Minesweeper or Mindsweeper?

Zen and the art of puzzle gaming.

Minesweeper is a wonderful game. It’s a beautiful mixture of fast reflexes, quick logic, guesswork, and general problem solving skills. In addition to being a baneful time waster, it really highlighted for me the incredible way that skill-testing games can produce an altered state of high-functioning consciousness. At a certain level of skill and familiarity with the game, it can actually transform from a linear, mechanical process into something altogether more exciting, even trancelike. Play requires all sorts of cognitive abilities from the user: deductive reasoning, spatial awareness, pattern recognition, and intuition, among other things. But the aggregation of these abilities, in combination with speed and a certain quality of — yes — mindlessness, can produce an incredible mental transformation.

I’m not an extraordinary minesweeper player. My best time to date is 168 seconds on Expert, and I lose 80% of my games. Admittedly, however, I lose most often because Minesweeper suffers from a fundamental design flaw: in almost every game there are frequently occurring positions that are logically undecideable. These are situations where there is a 50/50 chance that any one of two tiles will contain a mine, and no amount of logic or head bashing will help you. The only option for these situations is to guess. Statistically, you would thus expect my lost games to average out to 50%, but don’t forget the copious human error involved (and my general lack of skill: I frequently guess for decidable positions, simply because I haven’t mastered every logical subtlety yet; moreover, I miss-click, sometimes just plain miscalculate, or fail to notice an adjoining square, and so on. In truth, I probably only get to the endgame where most 50/50 guessing positions arise about 20% of the time, which means that a 10% win ratio sounds about right). But even in games I lose, I still manage on occasion to get into an effortless mind-space that I find deeply satisfying, and one I’ll try here to explain.

Without getting overly technical, I’ll just present a few positions from a single minesweeper game to illustrate my thinking. Minesweeper is a wonderful example of a game with a steep, but clearly noticeable and measurable learning curve. When I first sat down to play I had absolutely no idea what to do, and the game seemed impossible to me. Once I understood the fundamentals, namely that the numbers on each tile represented the quantity of mines touching that tile (either adjacently or diagonally), things began to move a lot more quickly. Now this very simple rule wasn’t in the least obvious at first, and I can even recall the first few times I played experiencing a vague sense of unease, as if the numbers represented a mysterious secret or hermetic truth that I could never actually grasp, or maybe a perverse anti-logic, as if the mines moved around or required profound analytical abilities, prayer, or alchemy to locate).

The truth is that most mines are extremely easy to find. In our game, since minesweeper is designed to give you an open area on your first click, I got this nice position:

The mine in the middle is dangling down like a cherry waiting to be plucked. There’s absolutely nothing else around and it couldn’t be more obvious. Another lesson is that corners are your friends. A great deal of the automatic play that develops later is simply perceiving corners as inherently mine-heavy. Once you start thinking that way, you start carving paths around and through them in a way that seems more instinctive than logical. The real magic starts to happen when you encounter advanced positions, and solve them quickly and spontaneously as if they were also ‘geographic’. I’ll get to that in a second, but first let me update this position with the mines I know I can detect (based on my limited logical analysis) from what’s available here already.

It only took me a couple seconds, without even clicking away any empty tiles, to locate all these mines. Once again, I’m not profoundly talented at this, but by practicing even the little I have, I now see 1s as very clear designators of emptiness when they are near corners. Now my intuition tells me that the question marked tiles contain mines, but I can’t prove it yet. But let’s clear away some of the dust and see what we’re left with.

So it seems like my intuition proved to be fairly accurate. Even the two touching question-marked tiles are now, without a doubt, mines. The other question mark is still undecided, but there’s nothing we can do about it for now. Let me fill in these mines and get to the next position.

Think of this way: let’s say you’re learning guitar. Someone teaches you the open C chord with 3-fingers. It’s a basic chord and easy enough to play, but for beginners it is quite difficult to find each appropriate fret corresponding to the right string, and if you happen to be learning theory at the same time add to that knowing the notes of each string and fret position, the chord structure, its key, etc. A novice will have more than enough to think about without even getting into the right amount of pressure for each finger, the best hand position, where to place fingers inside the fret for the best sound, rhythm, how to hold a pick, how to strum, and so on. But once you’ve internalized all these mechanics, you no longer think about them. More than becoming second nature, they actually lose their mechanical quality. They become fluid, spontaneous, and effortless. The quality of the action itself changes.

The same is certainly true for logic puzzles like minesweeper. See the top leftmost flag in the last picture? I am 100% certain it is a mine, and I was able to find it quite quickly. It simply has to be a mine (the “1” can only permit a single mine in those top two squares, while the “2” needs a second mine somewhere else to fulfill its value, necessitating the red flag here). It might take a beginner a while to see this (as it did me when I first started learning). For a while this sort of scenario wasn’t even apparent to me at all, but I can see it now almost instantly. Once you get faster at the mechanical work of playing the game, or in this case crunching the logic, at a certain point something exciting and complementary happens. It coincides with gaining momentum, or warming up, and carries with it the sense of finding your rhythm. It’s a glorious feeling, and I think it actually deserves to be called an altered state of consciousness.

