.
Being randomized in no way gets around the requirement of performing another randomization of the cards.
the first action says to search, I suppose flipping one card over is searching, but by definition of search is to pick up and look through. Then the card doesn't say to randomize, the card says to shuffle. that's a specific action which mtg has intended you to do. playing casually I'm sure most people wouldn't mind that you don't. tourney would require you to do so.
The definition does require you to "randomize the cards" and randomization requires a change of the current sequence. Even if no one knows the current sequence, there is one, and the requirement is that it changes. Even though that could be as small as a single cut.
Amusingly "701.18e If an effect causes a player to shuffle a library containing zero or one cards, abilities that trigger when a library is shuffled will still trigger." is impossible as per MTG's definition of shuffle if you know the last card, since you would know the order. Well I read that one wrong.
The search action permits you to know the order of cards in the library, whether or not you actually choose to look at all of the cards, the information was available to you. In order to bring the library back to a state where no player can have information on the card order (regardless of whether they actually chose to collect that information) a physical randomization is required. In the case described, the process of randomization should be simple however, as by mutual agreement, none of the other cards were viewed, so a very basic shuffle should suffice. This is similar to the shuffle when multiple search actions are performed without intervening actions, generally by mutual agreement, only one physical shuffle is needed at the end of the searches, even though the game would require and see a shuffle occur for each completed search.
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If you just look at the top card of your library and it is a land you need, do you still have to shuffle because you haven't looked at your library?
The MTR even says to "[bring] the deck to a state...". Being in a random state isn't good enough. You need to bring them to a state of randomization which, as I mentioned above, means to take an action that results in a random order of cards.
Being randomized in no way gets around the requirement of performing another randomization of the cards.
http://magic.wizards.com/en/articles/archive/shuffling-dos-donts-2006-07-07 here's a good article
Amusingly "701.18e If an effect causes a player to shuffle a library containing zero or one cards, abilities that trigger when a library is shuffled will still trigger." is impossible as per MTG's definition of shuffle if you know the last card, since you would know the order.Well I read that one wrong.