Chris Mascioli expands on the idea of “leveled thinking,” made famous by David Sklansky in his poker book. Which level are you playing on?

Leveled Thinking

It’s commonplace in Magic lingo to hear the term “level” thrown about, almost haphazardly; it is included in phrases such as “get on my level” and “you just got completely leveled” to the title of Chapin’s “Next Level Magic.” However clichéd it may appear, leveled thinking is an intricate area, and a greater understanding of the processes that go on in your (and your opponent’s) mind during the course of a match will lead to a greater overall prowess.

1. What Is Leveled Thinking?

The concept of leveled thinking (to the best of my knowledge) was first written about by David Sklansky in his book “No Limit Hold ‘Em: Theory and Practice” where he defines the different levels one can think at. His definitions of each level are summarized in the following table:

Level 0 — What do I have?

In this level the only thing that matters is what cards are in my hand and what order I should play them in; a player at level 0 is essentially always goldfishing. The important factor to consider at this level is:

How do I win this game given the cards available to me?

This is the level where one learns the nuts and bolts of playing Magic, and most players eventually advance to level 1. This is the level of play most frequently seen at FNMs

Level 1 — What could my opponent have?

This is the level where you first actually play the game known as Magic. Your decision process takes into consideration what your opponent can have, and you play in a way which will maximize your chance of winning against the hand you have placed him on. For instance, if you have six mana and the choice between playing Sword of Feast and Famine and Primeval Titan while you’re fairly confident that your opponent has a Mana Leak, your best course of action is to play the Sword (the level 0 player might also choose to play Sword here if, for instance, it would get rid of the last card in his opponent’s hand or kill his [I will use “his” for my singular pronoun every time; if you take issue with this, pretend I used “her” and get on with your life] opponent outright, but never because he’s taking into consideration what his opponent may do). The important factors to consider here are:

What cards can be in my opponent’s deck?

What are the consequences of them having those cards?

If he has those cards what can I do?

This is the level where the majority of players are at their apex and the level of play you’ll see out of most players in a PTQ.

Level 2 — What does my opponent think I have?

At this level, the game is no longer about what just you think but begins to incorporate the thought processes of your opponent. It is at this level where players begin to understand the concept of bluffing. (A bluff is when you represent a card you don’t have. For example, if my hand is Think Twice and Gideon Jura, but I make sure to leave at least two Islands and one Plains untapped, I am representing that I have a Dissipate.) It is important to make sure to tell a consistent story with bluffs in order to ensure their believability to an opponent. If for instance, you only leave 1UU open when you have nothing better to do for the turn, your opponent will most likely find your story incredulous and play their spell into your open mana. The important questions to consider at level 2 are:

Do I want to maximize or minimize the ambiguity of cards in my hand? (The correct answer is almost always to maximize [there are some corner cases where you don’t] and is why most players will tap their basics before their duals.)

Given my opponent’s actions last turn, is he continuing to buy my story, or has he already done something to prove himself incredulous?

Should I stick to my story, or is it time to tell a different tale?

This is the level where the top PTQ grinders and lesser pros reside.

Level 3 — What does my opponent think I think he has?

At this level, the game starts to become quite meta; you are essentially attempting to figure out how your opponent thinks you’re interpreting his actions. Take the role of the villain in the aforementioned Dissipate example: if your opponent is leaving WUU open every turn, he is intending for you to think he has Dissipate. After concluding this, it is then necessary to figure out several other factors:

Why does he want me to think he has Dissipate?

Does he actually have the Dissipate?

If he doesn’t have the Dissipate, what cards is he trying to mask with the illusion of Dissipate?

Level 4 — What does my opponent think that I think that he thinks that I have?

The articulation of this level would take up too much space to really be productive, but if you’re capable of thinking at this level, I doubt you’re actually reading this article, and a brief description of level 4 thinking will do nothing to help you reach it. There are actually infinite levels of thought, and “each successive level is to think about what your opponent might be thinking on the previous level” (Sklansky, 169).

One important note before we go on to look at leveled thinking in action: The most important factor is not what level you operate on, but the proper identification of the level your opponent is operating on. The task of identification, however, cannot be completed without knowing the options, hence the need for the explanation of each level given above.

2. Leveled Thinking in Action — Wine in Front of Me (WIFOM)

Before reading on, it is helpful if you watch the following scene from Princess Bride (slight spoiler if you haven’t seen the movie, but you should still watch it).

http://www.youtube.com/watch?v=U_eZmEiyTo0

Aside: In case you were involved with the two-week #mtgwolf craze that traveled around the MTG Twitterverse, you would often see people (mostly to give the impression that they were quite clever) claiming “WIFOM” and then go on to present circular reasoning (often for almost an hour) on why they were voting to lynch their particular selection.

The rules of the game set up in the scene are as follows (in case you’ve seen the movie, please ignore what actually happened for a bit):

1.  There are two cups of wine, one of which contains a deadly poison.
2. Your opponent knows which cup has the poison.
3. Your opponent places one cup in front of you and one cup in front of him.
4. You must select one cup and drink simultaneously along with your opponent.
5. If you select the cup with the poison, you die.

As Vizzini immediately points out, the game is “so simple, all [he has] to do is divine from what [he] know[s] of you; are you the sort of man who would put the poison into his own goblet or his enemy’s?” This is a reiteration and confirmation of the last point from the previous section: The identification of your opponent’s level is what is critical here. Now that the task has been given to identify what level your opponent is operating on, it is first necessary to determine what a person would do operating on each level.

