The AI revolution and the 3-3 opening point

Knotwilg · Post by **Knotwilg** » Thu Dec 19, 2019 6:20 am

The major paradox (apparent contradiction) in the AI revolution is that the bots like early 3-3 invasions but don't play 3-3 as an opening point. I have a theory about why that is so (and I'm curious to know yours and pro's) but first I wanted to understand how LZ thinks about the 3-3 opening point.

As a benchmark, on an empty board, assuming 7,5 komi, Black gets a 43% chance of winning.

To start, I fed it a parallel full 3-3 opening. Its policy then gives a clear priority to linking up high, which is as early a side move as we'll ever see one. Then it goes on to approach & enclose from 3-3 and break symmetry:

Click Here To Show Diagram Code: [go]$$B All 3-3 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . X . . | $$ | . . . , . . . . . , . . . 5 . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . 1 . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . 3 . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , 4 . . 2 . , . . . | $$ | . . O . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

LZ isn't very happy with this opening though, or it doesn't give its policy a clear starting point, because it briefly explores nearly every point on the 3rd or 4th line in the right half of the board for

Interestingly, she also explores the 4-4 shoulder hits and the low two space approach from the outside, but no other move on the left side. In particular, the symmetrical point for

, a high wedge, is not explored. When I feed it, it gets a comparable score to all other moves.

After 4k playouts, this position gets 42,9%

All other explored moves get 41 to 42,5 but with much fewer playouts.

As both players made the same "mistake", this position probably doesn't tell us much, so let's look at one where Black plays 4-4 and White 3-3.

Click Here To Show Diagram Code: [go]$$B 4-4 opposed to 3-3 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . 2 . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . a . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 1 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . O . . . . . . . . . . b . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

In this position, LZ gives Black 44,2% after 7,3k playouts for

. As a caveat, its symmetrical point A gets 43,9% after 2,6K playouts which urges even more care when interpreting any results of uneven playouts.

For such a clear preference to play 4-4 above 3-3, 1,2% is not a big increase to the benchmark.

B is a real alternative, getting 43,7% (4,9K playouts).

invades and we get a variation where Black develops a framework on the right side, while White makes large enclosures from his corners.

(see below)

Uberdude · Post by **Uberdude** » Thu Dec 19, 2019 6:27 am

I don't buy that there is a paradox in the observation "the bots like early 3-3 invasions but don't play 3-3 as an opening point", which generalised is:
player likes move B after move A, but doesn't like move B on its own as first move.

Here is another example which I don't think has us head scratching.

Humans have liked to approach a 4-4 at 6-4 for centuries:

Click Here To Show Diagram Code: [go]$$B $$ ------------------+ $$ . . . . . . . . . | $$ . . . . . . . . . | $$ . . . . . . . . . | $$ . . . . . 1 . . . | $$ . . . . . . . . . | $$ . . . . . . 2 . . | $$ . . . . . . . . . | $$ . . . . . . . . . |[/go]

But they tend not to like opening at 6-4 (except for a few wacky players):

Click Here To Show Diagram Code: [go]$$B $$ ------------------+ $$ . . . . . . . . . | $$ . . . . . . . . . | $$ . . . . . . . . . | $$ . . . . . , . . . | $$ . . . . . . . . . | $$ . . . . . . 1 . . | $$ . . . . . . . . . | $$ . . . . . . . . . |[/go]

P.S. iirc some versions of MiniGo did quite like to open at 3-3.

Knotwilg · Post by **Knotwilg** » Thu Dec 19, 2019 7:16 am

Uberdude wrote:I don't buy that there is a paradox

You may disagree that there is effectively a contradiction. I do too. That's why I called it an "apparent contradiction" or a paradox. I'll share my thoughts later why I don't think it's a contradiction.

dfan · Post by **dfan** » Thu Dec 19, 2019 7:25 am

I haven't analyzed it with bots, but one way this can happen is if 3-3 is a really important point to occupy given that there is an opponent stone on 4-4, but inefficient otherwise. (This hypothesis would be supported if the bots don't like to shoulder-hit an existing 3-3, although of course the situation with those two opposing stones is very different depending on who has the next move.)

Knotwilg · Post by **Knotwilg** » Thu Dec 19, 2019 8:43 am

I'll continue and try answering dfan's intermediate question: does LZ like shoulder hitting a 3-3, which should be particularly attractive when combined with a ni ren sei?

Click Here To Show Diagram Code: [go]$$B Shoulder hit $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . 5 . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . 4 . . . . . . . . . . . . . . . . . | $$ | . . . 1 3 . . 7 . , . . . . . X . . . | $$ | . . O 2 . . . . . . . . . . . . . . . | $$ | . . . . . 6 . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

After the well known 3-3 corner pattern up to

LZ gives Black 32,7% / 2K. Black has already lost 10%
Did Black make local mistakes? Or is the shoulder hit the root of the problem?

