Wednesday, October 29, 2008

The Laskers and the Go master

My father played Chess, Go and Bridge. I don't know much about the last two, but I recently came across this vignette from Edward Lasker (International Master and US Chess champion) about his and Emanuel Lasker's encounter with a Go master. Emanuel Lasker was world Chess champion for 27 years -- rated among the strongest players of all time -- and a mathematician as well.

Mr. Kitabatake one day told us that a Japanese mathematician was going to pass through Berlin on his way to London, and if we wanted to we could play a game with him at the Japanese Club. Dr. Lasker asked him whether he and I could perhaps play a game with him in consultation, and was wondering whether the master – he was a shodan – would give us a handicap.

“Well, of course,” said Mr. Kitabatake.
“How many stones do you think he would give us?" asked Lasker.
“Nine stones, naturally,” replied Mr. Kitabatake.
“Impossible!” said Lasker. “There isn’t a man in the world who can give me nine stones. I have studied the game for a year, and I know I understood what they were doing.”
Mr. Kitabatake only smiled.
“You will see,” he said.

The great day came when we were invited to the Japanese Club and met the master – I remember to this day how impressed I was by his technique – he actually spotted us nine stones, and we consulted on every move, playing very carefully. We were a little disconcerted by the speed with which the master responded to our deepest combinations. He never took more than a fraction of second. We were beaten so badly at the end, that Emanuel Lasker was quite heartbroken. On the way home he told me we must go to Japan and play with the masters there, then we would quickly improve and be able to play them on even terms. I doubted that very strongly, but I agreed that I was going to try to find a way to make the trip.

Edward Lasker:

While the baroque rules of Chess could only have been created by humans, the rules of Go are so elegant, organic, and rigorously logical that if intelligent life forms exist elsewhere in the universe, they almost certainly play Go.

I'm sympathetic to this point of view. The rules of Go seem to be a natural embodiment of two dimensional notions of encirclement and control of space. They are much simpler and less arbitrary than those of Chess. I can't say anything about the strategic and tactical subtlety of the game, since I don't play, but experts seem to think it is quite deep (certainly it is more challenging for AI than Chess, if only for combinatorial reasons). One problem with Lasker's contention is that Go doesn't seem to have been invented independently by any human civilizations other than ancient China (supposedly 4000 years ago)!


G said...

I've played both, and I actually consider Chess the harder game for a human - because in chess there is a clear advantage that raw computational power gives you ie. you can in a lot of circumstances search your way to a clear material advantage; however in Go that is essentially impossible (the computational space is much larger) so it relies on "softer" strategic skills that are more the product of experience. Not that Chess doesn't, it just has the extra ingredient because the computation is tractable.

smekhovo said...

No question, Go is the most challenging of games. That hypothetical intelligent species would probably be unimpressed by chess, but take to Go with delight.

David said...

The rules of Go seem to be a natural embodiment of two dimensional notions of encirclement and control of space.

This may capture the distinction the best. I'll take a [completely unfounded, totally aesthetic] wag at it. Good strategies in chess derive from scalar potentials and follow steepest descents. Goodness of strategies in Go is characterized by vector potentials and follow isoclines. [And maybe have non-trivial homotopy equivalence?]. I'd love to be able to take a couple of weeks and turn that into something meaningful [even if it means I'm a crackpot].

George Shen said...

GO or WEIQI in Chinese (Traditional: 圍棋; Simplified: 围棋), igo (囲碁, igo) or go (碁, go) in Japanese, and baduk in Korean (hangul: 바둑). Why this game is significant? And what makes it interesting to compare? GO has a long history in the oriental culture with the influence of literature, music, philosophy, and even military strategy. It's widely played by people in three countries Japan, Korea, and China. Japanese did a great job introducing the games into English literatures so many people in the West could learn it.

I play GO, Chess, and Chinese Chess. There are many similarities between Chess and Chinese Chess. I am also at a point where I can appreciate elegant and brilliant moves in each of these games. GO, no doubt, is the best game among all board games in my view, especially when supercomputers can consistently beat the strongest chess GM in the world. At amature level 2K (24k to 1k then 1 dan to 6dan for amatures), I am probably only in the middle of the scale of proficiency (by amature standard, mind you) and no supercomputer from this world can beat me (yet).

But that is not the only reason I appreciate GO. It's the simplicity of rules mixed with complex of strategy and philosophy that makes GO so intriguing. I encourage everyone study it and play it. It's absolutely FUN! (and takes life-time to master it!)

Roger Bigod said...


Good point. The way I think of it is that early in a game of Go one thinks of the board as a two-dimensional continuum, rather than a collection of points, and considerations of aesthetics and taste are useful, if only for remembering good moves. But in the middle game a tree analysis is required. There's long sequences of forced moves on both sides you have to follow. And the end-game is analyzable as a set of sub-positions for which values can be computed, including values with fractional points.

There are phase transitions in learning, which may not have a parallel in chess. In advancing through the handicap levels, people often stall at a particular leve, then advance two or sometimes three stones over a few days. It happened to me, and there were no changes I could verbalize.

Go anecdotes tend to be cheerful. My favorite concerns two young professionals who were arguing about the details of game tree algorithms applied to Go, and an older master standing around (Go Seigen IIRC) interrupted to say "You both have it wrong. Go isn't a game of competition; it's a game of coexistence. If you try to claim more space than your previous play entitles you to, you will lose. And if you don't take what your previous play entitles you to, you lose. So the winner is the best coexister." (I don't think this is an attitude often found in chess players.)

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