The Hardest Easy Game

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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... 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.
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Channel: Vsauce2
Views: 4,307,895
Rating: undefined out of 5
Keywords: strategic thinking skills, edward de bono, edward de bono thinking course, the l game, math games for kids, brain teasers, game you win by losing, parrondo’s paradox, game you quit, problem you’ll never solve, ant on a rubber rope, game you never win, game you always win, pizza theorem, what is a paradox, battleship algorithm, the dot game that breaks your brain, card game you can always win, can being stupid make you smart, vsauce 2, michael stevens, math tricks
Id: 64pA31_WJa0
Channel Id: undefined
Length: 11min 29sec (689 seconds)
Published: Mon Nov 04 2019
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