Chess and Luck

One of my favorite Chess places on the internet is the Mechanics’ Institute Chess Club Newsletter, by IM John Donaldson. If you are new to Chess and unaware, the Mechanics’ Institute is located at 57 Post Street, in San Francisco, California. The newsletter is published almost every Friday, unless IMJD, as he is known, is out of town, as in being a team captain for the US Olympiad squad. The MIN is a veritable cornucopia of Chess information, and it continues to get better and better, if that is possible. The edition this week, #809, is no exception. For example we learn, “An article at the singer Joni Mitchell’s web site mentions she polished her talent at the Checkmate coffeehouse in Detroit in the mid-1960s.” I have just finished reading, Joni: The Anthology, edited by Barney Hoskins, and the just published, Reckless Daughter: A Portrait of Joni Mitchell, by David Yaffe, awaits.

John writes, “Few have done as much as Jude Acers to promote chess in the United States the last fifty years and he is still going strong. View one of his recent interviews here.” I love the sui generis Jude the Dude! For the link to the interview you must visit the MIN.

We also learn that, “Noted book dealer National Master Fred Wilson will open his doors at his new location at 41 Union Square West, Suite 718 (at 17th Street) on December 20.” In MIN # 804 we learned that, “Fred Wilson earns National Master at 71.”(!) Way to go Fred! Congratulations on becoming a NM while giving hope to all Seniors, and on the opening of your new location. There is also a nice picture of Fred included, along with many other pictures, some in color, which has really added pizazz to the venerable MIN!

There is more, much more, but I want to focus on: 2) Top Individual Olympiad Performers. John writes: “Outside of the World Championship the biannual Chess Olympiad is the biggest stage in chess. Although it is primarily a team event, individual accomplishment is noted, and no player better represented his country than the late Tigran Petrosian. The former World Champion scored 103 points in 129 games (79.8 percent) and lost only one individual game (on time) in a drawn rook ending to Robert Hubner in the 1972 Olympiad.

Garry Kasparov is not far behind with 64½ points in 82 games (78.7 percent), and unlike Petrosian his teams took gold in every Olympiad he played. Garry won gold but he did lose three games.

Two of the players who defeated Kasparov in Olympiads were present during the Champions Showdown in St. Louis last month: Yasser Seirawan and Veselin Topalov. The latter had an interesting story to tell about the third player to defeat Garry—Bulgarian Grandmaster Krum Georgiev.

According to Topalov, one could not accuse his countryman of being one of Caissa’s most devoted servants. Lazy is the word he used to describe Krum, who loved to play blitz rather than engage in serious study. However it was precisely this passion for rapid transit which helped him to defeat Garry.

Before the Malta Olympiad Georgiev was losing regularly in five-minute chess to someone Veselin referred to as a total patzer. He got so frustrated losing with White in the same variation, over and over again, that he analyzed the line in the 6.Bg5 Najdorf inside and out and came up with some interesting ideas. You guessed it—Garry played right into Georgiev’s preparation. Who says there is no luck in chess.”

The game is given so click on over to the MIN and play over a Kasparov loss in which he let the Najdorf down. (http://www.chessclub.org/news.php)

I want to focus on the part about there being no luck in Chess. After reading this I something went off in my brain about “Chess” & “Luck.” I stopped reading and racked my aging brain. Unfortunately, I could not recall where I had seen it, but it definitely registered. After awhile I finished reading the MIN and took the dog for a walk, then returned to rest and take a nap. I could not sleep because my brain was still working, subconsciously, I suppose, on why “Chess” & “Luck” seemed to have so much meaning to me…It came to me in the shower. I have been a fan of Baseball since the age of nine, and I am also a Sabermetrician.

Sabermetric Research

Phil Birnbaum

Chess and luck

In previous posts, I argued about how there’s luck in golf, and how there’s luck in foul shooting in basketball.

But what about games of pure mental performance, like chess? Is there luck involved in chess? Can you win a chess game because you were lucky?

Yes.

Start by thinking about a college exam. There’s definitely luck there. Hardly anybody has perfect mastery. A student is going to be stronger in some parts of the course material, and weaker in other parts.

Perhaps the professor has a list of 200 questions, and he randomly picks 50 of them for the exam. If those happen to be more weighted to the stuff you’re weak in, you’ll do worse.

Suppose you know 80 percent of the material, in the sense that, on any given question, you have an 80 percent chance of getting the right answer. On average, you’ll score 80 percent, or 40 out of 50. But, depending on which questions the professor picks, your grade will vary, possibly by a lot.

The standard deviation of your score is going to be 5.6 percentage points. That means the 95 percent confidence interval for your score is wide, stretching from 69 to 91.