Level 0

If your opponent is thinking on this level, he places the poison in front of you, since he does not remotely consider what you might do or think, so he chooses the default option.

Level 1

If your opponent is operating on level 1, he will consider that you have the choice of which cup to drink from, and it would be far too obvious to place the poison in front of him.

Level 2

At this level your opponent will consider the fact that you may think that he is too clever to put the wine in his own glass, so he places the wine in front of himself.

Level 3+

The reasoning behind each level’s choice is circular and need not be presented (plus, giving the reasoning for levels 0-2 is enough for a proof by induction), but the solution can be summarized in the following table:

 The reward for correctly deducing your opponent’s level in this game was being able to live and getting the princess while the penalty for incorrect identification was death. The consequences in Magic aren’t as severe, and the rewards not as desirable (unless Darwin Kastle’s guide to dating is true #beexcellent), but misidentification of your opponent’s level can lead to a number of otherwise avoidable losses.

3. Level Identification

Now that the importance of proper identification of your opponent’s level has been established, the first logical question is “How do I identify my opponent’s level?” Of course, there’s no simple answer besides making sure to observe their in-game mannerisms and sequencing, but here’s some basic guidelines:

1. Deck choice: If your opponent is playing a known deck, they are more likely to be a level 1 or 2 player, but this relationship is not particularly strong all the time.
2. Sleeves: Lack of sleeves on a deck (in a real event) most likely indicate someone who’s new to the game and therefore most likely a level 0.
3. Shuffling: If your opponent shuffles like this you should probably be wary.
4. If your opponent continually plays into everything possible and spends very little time thinking, they are most likely level 0.
5. If your opponent plays around tricks but leaves essentially no ambiguity as to what’s in their hand, they are most likely level 1.
6. Have you ever heard your opponent’s name before? Have they won more than one PTQ or played on several Pro tours? If not, they’re most likely level 0 or 1.

4. How to play against people at different levels

Once the important ask of level identification has been completed, it is then necessary to figure out how to use this information in order to help you win. Once an opponent’s level is identified it falls into one of three categories: The same, lower, or higher.

A. The same level

If two players of the same level play against each other, the player with the better technical play and better mastery of that level will be favored. For example, if two level 0s play against each other, the one that is better capable of executing their game plan in order to win will be ahead, or if two players at level 1 are paired, the player who is better able to determine their opponent’s hand will be advantaged. At lower levels of competition, this will be the most likely case, so it is therefore of greater importance to focus on improving aspects of one’s own technical play/mastering the level one is currently at rather than attempting to develop higher levels of thinking.

B. A lower level

If your opponent is at a lower level, it is imperative that you change the level you are operating on to be only one higher than your opponent. Although this stratagem appears unintuitive (Why would you ever not want to take advantage of the levels of thought you spent so long mastering?) there’s a very real reason for it: The level one level above your opponent is the one where you can interact most favorably.

Let’s say a level 2 player plays against a level 0 player. The level 2 player will spend a considerable amount of thought and effort to bluff the correct spells in each location while their opponent will completely ignore what they are doing and play his cards how he feels like. The level 2 player, after losing the match, will go on to complain to his friends about how he “lost to a noob” and how he had “no respect for anything I was representing.” However, what the level 2 player is missing is that if he were to “lower” himself to level 1 and only focusing on determining what his opponent could have and assembling a game plan based solely on that (compared to what he did, which was focusing a game plan based on something his opponent had no knowledge of) he would have had a much better chance.

C. A higher level

This is the situation you least want to be in, and how outclassed you feel you are will determine how you play out the game. If you think you are relatively close in skill level to your opponent, you should play out your game as you normally would. Your opponent will be advantaged, but there’s not much you can really do but play your best Magic and hope for fortuitous draws or for your opponent to make mistakes that you can capitalize on.

On the other hand, if you feel like you are greatly outclassed by your opponent (for example, if I were to be paired against LSV or PV I would most certainly employ this technique), the best bet might be to adopt a modified version of the strategy advocated by Rodman and Nelson in their book “Kill Phil.” Essentially, they advocate a strategy (when playing against players much better than yourself) where rather than get involved in a game where you can be outplayed, you limit your decision tree to a binary one: either fold or go all-in on every hand. By doing this, you force the more experienced players to either have it or get out of the hand and show yourself as a player who can’t be bullied. Although occasionally the more experienced players will “wake up” with a hand and still take all your chips, you are not allowing them to play their best game, which takes some of their advantage away. In order to do the equivalent in Magic, you have to “lower” yourself to play at level 0 and just play your cards with almost no regard to what your opponent could be holding. Statistically you should draw better than your opponent about 50% of the time, and this method allows you to push drawing better than your much more skilled opposition as far as it will carry you and forces them to play a game they don’t want to play: “Do you have it?”

Quotes:

[SarcasticRat] some riot grrrl from New Zealand added me on last.fm
[SarcasticRat] bet brim is jealous

[snoopster] also, i think i’m as good at drafting as lsv

My wall after the Worlds PWP change:

Chris Mascioli

chrism315 on modo

@dieplstks on Twitter (you should really follow me)

I even have a blog (people say it’s too depressing though): dieplstks.tumblr.com