I was just wondering if anyone here has tried to play on boards bigger than 19x19. Is it fundamentally different than playing in a normal-sized board? Is it more complicated or simply somewhat different?

Edit: also, did anyone tried to play in a rectangular board (say, 19x21)? How do you think the gameplay would be affected?

37x37 is crazy! Apart from that, not really tried

Getting territory (edge-facing stuff) becomes less valuable, getting influence (center-facing stuff) becomes more valuable, then everything follows from that.

I'm not so sure. I recall reading somewhere that the common pro opinion about 21x21 is that it emphasizes corners more and sides less. The reasoning behind that is that it's much easier to invade and much harder to attack the invasion because there is more space. If you use "normal" 19x19 joseki, you can basically first take the corners, giving away influence, and then invade the side without much problems...

I don't remember what the conclusion was about center facing influence, though.

I found on 37x37 the only thing you could be sure of was corner sequences. Edges were easier to claim than anything towards the middle. The center was an armageddon zone. Influence facing the center from the side wasn't that useful, it was just all a bit of a mess.

Click Here To Show Diagram Code

[go]$$B 21x21 Sanrensei
$$ -------------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . . . |
$$ | . . . 4 . . . . . . , . . . . 9 . 1 . . . |
$$ | . . . . . . . . . . . . . . . . . . 7 . . |
$$ | . . . . . . . . . . . . . . . . . 8 6 . . |
$$ | . . . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . 0 . . |
$$ | . . . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . . , . . . . . . 5 . . . |
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$$ | . . . . . . . . . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . . , . . . . . . 3 . . . |
$$ | . . . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . . . |
$$ -------------------------------------------[/go]

The 21x21 is wide enough that sanrensei leaves room for the opponent to invade and make a two space extension. As people have pointed out, that makes a moyo game more difficult.

Every New Year's the Nihon Kiin has a 21x21 rengo. It would be interesting to see some of those games.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Another argument is that on 9 x 9 and smaller boards, opening on tengen is obviously a very good move. It may well be the best (if this is true on 19x19, we have little reason to believe it).

The argument is rather limited, but what it does show is that the importance of center influence does not monotonically increase with the size of the board.

_________________
Occupy Babel!

Except that since the corners and edges are worth comparatively less, it may be that the appropriate response to the invasion is different on a 21x21 board. For instance, preventing the extension but letting him live in the corner may be worth more.

EDIT: Further, for all we know making an invasion like that and giving black sente with only a nirensei opening with white might be a poor choice of play. White's side is even more open than usual, and his two point extension has done less overall damage than it would on a 19x19 board.

For all you and I know, maybe. But it's much harder to be true for all Bill knows, and his informants may know even more than he does.

_________________
Occupy Babel!

I was not advocating that invasion, just pointing out the extra space.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I was just pointing out that I don't think it follows that the Moyo game is necessarily more difficult because there is extra space to invade, something which you did say. It might be that the extra space only makes it more difficult if you give a particular response which is standard on a 19x19 board (e.g. the kick and extend). Especially with Moyo play, I think it is rather unlikely that standard play on a 19x19 board would remain optimal on a larger board. Any analysis would have to be much more thorough and start, to some degree, from scratch.

If you're beerslayer, 37x37 is standard.

I played beerslayer once on a 37x37.


I have nothing to substantiate it, but I think go strategy is somewhat fractal on larger boards. Roughly speaking, if a single stone is a fence post for a small group, then small groups are fence posts for larger groups and so on.

_________________
19/02/2011: this grumpy person takes a voluntary holiday from L19.

Why do you think that's the case? I'm pretty sure it's the other way round, that corners are worth more in comparison to outward facing influence.

Why should e.g. a 3-3 invasion be worth less on a bigger board? It still makes exactly the same amount of territory. But the resulting outward influence is (supposedly) worth less, because it's easier to invade the bigger space.

Eh, I don't buy either story.

It's the same wall, it projects the same strength outwards. The only thing to question is the value of that projected strength relative to the points gained in the corner. If we simply ask ourselves how we would approach to or extend from that wall, isn't the answer the same, regardless of board size? Would you really play any closer just because the board is bigger? Assuming your answer is 'no', then you're really saying that the wall is doing the same amount of work relative to the points in the corner, whatever the board size (well, unless it's on a really small board where its influence is truncated).

