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
by Mack Weldon who is dedicated to smartly
designing men’s basics. Like their silver-woven
underwear and silver-woven shirt that are
naturally anti-microbial or these Sunday Lounge
Pants that are my favorite pants. You can't
really see them like this. Let me just take
off my pants. There we go. Ah.. These are
my favorite indoor pants of all time. They
look really nice but they're also extremely
comfortable so you can wear them around your
house or your dorm in style. So for 20% off
your first order, go to mackweldon.com and
enter promo code vsauce2 -- all lowercase.
I know it sounds weird but I'm genuinely obsessed
with these pants and I need to order like
six more pair so I can wear them every single
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 4x4
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 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 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 5x8 grid], which is one of 99,352
ways these pieces can fit within these boundaries.
Or this 4x10 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.
