Malweth’s Metablog

Yesterday I became an 8-kyu and promptly fell back to 9-kyu! I’m not too surprised, but it does indicate that I’m on the border and probably just need to play more!

Today I’ve been thinking about “out of reach.” What I mean by “out of reach” is: you know an ability exists, you see an occasion to use such an ability, and the outcome is “out of reach” because you don’t actually have that ability!

What does this mean in relation with Go? I’ve mentioned in the past (and if I haven’t, I should) that at a certain point you start gaining an understanding of go - you can see the whole board and build territories; you can hold your own in a tactical fight, especially against an equal but sometimes versus your teacher; you understand the basic flow of the game, but may be unable to turn that to your advantage.

It’s said that everything in Go requires reading (and if it wasn’t said, I’ll say it now). I know my reading ability and where basic Tesuji and other one-way-path sequences are involved I begin to read quite far. The real problem arises in the wide open spaces. I may have mentioned it before: we always hear the stronger players (yes, Dan level) say “that corner can become a ko” before anyone’s even played there! This is something that obviously comes partially through experience, but also with lots of reading ability. What is it that allows you to look at a position and say “this can have one of these 3 results?” I think the next step (perhaps the 5-kyu or shodan barriers) is one of multi-threading. If I can read down 20 paths, keep them all in my head, say which path gives the best result, and play accordingly (or kibitz accordingly, as the case may be maybe I turn into a shodan… or perhaps a 7 dan - just where does this kind of reading ability fit?

The real issue I have, and the reason I’m writing this, is the frustration involved. If you’re in the middle of a game and see an interesting corner (perhaps a 3×3 invasion that you’re not sure about), you’ll mentally place a stone there and mentally respond. Perhaps you’ll go down one path and decide to play, completely missing the failure path that your opponent takes. Even if you’re not playing there’s the ever present frustration of not knowing! I’ll look at a group and say “something can happen there” but be unable to say just what can happen.

As a basic, non-go, example… picture your basic math from 2nd grade. Certainly now you know that 6×9 is 54. Even if you hadn’t memorized it yet, you can figure it out the long way - 6+6+6+6+6+6+6+6+6. Now imagine that you don’t know what “x” means. You need to figure out 6×9, and someone with more ability can tell you the answer, but you’re unable to add 6 nine times. This correlates well with reading ability in go. From perhaps Shodan onward you know 6×9; you’ve done 6×9 so many times that you could figure it out in your sleep. The 9-kyu up to shodan knows about 6×9: they may have seen it once or twice, or just heard about it from one of the ones who knows it; the 9-kyu may be able to figure it out given enough time, but may require pencil and paper to visualize the nine 6s. And from the beginner until that epiphany of reading ability has been reached knows nothing of 6×9; they’ll take the shodan’s word on 54 but can’t see how the answer is derived. (The beginner is naive and pure - the intermediate sullied - the shodan used).

Is the perfect game possible? My inclination is no. Firstly, a perfect game must reach jigo (a win of 0.5 by one side or the other). A definite win is possible as a perfect game, but highly unlikely. If I explain mathematically… Assume that the perfect game exists. This perfect game must start with a move on the board as black. Only one such move is possible if there exists only a singular “perfect game” (up to four moves if symmetry is taken into effect). Immediately there’s a problem. White must move - which must mean there’s a single move which, when made by White, results in a perfect game. No other move gives the most advantage to White. This also must mean that any other move, when played by White, can be taken advantage of by Black to result in a >0.5 point win. (Again, symmetries are not taken into account). Because of the nature of the board, it is unlikely there’s a single point that always results in a jigo. In respect with the fuseki, it’s unknown whether the 3-4 or 4-4 point is best. Why is this the case? Because Go is a game of balance, not perfection. Every move has either a discrete value or a potential value. This is easiest seen in the end game when a 2 point move is played before a 1 point move (where both moves are equal with respect to sente and ko). If you begin viewing at yose and work your way backward through a “good game” (a jigo that may or may not be perfect) it’s evident that there are many 1 point moves that can be played in any order and by either player. This alone indicates that there cannot be a single “perfect game.” To make an assumption, let’s continue working our way back from yose… In the middle game, it isn’t uncommon to choose between two moves of equal value. One may provide more moyo and less secure territory whereas another may prevent an attack. Two moves, both worth 13 points and approximately equal in terms of aji (influence), is a possible situation. Another common situation would be a move worth 13 points (perhaps a corner invasion) and another move worth only 3 points but with much stronger aji (and/or much less reverse aji). Both moves are gote: which of these should be chosen in the “Perfect” game? The illustration I’m trying to make is that, at a certain point, one has to decide upon the value of aji created. At these important junctures, the aji value can only be found by using the aji. This is more easily said - your opponent may have the ability to lessen your influence by strengthening his own position. If an invasion becomes impossible, the aji is destroyed and the 13 point corner invasion becomes the better choice. However, in this example, the opponent chooses to defend the weak territory. At a certain point, the number of these “perfect” games becomes extremely high… and when you’re talking about a game that has an estimated 10^71 total possible games, the number of perfect games must also be very large. Even if 0.0000000001% (10^-12) of all games can be considered “perfect,” this would mean there are 10^58 perfect games. Even if 10^-59% of all games are perfect, this means there are 10^10 perfect games. Let’s assume that all perfect games begin with one of two points (3-3 and 3-4) which means, with symmetry, there are 8 perfect beginning moves which leaves 8/361 of all games as potentially perfect with regards to the first move. This is as much as 2.2% of all games, or on the order of 10^69 games! Certainly the “perfect” tree is much smaller than 10^69, but here’s the big problem… as soon as your opponent plays outside of the perfect games tree, you must be able to take advantage of such a mistake. This means you must also have knowledge of all non-perfect games! What do all these numbers mean? (all values estimated - most found on Sensei’s Library) 10^50 - Maximum legal chess games 10^69 - Total number of atoms in the galaxy 10^69 - Total number of semi-perfect games in Go (Estimated above) 10^71 - Total number of games of Go * In essence, a perfect game may exist, but there must be more than one. * Even if all perfect games are known, imperfect games must be known to take advantage of your opponent’s mistakes. * Let a perfect player = someone who plays perfectly to a jigo or win in every game. - Therefore the perfect player cannot exist. This leads me to the conclusion that a perfect game will be found long before a perfect player. Computers should strive toward finding a perfect game as a person finding a perfect game will only be by chance - and will likely be completely overlooked. The biggest problem, however, is that Computers need to be much stronger to even strive towards finding such a game - since begin game moves are not easily valued, finding this perfect play by current computers is also a trial-error tree. It could be done systematically (assuming the program was able to score a game correctly) but this would take eternity to complete! This is go