What’s a good one-pass pseudo-random shuffle? [closed]

If you have a shuffled desk, into which you wish to shuffle a batch of new cards (and you know that none of the cards are duplicates), then I think the following is valid.

ForEach card in batch:
    gap = random(deck.size() + 1)  # choose a gap between cards, before first, or after last.
    deck.insertAt(gap,card)

Distribution

The distribution of random is uniform, and the order of the deck is unchanged, so still uniform.
I think the result should be uniform. (My stats is too rusty to be sure).

Time

Assuming that insertAt is O(1) not O(N) – which depends upon the implementeation of deck – the whole routine is O(batch size) – which is the best you can hope for becuase you have to handle each card.