How to Infinite-Level Your Opponent
What do you think when your opponent does something obviously stupid in Magic game (or any competitive strategy game with hidden knowledge), like attacking a small creature into a blocker that can destroy it and survive?
Level 0: "Sweet, free advantage for me! I'll block it!"
Level 1: "They might have a trick hidden in their hand that could save their creature and kill mine if I block. I'd better not block."
Level 2: "But they might assume I'm not going to block, so they're just bluffing to get a small amount of free damage. I should block anyway."
Level 3: “This opponent knows I called a similar bluff last game, so I don’t think they’d do it again. They probably have a trick ready. I won’t block.”
Taking this endless series of second-guessing higher and higher is usually not productive. You simply thrash back and forth. Every new assumption jumps you to a different choice.
But by thinking in terms of next-leveling your opponent in the first place, you are assuming they are not acting perfectly rationally. Rationally, you can break out of this endless loop by looking at the possibilities independently of your opponent's skill. This is the fundamental trick of Game Theory.
Possibility 1: You choose the most obvious play, and your opponent plays a trick. They blow you out.
Possibility 2: You choose the most obvious play, and your opponent doesn't have any tricks. You gain a solid advantage.
Possibility 3: You play around the possible trick, and your opponent had it. Their trick is wasted or at least made less useful.
Possibility 4: You play around the possible trick, but your opponent didn't have it. You play a suboptimal strategy.
It's important to realize that whether your opponent made a dumb mistake or tried a clever ruse, the results are the same. Either way, there are only those four possible results. In a game like Magic: the Gathering that allows a relatively large amount of time for each decision, taking a step back and looking at the results like this will often show that one decision is far superior for you, regardless of why your opponent made that play.
Magic experts consistently say that playing in a fundamentally sound way will gain you more victories than trying ruses and tricking your opponent into making a mistake. (Both Reid Duke and Patrick Chapin have written about this, and there are probably other writers I don’t remember.)
However this is not the case for every strategy game! Some games such as Poker present you with more situations in which reading your opponent is more important. These games, because of the way they are designed, make bluffing and reading your opponent a much bigger part of the game, while Magic requires that only infrequently.
The situation is far different for quick games like competitive fighting games. Dave Sirlin's articles about donkeyspace and the strategies of luring your opponents into misreading you are fascinating. I don't have any experience playing those games competitively, but I can see how they could be very different.