The Hardest Easy Game

Updated : Nov 10, 2019 in Articles

The Hardest Easy Game

Vsauce! Kevin here, with a game so complex
and so important that it’s the basis for an entire 5-day course on strategic thinking. This is it? That’s it? What is this? Welcome to the L-Game. Developed by Edward
de Bono over 50 years ago, the L-Game was designed to be the simplest possible game
that could stretch the players’ ability to find not just any solution, but the best
solution, in a constantly-changing environment. Here’s how it works… Real quick, this video is actually sponsored
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day of my life. Get these pants! Okay now back to our game. The L Game only has a handful of pieces, a
very tiny board, and hardly any rules — and it’s deliberately indeterminate, meaning
that two perfect players could theoretically play forever with no winner. And there’s
a point to that. Let’s look at the board: it’s just a 4×4
grid, and each player has a single L-shaped piece that takes up 4 total spaces. There
are also two neutral pieces — these pennies — that can be moved by either player. And
we start the game by nestling the two Ls in the center and putting the neutral pennies
in the top left and the bottom right corners. So get ready to L. Each player is required to move their L piece
into a new, unoccupied spot on the board by picking it up and moving it, flipping it,
twisting it, turning it… whatever, as long as it cleanly occupies 4 squares. So like
this. Or like this. Not like this or like this. You can’t do that. That doesn’t work.
As long as at least one square is new and it doesn’t overlap with the other L piece
or a neutral spot, then the move is legal. After that move, the player can choose to
move either neutral piece to an open space — or not. It’s totally up to you whether
you want to play defense. But you can’t move the neutral piece before you move your
L. The only object of the game is to make it
so the other player can’t move their L piece. If they can’t move, then you win. Like if our pieces were in this position,
I could move my L here and the neutral piece here and I win. Your L is locked in, you can’t
go anywhere, see? And that’s it! It’s game over. It seems so easy! So… how can this game possibly take 5 days
to master? Consider the following board position, which
de Bono uses in his 1967 book, “Five-Day Course in Thinking” — which is actually
three 5-day courses, the L Game is just one of them. I’ll be Player 1, pink, and you’ll
be Player 2, orange. I only have three possible moves here… uhh let me show ya. It’s not
that difficult to choose one. Right? Wrong. Choosing a legal move is easy. Choosing
the best move isn’t. I need to think about what’s likely to happen after I make my
move — what will you do on the next turn? And what kind of board position will you put
me in for my next move? Will you play perfectly, or will you make a mistake that gives me an
advantage? And… if that’s what I have to consider to make the best move, what do you
need to think? It seems impossible to know — and that difficulty
is at the heart of de Bono’s strategic thinking. You can employ a few basic strategies to survive
and conquer, like blocking off a 3×3 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 about the grid as two halves and lock your opponent
in one half of the grid. Those strategies are pretty good, but they’re far from perfect. Let’s go back to my earlier scenario. Given my three possible moves, you have counter-moves
for each… counters A and B both result in a loss for me because there’s just nowhere
for me to put my L — because remember, the neutral spot can only be moved after a player
moves the L piece. Counter move C is my best possible move — because I’m not locked in,
I don’t automatically lose with C. The trick is whether I can see this coming in advance
so that I can avoid… taking the L. Alright. Got it, 3 moves, think ahead. No
big deal. But what if we have this situation… this
has 195 possible moves, with only one of them being is the best. That’s 1 out of 195. Awesome. Given the confines of the board, there are
82 possible positions for the L pieces and 2,296 board states altogether. De Bono teaches
that we should learn how to think about the L-Game by mentally ranking a move in one of
four ways: fatal, in which your opponent wins on the next move; weak, which leads you into
a defensive position; neutral, which changes nothing for either player; 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
keep track of them, two or three moves down the line? Perfect play entails collecting
and evaluating every possible move and making the best choice based on those results…
which is perfectly impossible even for a human mind obsessed with tetrominoes. Like, everyone. Modern humans love tetrominoes, which are
geometric shapes made 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, square, Z, Line
and the T. And Tetris also has the two chiralities of the L and the Z. They can be shifted, rotated,
re-jiggered or reflected to fit together… like in this 5×8 grid], which is one of 99,352
ways these pieces can fit within these boundaries. Or this 4×10 rectangle, which can be formed
any of 57,472 ways using tetrominoes. Until Minecraft, Tetris was the #1-selling game
of all time because our brains are fascinated with geometry puzzles and considering the
unknowns a few moves ahead. Or 100,000 moves ahead. Okay, let’s go back to L. On Day 3 of training, de Bono says that a
player can note the positions that made them lose and the positions that made the other
player win. That mindset is simple: you’ll eventually learn to avoid the bad spots and
put yourself in the good spots. Experience matters, and it trains us to think… but
it means it takes time, and you’ll lose a lot of games along the way. You need strategic
principles. And if you want to play it yourself I put
a link down below to an online version of the game. It’ll show you how many possible
moves you have in each board state and let you 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 realtime, de Bono advocates creating a set of several guiding principles
that can inform your strategy… like always keeping a neutral piece adjacent to your L
piece, or taking corner positions whenever you can. There aren’t any 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 single possible move. The more you play, and the better your mental
grouping of game situations develops, the more accurate your guiding strategic principles
will be. 15 years after de Bono’s book came out,
N. E. Goller devised a simple system that will guarantee a player at least an indefinite
draw — and provide opportunities to win if their opponent makes a mistake. If you can
get your L piece so that it occupies three of the four central squares in the grid, OR
so it occupies two central squares and no neutral piece occupies any of the squares
marked X, you’re in good shape to not lose. Beyond that, it’s up to you to use your
strategic thinking skills to win the game. In an academic mathematical game, you could
spend a few years working out all the moves and ranking their utility. But in real life
— when you’re sitting across the table from the other player just like you’re sitting
across the table from me — you can’t take forever. You’ve got to move, and the player
who can accurately think the furthest in advance is going to win. Which is what we all do every day in our own
ways, in our own lives. Today is another day in our never-ending course on strategic thinking. We don’t rotate L’s on a board, but we
do envision the future and alter our decisions in the present to give ourselves the best
opportunity to succeed. We break down 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 gain experience and make shortcuts to give us the optimal chance… To avoid L’s and manifest W’s. And as always, thanks for watching. I am a Ghostbuster. Seriously you can watch
me play a Ghostbuster in Jake’s newest Vsauce3 video — Could You Survive Ghostbusters? It’s
part of his amazing new series Could You Survive The Movies? Click over here to watch that.
My Achilles and the Tortoise paradox shirt is also available in my new Vsauce2 store.
I have a store! Check out my store. Check out everything. Everything is great. Bye.


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