The Hardest Easy Game

Vsalsa! Kevin here, with a

game

so complex and so important that it is the basis of an entire five-day course on strategic thinking. That's all? That's all? What is this? Welcome to the L-Game. Developed by Edward de Bono more than 50 years ago, the L-Game was designed to be the simplest possible

game

that could expand players' ability to find not just any solution, but the best solution, in an ever-changing environment. Here's how it works... The L Game has only a handful of pieces, a very small board and almost no rules, and is deliberately indeterminate, meaning that, in theory, two perfect players could play forever with no winner.

And that has a point. Let's look at the board: it's just a 4x4 grid and each player has a single L-shaped piece that takes up 4 spaces in total. There are also two neutral pieces (these pennies) that either player can move. And we start the game by placing the two L's in the center and placing the neutral coins in the upper left and lower right corners. So get ready for L. Each player must move their L piece to a new, unoccupied spot on the board by picking it up and moving it, flipping it, turning it, rotating it... whatever, as long as it neatly occupies 4 grids.

So like this. Or this way. Not like that or like that. You can not do that. That does not work. As long as at least one square is new and does not overlap the other L piece or a neutral point, then the move is legal. After that move, the player can choose to move any of the neutral pieces to an open space... or not. It's totally up to you if you want to play defensively. But you can't move the neutral piece before moving your L. The only goal of the game is to make sure the other player can't move their L piece.

If they can't move, then you win. If our pieces were in this position, I could move my L here and the neutral piece here and I would win. Your L is locked, you can't go anywhere, see? And that is! Game over. It seems so

easy

! So... how come this game takes 5 days to master? Consider the following board position, which De Bono uses in his 1967 book, “Five-Day Course of Thought,” which actually consists of three five-day courses, Game L being just one of them. I will be Player 1, pink, and you will be Player 2, orange. I only have three possible moves here... uhh, let me show you.

It's not that difficult to choose one. Good? Mistaken. Choosing a legal move is

easy

. Choosing the best move is not. I need to think about what will probably happen after I make my move: what will you do next turn? And what kind of position on the board will they put me in for my next move? Will you play perfectly or will you make a mistake that will give me an advantage? And… if that's what I have to consider to make the best move, what do you have to think about? It seems impossible to know, and that difficulty is at the center of De Bono's strategic thinking.

You can employ some basic strategies to survive and conquer, such as blocking a 3x3 grid in the corner of a board using your L and a neutral piece, and then manipulating the other neutral piece to eliminate your opponent's possible moves. Or you can think of the grid as two halves and lock your opponent into one half of the grid.   Those strategies are pretty good, but they are far from perfect. Let's go back to my previous scenario. Given my three possible moves, you have countermoves for each... counters A and B result in a loss for me because there is simply nowhere to put my L, because remember, the neutral point can only be moved after a player moves the L piece.

Countermove C is my best possible move, because I'm not locked in, I don't automatically lose with C. The trick is if I can see it coming in advance so I can avoid... taking the L. Okay. Got it, 3 moves, think ahead. It is not a big thing. But what if we have this situation? This has 195 possible moves, and only one of them is the best. That's 1 out of 195. Awesome. Given the boundaries of the board, there are 82 possible positions for the L pieces and 2296 board states in total. De Bono teaches that we must learn to think about the L Game by mentally classifying a move in one of four ways: fatal, in which your opponent wins on the next move; weak, which puts you in a defensive position; neutral, which does not change anything for any of the players; and strong, which gives you the advantage.

In this board position, there are 65 possible moves: 22 fatal, 17 weak, 26 neutral and 0 strong. Can you consider all those possibilities and follow them, two or three moves down the road? The perfect game involves collecting and evaluating every possible move and making the best decision based on those results... which is perfectly impossible even for a tetromino-obsessed human mind. Like everyone. Modern humans love tetrominoes, which are geometric shapes made up of 4 equal squares joined edge to edge. There are 5 “free” tetrominoes, which are the basic shapes you'll probably recognize from Tetris: the L, the square, the Z, the Line, and the T.

And Tetris also has the two chiralities of the L and the Z. They can be shifted, rotated, rearranged, or mirrored to fit... like in this 5x8 grid], which is one of the 99,352 ways these pieces can fit within these boundaries. Or this 4x10 rectangle, which can be formed in 57,472 ways using tetrominoes. Until Minecraft, Tetris was the number one selling game of all time because our brains are fascinated by geometric puzzles and considering unknowns a few steps ahead. Or 100,000 moves ahead. Ok, back to L. On day 3 of training, de Bono says that a player can write down the positions that made him lose and the positions that made the other player win.

That mentality is simple: over time you will learn to avoid the bad moments and place yourself in the good ones. Experience matters and it trains us to think... but it means it takes time and you will lose a lot of games along the way. You need strategic principles. And if you want to play it yourself, I've put a link to an online version of the game below. It will show you how many possible moves you have in each board state and allow you to run simulation after simulation to see how complex this simple-looking game really is.

To make sense of the impossibility of calculating every possible move in real time, de Bono recommends creating a set of several guiding principles that can inform your strategy... such as always keeping a neutral piece adjacent to your L piece, or taking positions in the corners whenever you can. There are no magic answers; The possibilities here are endless. But your strategic principles informed by your experience are essentially shortcuts to success, allowing you to avoid playing 10 million L-Games or considering every possible move. The more you play and the better your mental grouping of game situations develops, the more precise your guiding strategic principles will become. 15 years after the publication of De Bono's book, N.

E. Goller devised a simple system that will guarantee the player at least an indefinite draw and give him opportunities to win if his opponent makes a mistake. If you can get your L piece to occupy three of the four center squares of the grid, OR have it occupy two center squares, and no neutral piece occupies any of the squares marked with an X, you are in good shape not to lose. Beyond that, it's up to you to use your strategic thinking skills to win the game. In an academic math game, you could spend a few years working out all the moves and ranking their usefulness.

But in real life, when you're sitting across from the other player at the table, just like you're sitting across from me, it can't take forever. You have to move, and the player who can think accurately the furthest in advance will win. Which is what we all do every day in our own way, in our own lives. Today is another day in our endless course on strategic thinking. We don't rotate the L's on a board, but we envision the future and modify our decisions in the present to give ourselves the best chance of success. We break our life boards into smaller, more manageable sections and create little systems based on what we've learned and what we've come to value.

We gained experience and took shortcuts to give ourselves the optimal opportunity... To avoid the L's and manifest the W's. And as always, thanks for watching.