In many card games, players are dealt a hand and then sort it for their own convenience. It occurred to me that this might be a way of leaking information about your hand, although probably not in a way that a human observer could use. But for the purposes of the question we'll assume we have a computer.
In a game like hearts or bridge, you get a random set of 13 cards in random order. For simplicity, we'll assume that the humans sort their hands like a computer, rigidly executing a specific algorithm (like insertion sort), and not trying to do anything clever like changing the ordering of the cards (like sorting your hand 10 < J < Q ... < 8 < 9). As a player, I can see the set of insertions you make (e.g. 1, 2, ... , 13 -> 1, 4, 2, ... , 13). I also have my own hand, which gives me some information.
Question: Given this information, can I make any useful inferences about the strength or contents of your hand? Has this question (or anything similar) been studied?
In theory, the way you've asked the question, you probably cannot make any such inferences. In practice, you probably can.
Suppose that: 1) people sort their hands by rigidly executing a deterministic comparison sort algorithm (such as insertion sort), 2) no two cards are ranked alike, and 3) the deal is perfectly fair.
Because of 1) and 2), the steps taken to sort the algorithm depend only on how your originally-dealt hand is permuted relative to the sorted version. Because of 3), every permutation of any given hand is equally likely, which also implies that every hand has the same probability of being dealt in any given permutation. So knowledge of the permutation (which is all you get) gives you no knowledge of the hand.
In practice, 1) is almost certainly false. Human card-sorting procedures are likely to be of the sort that begin "put all the spades together", which is not a comparison sort. In that case it's possible that information will leak. This is likely the reason behind the use of screens mentioned in the comments. 2) is likely true, but if it's false you might be able to conclude that someone who transposes fewer cards in sorting probably has more equally-ranked ones. 3) may or may not be true, depending on how good you are at shuffling.
In any case, even if you can sort your hand in a way that doesn't leak information, you will probably leak information when you start playing from a sorted hand (e.g., if you play the ace of spades from the far right end of your hand and the two from the middle, you likely have a long spade suit).