Working backward to solve problems - Maurice Ashley

Transcriber: Andrea McDonough
Reviewer: Bedirhan Cinar

There's a myth that grandmasters can see ten, fifteen, twenty moves ahead. And it's a great myth because I'm a grandmaster and it makes me look like a super freaking genius. But the truth is, in just the first four moves, there are 318 billion ways you could play. Now, that would be cool if I could pull that off, but grandmasters just can't; it's too much.

So we use different techniques to be able to look ahead. And some of these techniques include chunking, which means taking a group, a chess position, and seeing what possibilities can come from just that group; or pattern recognition, which is just going over a lot of positions that look very similarly and extrapolating truths from that; the stepping-stone method, which is to take a position, freeze it in your mind, and go from there to guess the next position. But one of my favorites that I love to solve these kind of chess puzzles is called retrograde analysis.

And what you do with retrograde analysis is that in order to look ahead, it pays to look backwards. Now, why is this so useful? Well, in chess, it's a very complicated case. You got all these chess pieces; it's 32 pieces. But after five moves, the position starts to evolve a little bit. And the game starts to go on and you see the chess position get a little simpler, and a little bit simpler, and less pieces on the board, until finally -- in this case, a game that I played in a tournament in Foxwoods, it gets to something like this.

When great players play, it often gets to something like this. You don't see some easy, early checkmate. Grandmasters see through all that stuff. What you see is some end game, something really, really simple. And we like to study things like this; grandmasters do, so that if we get to them, we know how to play them cold, but also so that we can steer the position that's in front of us, the more complex ones you saw earlier, to something this easy, something this simple.

So in this way, when you're dead, I already knew like ten moves ago because I knew where we were going. Now, why is this so effective? Well, it's something about the human mind; the problem with the human mind. We're very logical creatures. So I want you to play along with me a few games. Take a look at this sentence.

[After reading this sentence, you will realize that the brain doesn't recognize a second "the."]

Now, most of you reading the sentence the second time around will realize that you missed the word "the" the first time around. Your mind is very logical; it proceeds forward, it just ignores anything that breaks with its logical stream, and so you don't see the word "the" the first time, the second "the," the first time you read it. But if you read this sentence backwards, you would automatically catch it. You'd go backwards, and you get to "brain," you get to "the," and then you say, "Whoa, there are two 'the's' in the sentence." This is a really cool trick for proofreading papers. You're writing your paper and there are these silly mistakes. Why are these mistakes in my paper?

You read it backwards, you'll catch all of them. Alright, let's go on to this problem, an interesting problem. "Bacteria that double every 24 hours fill a lake it has infested after precisely 60 days. On what day was the lake half-full?" Now, a lot of people see this problem and they'd think, "30, like, you know, you split it in half." Well, that's not the right answer. And also, people might want a calculator. It's too big; it's math; it's boring; I don't want to do that either. But if you do this problem backwards, you get the answer right away.

What's the answer? 59, obviously. You start at the end, you go backwards; it's like, "Oh yeah, it's half-full, the answer is 59." Here's another puzzle, a little bit more complicated. You have six numbers, 1 through 6. The cards are face down. You and I are going to pick a card. You pick a card and you look at it, and it says the number 2. I look at my card, I think about it for a minute, and I say, "I want to trade."

The reason I want to trade: we're going to trade to see who has the highest number at the end. Do you trade with me? Most people say, "Of course, I got a 2; 2 sucks! There are four numbers higher; probability says I'm going to do better." Wrong answer; you're playing a grandmaster. You start from the back and you work it out. If I had the number 6, would I offer to trade? Of course not; I'm not dumb.

What about the number 5? Probably not either, because you're not going to say yes if you have a 6. If 5 is not going to trade and 6 is not going to trade, 4 is going to be like, "I'm not trading either, because 5's and 6's don't trade." So you see what happens as we work backwards. 3 is going to realize: 4, 5, and 6 -- they don't trade, so the offer is definitely a 1, and all of you who said yes, thanks for your money. (Laughter)

So, this retrograde analysis is used in different places. It's used to prove intoxications hours after an alleged DUI by Pennsylvania police officers, which is kind of cool. Well, it means don't drink and drive. The use of retro-analysis is used in law, science, medicine, insurance, stock market, politics, career planning. But I find its use to be in a more interesting place; maybe one of the most interesting uses is in this movie, which I know a lot of you know, "The Curious Case of Benjamin Button," where Brad Pitt plays a guy who's living his life backwards.

And what this movie makes me think of is that great quote, that quote you often hear from people who are older, that youth is wasted on the young. Well, if you can see the end game, your youth will not be wasted on you. Thank you very much. (Applause)