That's not to say I would discount any effect of increasing board size, just that I doubt it'd be so straightforward. If I were to guess, I'd guess at cycles or oscillations. e.g. on boards just the right size such that the game ends just after the 3-3 invasion sequence (because there's no room for the invading player to play again on the other side of the wall), then I would expect the wall to become more effective with increasing board size up until the point where it becomes possible to play and live on the other side. Then it might drop dramatically and increase again up until the point where a stone claiming the other corner also happens to be the right amount to extend from the wall. Perhaps the oscillations would become smaller the larger the board size. Or to put it another way, on small boards tactical considerations might swamp any of our nice generalized go theories (i.e. those theories break down at a small scale), with those same tactical considerations having relatively less effect as board size increases, and no reason for them to have any kind of linear effect. Not that I'm pretending to have a clue, just that if I were to pick a story to believe (going on no evidence), I'd pick that kind of story .

_________________
19/02/2011: this grumpy person takes a voluntary holiday from L19.

Exactly. The strength of walls is approximately the same on large enough boards. The shift from 19x19 to 21x21 hardly matters in that regard.

Now, the influence of a stone or group depends upon its strength. That was the point of my sanrensei comparison. The influence of the sanrensei stones is approximately the same, but an invading group of a 21x21 sanrensei is stronger than a corresponding invading group of a 19x19 sanrensei. That means that side spanning frameworks, such as sanrensei or Chinese or Kobayashi, will be thinner and less effective on the 21x21.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

But that's assuming that you use outward thickness to surround territory. Usually you don't

Would I play closer to the wall if the board were bigger? Certainly not. The argument goes exactly the other way round: On a smaller board, I might *have* to play closer to the wall, because there is not as much space available. And that's bad.

An example:

Click Here To Show Diagram Code

[go]$$ 15x15
$$ +------------------------------
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . O . . . . . . . . .
$$ | . . O O . O . X . . . . . . .
$$ | . . X X X . . . . . . . . . .
$$ | . . . . . . X . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . X . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . X . . . . . . . .
$$ | . . X X X . . . . . . . . . .
$$ | . . O O . O . X . . . . . . .
$$ | . . . . . O . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ +------------------------------[/go]

The left side is pretty much secure black territory. An invasion would be pretty reckless. Here black simply has more territory than white.

Click Here To Show Diagram Code

[go]$$ 19x19
$$ +------------------------------
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . O . . . . . . . . .
$$ | . . O O . O . X . . . . . . .
$$ | . . X X X . . . . . . . . . .
$$ | . . . . . . X . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . X . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . X . . . . . . . .
$$ | . . X X X . . . . . . . . . .
$$ | . . O O . O . X . . . . . . .
$$ | . . . . . O . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ +------------------------------[/go]

That's a standard pattern in 19x19 after san-ren-sei. There are reduction and invasion possibilities. Considering white has sente, that position is even.

Click Here To Show Diagram Code

[go]$$ 27x27
$$ +------------------------------
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . O . . . . . . . . .
$$ | . . O O . O . X . . . . . . .
$$ | . . X X X . . . . . . . . . .
$$ | . . . . . . X . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . a . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . b . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . X . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . c . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . d . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . X . . . . . . . .
$$ | . . X X X . . . . . . . . . .
$$ | . . O O . O . X . . . . . . .
$$ | . . . . . O . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ +------------------------------[/go]

On this very large board, black doesn't really have that much. White has room for two groups around a-b and c-d, each of which has room enough to make a very comfortable base. Whereas white still has the same amout of points in the corners. In this position I would definitely prefer white.

It's just a thinking aid, similar to how we might put down imaginary stones near a group to aid in score estimation.


