The perfect game

[RobertJasiek]

maybe mathematical research could help to find building blocks of perfect play

Mathematical theorems DO describe perfect play for certain (classes of) positions, such as certain (classes of) positions with very late endgame, semeais or kos. (What do you mean with "(building) blocks"?)

[moha]

We can learn from what happens in the chess world. Not even the most hubristic grandmaster denies that computers are much stronger than humans, but few, if any, seem to try to use computers as a direct learning tool. Instead they use them for blunder checking and for opening preparation (which can be seen as form of blunder checking). They do not use them to make strategic decisions. In fact, many grandmasters still seem to mistrust computers' strategic judgements.

But this is because current chess programs are strong tactically but not strategically, and still not "really" strong overall, as shown by AlphaZero (which is probably still not close to perfect play). Some people may change their opinion if a near-perfect program were available.

[Baywa]

maybe mathematical research could help to find building blocks of perfect play

Mathematical theorems DO describe perfect play for certain (classes of) positions, such as certain (classes of) positions with very late endgame, semeais or kos. (What do you mean with "(building) blocks"?)

Actually, that - classes of positions - was what I had in mind with "building blocks". But then, the problem with mathematical classification is that it tends to be either too coarse (too few classes) or too fine (too many classes). Of course, in order to find perfect play, such a classification must also include positions in the opening and middle game. Somehow I had an approach in mind, similar to the proof of the Four colour theorem...

[Kirby]

We can learn from what happens in the chess world. Not even the most hubristic grandmaster denies that computers are much stronger than humans, but few, if any, seem to try to use computers as a direct learning tool. Instead they use them for blunder checking and for opening preparation (which can be seen as form of blunder checking). They do not use them to make strategic decisions. In fact, many grandmasters still seem to mistrust computers' strategic judgements.

But this is because current chess programs are strong tactically but not strategically, and still not "really" strong overall, as shown by AlphaZero (which is probably still not close to perfect play). Some people may change their opinion if a near-perfect program were available.

The difference in skill is too significant to be meaningful.

A chimpanzee can try to imitate Bill Gates to become rich and buy a lot of bananas, but he doesn’t even comprehend the problem space.

We are the chimps here.

[moha]

We can learn from what happens in the chess world. Not even the most hubristic grandmaster denies that computers are much stronger than humans, but few, if any, seem to try to use computers as a direct learning tool. Instead they use them for blunder checking and for opening preparation (which can be seen as form of blunder checking). They do not use them to make strategic decisions. In fact, many grandmasters still seem to mistrust computers' strategic judgements.

But this is because current chess programs are strong tactically but not strategically, and still not "really" strong overall, as shown by AlphaZero (which is probably still not close to perfect play). Some people may change their opinion if a near-perfect program were available.

The difference in skill is too significant to be meaningful.

The difference in tactical skill and reading. But do you think the same grandmasters consider the program much stronger strategically as well, and at the same time "mistrust computers' strategic judgements"?

Or did you mean the hypothetical near-perfect program of the future? That will create a different situation: having THE correct answer, and the task of study gets reduced to finding the explanation. Maybe this is not to everybody's taste, but it will still open a new door.

OC, the same question can be asked like with current AG analysis: how many of it's moves will have real strategic meaning, and how many will just happen to work, because of a certain minimax line? But this tells more about the nature and the quality of the game than the level of human skill.

[Kirby]

Or did you mean the hypothetical near-perfect program of the future? That will create a different situation: having THE correct answer, and the task of study gets reduced to finding the explanation.

I am thinking that the explanation will be sufficiently complex that it will be about meaningless to humans. We get some fads from AlphaGo like the early 3-3 invasion, etc., which may give us new ideas, but we're far from understanding the real rationale. If we have a go program that plays perfectly, I imagine the situation will be pretty similar.

[Tryss]

I am thinking that the explanation will be sufficiently complex that it will be about meaningless to humans. We get some fads from AlphaGo like the early 3-3 invasion, etc., which may give us new ideas, but we're far from understanding the real rationale. If we have a go program that plays perfectly, I imagine the situation will be pretty similar.

Worse than that. Because you'll know the reason why the perfect program played a move : because all the possible following plays lead to victory

And that's absolutely useless for humans.