And, if you’re comparing two students, 2 SD of the difference in their scores is even higher — 16 points. So if one student scores 80, and another student scores 65, you cannot conclude, with statistical significance, that the first student is better than the second!

So, in a sense, exam writing is like coin tossing. You study as hard as you can to learn as much as you can — that is, to build yourself a coin that lands heads (right answer) as often as possible. Then, you walk in to the exam room, and flip the coin you’ve built, 50 times.

——

It’s similar for chess.

Every game of chess is different. After a few moves, even the most experienced grandmasters are probably looking at board positions they’ve never seen before. In these situations, there are different mental tasks that become important. Some positions require you to look ahead many moves, while some require you to look ahead fewer. Some require you to exploit or defend an advantage in positioning, and some present you with differences in material. In some, you’re attacking, and in others, you’re defending.

That’s how it’s like an exam. If a game is 40 moves each, it’s like you’re sitting down at an exam where you’re going to have 40 questions, one at a time, but you don’t know what they are. Except for the first few moves, you’re looking at a board position you’ve literally never seen before. If it works out that the 40 board positions are the kind where you’re stronger, you might find them easy, and do well. If the 40 positions are “hard” for you — that is, if they happen to be types of positions where you’re weaker — you won’t do as well.

And, even if they’re positions where you’re strong, there’s luck involved: the move that looks the best might not truly *be* the best. For instance, it might be true that a certain class of move — for instance, “putting a fork on the opponent’s rook and bishop on the far side of the board, when the overall position looks roughly similar to this one” — might be a good move 98 percent of the time. But, maybe in this case, because a certain pawn is on A5 instead of A4, it actually turns out to be a weaker move. Well, nobody can know the game down to that detail; there are 10 to the power of 43 different board positions.

The best you can do is see that it *seems* to be a good move, that in situations that look similar to you, it would work out more often than not. But you’ll never know whether it’s 90 percent or 98 percent, and you won’t know whether this is one of the exceptions.

——

It’s like, suppose I ask you to write down a 14-digit number (that doesn’t start with zero), and, if it’s prime, I’ll give you $20. You have three minutes, and you don’t have a calculator, or extra paper. What’s your strategy? Well, if you know something about math, you’ll know you have to write an odd number. You’ll know it can’t end in 5. You might know enough to make sure the digits don’t add up to a multiple of 3.

After that, you just have to hope your number is prime. It’s luck.

But, if you’re a master prime finder … you can do better. You can also do a quick check to make sure it’s not divisible by 11. And, if you’re a grandmaster, you might have learned to do a test for divisibility by 7, 13, 17, and 19, and even further. In fact, your grandmaster rating might have a lot to do with how many of those extra tests you’re able to do in your head in those three minutes.

But, even if you manage to get through a whole bunch of tests, you still have to be lucky enough to have written a prime, instead of a number that turns out to be divisible by, say, 277, which you didn’t have time to test for.

A grandmaster has a better chance of outpriming a lesser player, because he’s able to eliminate more bad moves. But, there’s still substantial luck in whether or not he wins the $20, or even whether he beats an opponent in a prime-guessing tournament.

——

On an old thread over at Tango’s blog, someone pointed this out: if you get two chess players of exactly equal skill, it’s 100 percent a matter of luck which one wins. That’s got to be true, right?

Well, maybe you’re not sure about “exactly equal skill.” You figure, it’s impossible to be *exactly* equal, so the guy who won was probably better! But, then, if you like, assume the players are exact clones of each other. If that still doesn’t work, imagine that they’re two computers, programmed identically.

Suppose the computers aren’t doing anything random inside their CPUs at all — they have a precise, deterministic algorithm for what move to make. How, then, can you say the result is random?

Well, it’s not random in the sense that it’s made of the ether of pure, abstract probability, but it’s random in the practical sense, the sense that the algorithm is complex enough that humans can’t predict the outcome. It’s random in the same way the second decimal of tomorrow’s Dow Jones average is random. Almost all computer randomization is deterministic — but not patterned or predictable. The winner of the computer chess game is random in the same way the hands dealt in online poker are random.

In fact, I bet computer chess would make a fine random number generator. Take two computers, give them the same algorithm, which has to include something where the computer “learns” from past games (otherwise, you’ll just get the same positions over and over). Have them play a few trillion games, alternating black and white, to learn as much as they can. Then, play a tournament of an even number of games (so both sides can play white an equal number of times). If A wins, your random digit is a “1”. If B wins, your random digit is a “0”.

It’s not a *practical* random number generator, but I bet it would work. And it’s “random” in the sense that, no human being could predict the outcome in advance any faster than actually running the same algorithm himself.

http://blog.philbirnbaum.com/2013/01/chess-and-luck.html

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