Now as I’m playing through this particular game, I’m deliberately exposing all the mines I can positively identify through logic before removing empty squares. I’m doing it this way for demonstrative purposes, but it is by no means the fastest way of playing. In fact, minesweeper offers a few wonderful heuristics (shortcuts) for speeding up your game. For example, if you double-click on a numbered square next to a flagged square, it’ll remove a 3×3 square of boxes for you. This isn’t cheating though: if you’ve mislabelled a flag, you’ll expose a mine somewhere, and lose. But if used properly it does greatly accelerate the game play. Another trick is to actually place all those question marks in your head, instead of wasting precious seconds double right-clicking. Most importantly, and again this comes back to the question of speed, the best tactic is to flag the easiest mines first, because doing so will reveal more information about otherwise potentially complex regions of the board. This is important because skill, and the intangible quality of finding one’s groove that I spoke about earlier, is strongly correlated with your momentum.

This might sound wishy-washy, but I can swear by it. The faster you play, and the more rapidly you accumulate successes, however minor, (e.g., little victories in the form of individual correctly marked flags and exposed empty tiles) builds up a sort of repository of good-feeling. Your brain starts coasting on the high that success gives you. Your thinking speeds up, and your accuracy improves. I’ve seen this happen to me again and again. The inverse happens as well: when I start making errors, and getting frustrated, and if I get bogged down on a particularly tricky section of the board, my play begins to disintegrate, the number of errors I make increases, and so on. One good example of a tiny victory is in the case of that “1” on the middle left of the board, sandwiched between a flag and a plain blue tile. I found that “1” tile based on logic, and then was able to uncover an entire swath of board by extending the implications of its presence even further. Sudden accomplishments like this give me a burst of energy and speed; it’s like getting a second wind after scoring in a game like soccer. It also gives you quick access to a lot of easy grist to quickly chew through, which only adds to your speed and confidence. Let me fast forward a little bit now.

At this point in the game I’ve reached an impasse where I can no longer advance by using straightforward logic. There are really two kinds of logic that can be applied to a game like minesweeper (before running into guesswork and probabilities). The first is pattern recognition and consists of “folding” sequences of logical deduction into single flashes of judgment. Logic, by and large, proceeds through conditional statements: if this is true, then the following is also true (if x then y), a rule sometimes called modus ponens (also common is the negative inversion of this, called modus tollens: if x then y; because not x, then not y). You can find logical inferences all over the place in minesweeper (e.g., whenever I see 2 1 2 in a row without any other surrounding tiles, the “1” is always a mine); one inference then usually leads to another, and then another. Group these commonly occurring sequences of logical inference into larger, but really quite subtle, patterns, and the speed of your analysis increases exponentially. In the above scenario, however, this heuristic “shorthand” form of logic will not work. All the positions are too complicated (at least, for my current level of understanding of the system).

The second kind of logic you can use is a counter-factual brute force approach. This also uses methods of deductive inference, but rather than folding commonly recurring sequences into easily identifiable patterns, it takes an uncommon section of the game and works through every possible variation until one “good” one is found. It is time consuming, laborious, and inimical to the speed of success. It is also very difficult to get quick at this mode of reasoning, without converting a painfully worked out logical sequence into a rule. That’s right: all the examples of the first series of pattern recognition logic are tricks and shortcuts I discovered by working through a whole heap of brain-freezing “if-then” counterfactual scenarios, using brute-force and trial and error. Through practice, I gradually converted these from the slow, second type of logic to the first, expedient type. By internalizing the “proof” for each of these tricks, I could eventually call them rules of the system, with 100% certainty. But that certainty had to be earned.

There is a third approach, however, and that’s just flat-out guessing. It’s unfortunate that minesweeper so often requires this, but such is life.

Rather than work through every possible if-then situation from the previous picture, I just guessed. Once. The rest of the board opened up like a boiled clam. Only now, as you can see, I’ll have to guess again at least once more to win the game. There’s no escaping it. But leading up to these two guessing-impasses, I was able to get a taste of that special state of rapid pattern recognition that makes puzzle-solving such a joy. It’s no exaggeration that you can begin to experience minesweeper as a conceptual landscape, with its own architecture and geography. I am convinced that once a certain threshold is passed in the skill of a player (reflecting both the quantity of patterns learned, and the degree to which they have been assimilated), he or she actually stops thinking. The mind shuts off; the calculating part of the brain goes from working furiously to not working at all. It is an incredible feeling, a zen state of no-mind, that nevertheless preserves (and in fact produces) a very high level of technical skill.

And sometimes, it even helps you win!