Vsauce! Kevin here, with a game so complexand 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 Edwardde Bono over 50 years ago, the L-Game was designed to be the simplest possible gamethat could stretch the players’ ability to find not just any solution, but the bestsolution, in a constantly-changing environment.
Here’s how it works.
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The L Game only has a handful of pieces, avery tiny board, and hardly any rules — and it’s deliberately indeterminate, meaningthat two perfect players could theoretically play forever with no winner.
And there’sa point to that.
Let’s look at the board: it’s just a 4x4grid, and each player has a single L-shaped piece that takes up 4 total spaces.
Thereare also two neutral pieces — these pennies — that can be moved by either player.
Andwe start the game by nestling the two Ls in the center and putting the neutral penniesin the top left and the bottom right corners.
So get ready to L.
Each player is required to move their L pieceinto 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.
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 pieceor a neutral spot, then the move is legal.
After that move, the player can choose tomove either neutral piece to an open space — or not.
It’s totally up to you whetheryou want to play defense.
But you can’t move the neutral piece before you move yourL.
The only object of the game is to make itso 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'tgo anywhere, see? And that's it! It's game over.
It seems so easy! So… how can this game possibly take 5 daysto master? Consider the following board position, whichde Bono uses in his 1967 book, “Five-Day Course in Thinking” — which is actuallythree 5-day courses, the L Game is just one of them.
I’ll be Player 1, pink, and you’llbe Player 2, orange.
I only have three possible moves here… uhh let me show ya.
It’s notthat difficult to choose one.
Choosing a legal move is easy.
Choosingthe best move isn’t.
I need to think about what’s likely to happen after I make mymove — what will you do on the next turn? And what kind of board position will you putme in for my next move? Will you play perfectly, or will you make a mistake that gives me anadvantage? And… if that's what I have to consider to make the best move, what do youneed to think? It seems impossible to know — and that difficultyis at the heart of de Bono’s strategic thinking.
You can employ a few basic strategies to surviveand conquer, like blocking off a 3×3 grid in the corner of a board using your L anda neutral piece — and then manipulating the other neutral piece to eliminate your opponent’spossible moves.
Or you can think about the grid as two halves and lock your opponentin 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-movesfor each.
counters A and B both result in a loss for me because there’s just nowherefor me to put my L — because remember, the neutral spot can only be moved after a playermoves 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 advanceso that I can avoid… taking the L.
Got it, 3 moves, think ahead.
But what if we have this situation… thishas 195 possible moves, with only one of them being is the best.
That's 1 out of 195.
Given the confines of the board, there are82 possible positions for the L pieces and 2, 296 board states altogether.
De Bono teachesthat we should learn how to think about the L-Game by mentally ranking a move in one offour ways: fatal, in which your opponent wins on the next move; weak, which leads you intoa defensive position; neutral, which changes nothing for either player; and strong, whichgives you the advantage.
In this board position, there are 65 possible moves: 22 fatal, 17weak, 26 neutral, and 0 strong.
Can you consider all those possibilities andkeep track of them, two or three moves down the line? Perfect play entails collectingand 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.
Modern humans love tetrominoes, which aregeometric 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, Lineand 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, 352ways these pieces can fit within these boundaries.
Or this 4×10 rectangle, which can be formedany of 57, 472 ways using tetrominoes.
Until Minecraft, Tetris was the #1-selling gameof all time because our brains are fascinated with geometry puzzles and considering theunknowns 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 aplayer can note the positions that made them lose and the positions that made the otherplayer win.
That mindset is simple: you’ll eventually learn to avoid the bad spots andput yourself in the good spots.
Experience matters, and it trains us to think… butit means it takes time, and you’ll lose a lot of games along the way.
You need strategicprinciples.
And if you want to play it yourself I puta link down below to an online version of the game.
It’ll show you how many possiblemoves you have in each board state and let you run simulation after simulation to seehow complex this simple-looking game really is.
To make sense of the impossibility of calculatingevery possible move in realtime, de Bono advocates creating a set of several guiding principlesthat can inform your strategy… like always keeping a neutral piece adjacent to your Lpiece, 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 experienceare essentially shortcuts to success, allowing you to avoid playing 10 million L-Games orconsidering every single possible move.
The more you play, and the better your mentalgrouping of game situations develops, the more accurate your guiding strategic principleswill be.
15 years after de Bono’s book came out, N.
Goller devised a simple system that will guarantee a player at least an indefinitedraw — and provide opportunities to win if their opponent makes a mistake.
If you canget your L piece so that it occupies three of the four central squares in the grid, ORso it occupies two central squares and no neutral piece occupies any of the squaresmarked X, you’re in good shape to not lose.
Beyond that, it’s up to you to use yourstrategic thinking skills to win the game.
In an academic mathematical game, you couldspend 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 sittingacross the table from me — you can’t take forever.
You’ve got to move, and the playerwho can accurately think the furthest in advance is going to win.
Which is what we all do every day in our ownways, 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 wedo envision the future and alter our decisions in the present to give ourselves the bestopportunity to succeed.
We break down our life-boards into smaller, more manageablesections, and create little systems based on what we’ve learned and what we’ve cometo 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.
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