Everyone brings a wrapped present and puts it under the tree. In random order, each person gets a turn, which means you get to select a present. You can select and unwrap a present from under the tree, or you can select a present that someone else has already taken. If someone takes your present, you now get to select a present. Presents can't change hands more than once a turn, and once a present passes to its third owner it stays there for the rest of the game.

The end effect is that each person arrives with a present and leaves with a present, and there's a lot of excitement as presents bounce around between people.

So when should you open a mystery present? You have some estimate for how good the typical present under the tree is, which will be partly from expectations and experience and partly from seeing what presents have already come out so far. You also can see the range of presents available. So if you'd like to select the best present you can you should pick a mystery present when none of the available ones are better than your estimate. [1] Generally, this means you should strongly prefer open presents.

If you're risk averse, which you probably shouldn't be with a Christmas gift exchange, then you should prefer open presents to reduce your risk of getting something that you don't like and no one wants to take from you. Similarly, if you're loss averse you should try to get presents that you would be the third and final owner for, so no one can take them away from you.

There may be more complicated logic to handle selecting gifts that you think other people will want to take from you so you can go again later when there will be more options, but this seems hard to evaluate.

[1] This may seem like a trivial claim, but talking to several people it's not something that had occured to them.