[moha]

I am thinking that the explanation will be sufficiently complex that it will be about meaningless to humans. We get some fads from AlphaGo like the early 3-3 invasion, etc., which may give us new ideas, but we're far from understanding the real rationale. If we have a go program that plays perfectly, I imagine the situation will be pretty similar.

Worse than that. Because you'll know the reason why the perfect program played a move : because all the possible following plays lead to victory
And that's absolutely useless for humans.

This is exactly why I wrote:

OC, the same question can be asked like with current AG analysis: how many of it's moves will have real strategic meaning, and how many will just happen to work, because of a certain minimax line? But this tells more about the nature and the quality of the game than the level of human skill.

In other words: if (and to the extent of) the correct moves of a game can only be reasoned by minimaxing, that game is worthless, or rather, not a game at all. And this is not just because of some limitation of the human skill, but because of the lack of the high level aspects that make a game interesting and worthwhile for an intelligent being. (A "game" is basically a simplified practice for efficient (!) real world problem solving.)

Consider prime factoring, for example. Would that make a decent game? Yes, but only to the extent there are potential algorithms for more efficient solutions than brute forcing. There are humans enthusiastically playing that game - researching such algorithms. But how about cryptography, where a certain encoding is proved to be completely secure (so only brute force attacks remain)? IMO the moment such proof exists the "game" part disappears (except the interest in the proof itself, as that may be useful in other "games" as well).

But with AG the situation doesn't seem that bad. I think about half of it's unusual moves do have understandable meanings. Go is not completely random at least.

[RobertJasiek]

There are lots of theorems not (or not only) using minmax. Since those include those for the very late endgame, opening and middle game also do not only reduce to boring minmax.

[Pio2001]

Hi,
What's the largest goban size for which perfect play is known (from an empty board) ? Is there a record of the perfect game, with the final score ?
If this size is even, is there a record of the perfect play on the largest odd goban size ?

[Uberdude]

Hi,
What's the largest goban size for which perfect play is known (from an empty board) ? Is there a record of the perfect game, with the final score ?
If this size is even, is there a record of the perfect play on the largest odd goban size ?

See forum/viewtopic.php?f=18&t=11608&hilit=li+zhe+solved

It seems 5x5 and 5x6, though human pro Li Zhe claims to have a very weak solve of 7x7.

[Bill Spight]

Hi,
What's the largest goban size for which perfect play is known (from an empty board) ? Is there a record of the perfect game, with the final score ?
If this size is even, is there a record of the perfect play on the largest odd goban size ?

See forum/viewtopic.php?f=18&t=11608&hilit=li+zhe+solved

It seems 5x5 and 5x6, though human pro Li Zhe claims to have a very weak solve of 7x7.

One trouble, from comments I have heard, with the top neural network programs is that they are trained on specific conditions, a specific board size and specific komi. Presumably a good bit of what they have learned will apply to other conditions, but the question is, how well?

I imagine that AlphaZero, if trained on a 7x7 board with different values of integer komi, could produce perfect play on an empty board with each value of komi within a day or two.

[John Fairbairn]

I'm ignorant about these things, but curious. If the ultimate test is to play everything out by computer, why do we need a mathematical proof? I can see that a proof might be intellectually interesting and have implications for cases that computers cannot handle yet, but it seems easiest just to wait for faster hardware, especially given the rate of progress so far.

And if there is a good reason for being able to write down a proof, would it have any value outside of go?

[Kirby]

Playing everything out by computer would be one form of proof, if it meant iterating all combinations of play. It’ll be a long time before that’s feasible for large board sizes.

[Baywa]

You need to apply mathematical methods in order to reduce the number of possibilities (its not about aesthetics). The number of board positions is of the order of 3^361 ~= 1.7*10^172 which is a pretty huge number. If your computer works at a speed of 10^12 operations per second and with each operation you check one position you'll still need about 5.5*10^152 years to sort it all out. Even with parallelization and an enormous increase of speed and using hypothetical, fancy new technology this task may never be achieved.

That means you need to use (applied) mathematics to reduce the number of possibilities by many, many orders of magnitude. There are already methods of tree-pruning available but lot more methods are needed. I have no idea whether such methods are within reach but it would be pretty cool, even for a 9x9 board.