As for your examples, I can play this game too . Make the board bigger again, at some point we might find that a white invasion leaves black with a 3rd wall again ideally distanced from one of the two original walls. Bigger again and it's not ideally distanced and there's room for a 2nd white invasion. Bigger again and we get a 4th wall ideally distanced from one of the first 3 walls, and so on and so forth, with that ideal distance becoming a smaller area relative to total board size, resulting in a kind of attenuation in the oscillations and so the wall settles on a fairly constant value :p.

Also, one would have to question the positioning of that center stone on the larger board with respect to both walls (which I gather is the kind of thing Bill is thinking about). If we assume both walls need an extension, and that the walls project the same strength regardless of board size, then the ideal extension is the same regardless of board size, then on a large board simply putting a stone smack in the middle of two walls is being wishy washy and you shouldn't be basing your strategy around the happy coincidence of the star point being ideally distanced from possible walls created near two corners (because there is no longer such a happy coincidence) :p.

_________________
19/02/2011: this grumpy person takes a voluntary holiday from L19.

I don't think it works that way. The bigger the board, the less severe the attack on the invasion is going to be, so it's unlikely black will be able to build another wall on a bigger board. The bigger the board, the better the invasion move will be. On a 19x19 board, invading immediately and deeply is usually a mistake because you're going to be attacked severely. On the 27x27 board, an immediate deep invasion is certainly playable. Black will get less profit from the attack, because defending is easier. Above a certain board size, there will be no attack at all. When the side is that big, why play near the wall at all? There will never be a second, third and so on wall. White will just build a stable position at a safe distance, and the thickness will be wasted.

Of course, all my examples are assuming that the players will just play normal 19x19 sequences. Generally one can say that what's joseki on 19x19 is not necessarily joseki on other board sizes. In fact I think on a big board, black should block on the other side... Why? Because the side hoshi stone is too far away for the wall to be effective. That's similar to it being a mistake blocking on this side without having a stone on the side hoshi on 19x19, because the corner gets larger without a clear benefit. And that again leads us to the original point: The outside influence is not able to compensate the additional territory in the corner on a larger board (in that particular situation).



But the hoshi stone was there before the corner invasions.

This is just another example of influence being less useful on larger boards. Let's assume the hoshi stone was not there. On 19x19 you have one move that's an ideal extension from both walls. On a larger board, you don't have that play. That's another reason why the walls are less useful on the larger board

Of course, when I say "less useful", I mean in comparison with territory.
Let's look at a simple example: Let's say white invades at the 3-3 point under a 4-4 point stone, on an otherwise empty board. White gets about 10 points in territory. We don't know what the wall is worth exactly, but that's not so important, lets just call that A points. Later, black may want to make an ideal extension from the wall. Let's say that's about B points gain. A longer extension will be worth less.
Let's now assume black has a ni-ren-sei formation, and white invades both corners for 20 points, that's the same regardless of board size. Let's again assume later black wants to extend.

On a 19x19 board, one move is the ideal extension from both walls, so we can say it gains about twice as much, that is 2*B points, for a total profit of 2*A + 2*B points for black resulting from both wall plus the extensions.
On a larger board, let's just assume the walls themselves are rally worth A points. Now black has two possible choices: Play the middle, that's not optimal for both sides, for a total of 2*A + 2*(B-something). Or play the ideal extension from one wall, for 2*A + B + a little bit (because the ideal extension from the one wall may still affect the other wall a little bit ). That's less than on the 19x19 board, but white still got exactly the same about of territory.

So even if you assume the value of the walls is the same regardless of board size, the total usefulness compared to other plays on the board is still lower. Not because the walls are worth less, but because other plays (such as invasions) are worth more.

Because the 3-3 gives the person performing the 3-3 invasion less of the overall points being competed for on the board, whereas the outwardly facing influence has an effect on a larger part of the board. The law of diminishing returns applies, of course. But it is still the case that the advantage influence nets you in a running battle will be slightly larger because there is a larger portion of the board in which to take profit as you attack your opponent. The way in which influence is optimally taken on a larger board probably involves lighter and less concentrated play with an aim towards preventing invading groups from stabilizing and would probably be more difficult only because it would require much more extensive reading and counting. That doesn't mean it is an inherently suboptimal strategy, though.

Basically, I think where we differ is in the view that influence is worth the same amount on every board.