Any card is a guess
You cannot see the cards you take from, so no pick is better than another. Old Maid is a game of luck, which is why young children can beat grown-ups at it.
Shuffle after someone takes from you
The one thing you control is the order of your own hand. If you always put a new card at the end, or always keep a queen in the middle, the player on your right can learn where to pick. Press Shuffle my hand after your turn and there is nothing to learn.
Pick from different places
The same works the other way. If you always take the first card, a player who notices can leave the queen there for you. Against the Expert computer this matters: in two-player games where you always take the first card, Expert leaves you holding the Old Maid 91% of the time, against 53% for Easy (3,000 simulated games each). With four players the same habit costs much less, about 37% against 31%, because only one player ever takes from you.
Why the computer level barely matters
Easy never rearranges its hand. Standard shuffles after someone takes from it. Expert shuffles every turn and keeps a queen or joker where its taker has picked most often, even one it has just taken. Against players who pick at random, all three lose about one game in four at a four-player table, which is the same as luck. The levels are there so you can see the difference a habit makes, not because one computer plays better.