We'll take 2K playouts for every move and see:
- empty board: 43%
- before shoulder hit: 44,2%
-

shoulder hit: 42,6%
-

stretch: 42,4%
-

jump: 38,3% big mistake, should turn (44,9% - White's keima wasn't optimal either)
-

jump: 32,7% big mistake, should play away

So, let's not judge the shoulder hit by this pattern and look at the local best result for both according to LZ:

Click Here To Show Diagram Code: [go]$$B Shoulder hit $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . a . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . 5 . . 7 . . . . . . . . . . . | $$ | . . . 1 4 3 . . . , . . . . . X . . . | $$ | . . O 2 6 a . . . . . . . . . . 8 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

LZ slightly prefers

and then a typical sequence follows, with Black lightly playing away with

aiming to drop down at A next.
LZ has White tenuki and after

Black gets 42,8%/2K

This means the shoulder hit loses approximately 1,4% to enclosing one of Black's corners with a keima inside or outside. White recovers the loss she incured by playing two 3-3's.

%%%%%

What can we conclude? IMO, not much. Here's a half-speculation.

A 3-3 opening loses a bit but not much. Black's 4-4's can be used to build a framework, which is more likely to compete against White's corners than if White were to play other opening moves. Perhaps, on a global scale, White is too much committed to the corner territory and has lost some of its original flexibility to deal with whichever choice Black makes.

A 3-3 does not invite a 4-4 shoulder hit like the 4-4 invites a 3-3. White is happy to restore the original probabilities by taking the corner and Black's influence is perhaps too far from his 4-4s to make an effective framework.

Knotwilg · Post by **Knotwilg** » Thu Dec 19, 2019 9:31 am

As a third construct, what happens if we play 3-3 stones against non-opposing parallel 3-4 stones?

Click Here To Show Diagram Code: [go]$$B 3-3 vs 3-4 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . 1 . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 3 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . a 2 . . . | $$ | . . . . . . . . . , . . . 4 . . . . . | $$ | . . O . . . . . . . . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

When White has taken tight control of the corners, we observe a couple of slightly unusual choices on the right:
-

encloses high but small, while usually the preference is high and large
-

approaches high, while usually the preference is to approach low
-

pincers, while usually the preference is to attach underneath and keep the corner

After

Black A leads to a fight.

%%%%%

And how about the orthodox fuseki?

Click Here To Show Diagram Code: [go]$$W 3-3 vs orthodox $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . X . . . . | $$ | . . . , . . . . . , . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . , . . . . . X . . . | $$ | . . O . . . . . . . . . . a . . b . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

In this position, LZ likes both A and B equally well for White, giving Black 44,5% (A:2,6K, B:3,8K)

Click Here To Show Diagram Code: [go]$$W 3-3 vs orthodox $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . X . . . . | $$ | . . . , . . . . . , . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 2 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . , . . . . 9 X . . . | $$ | . . O . . . . . . . . . . 1 6 3 4 . . | $$ | . . . . . . . . . . . . . 0 8 7 5 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

We get this variation: Black takes a stance on the lower side, White takes the corner.

Click Here To Show Diagram Code: [go]$$W 3-3 vs orthodox $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . X . . . . | $$ | . . . , . . . . . , . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 2 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 1 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . , . . . . 6 X 4 . . | $$ | . . O . . . . . . . . . . . . 5 3 . . | $$ | . . . . . . . . . . . . . 7 . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

If White approaches inside, Black gets 46,8% / 2,5K

%%%%%

The 3-4 variation again seems to suggest that Black can build a framework, while White's 3-3's are not efficient enough in dealing with it, i.e. the choice for territory has already been made and now expanding from it is not as efficient as from a 3-4 or 4-4.

Bill Spight · Post by **Bill Spight** » Thu Dec 19, 2019 9:34 am

dfan wrote:I haven't analyzed it with bots, but one way this can happen is if 3-3 is a really important point to occupy given that there is an opponent stone on 4-4, but inefficient otherwise. (This hypothesis would be supported if the bots don't like to shoulder-hit an existing 3-3, although of course the situation with those two opposing stones is very different depending on who has the next move.)

Elf, and I believe other top bots, like the 3-3 invasion against the 5-3 and 5-4, as well.

Bill Spight · Post by **Bill Spight** » Thu Dec 19, 2019 10:04 am

Knotwilg wrote:I'll continue and try answering dfan's intermediate question: does LZ like shoulder hitting a 3-3, which should be particularly attractive when combined with a ni ren sei?

{snip}

This means the shoulder hit loses approximately 1,4% to enclosing one of Black's corners with a keima inside or outside. White recovers the loss she incured by playing two 3-3's.

What winrate do you get for White's top response to a) the outside keima, b) the inside keima, and c) the shoulder hit? Thanks.

Knotwilg · Post by **Knotwilg** » Thu Dec 19, 2019 10:39 am

Bill Spight wrote:
Knotwilg wrote:I'll continue and try answering dfan's intermediate question: does LZ like shoulder hitting a 3-3, which should be particularly attractive when combined with a ni ren sei?

{snip}

This means the shoulder hit loses approximately 1,4% to enclosing one of Black's corners with a keima inside or outside. White recovers the loss she incured by playing two 3-3's.
What winrate do you get for White's top response to a) the outside keima, b) the inside keima, and c) the shoulder hit? Thanks.

For outside and inside keima, White's top choice and 2nd choice are the same: approach other corner, 3-3 other corner
The percentages are slightly different for similar playouts: 56,4 and 56,2 for outside keima, 56,1 and 55,9 for inside keima

For the shoulder hit White's top choice is the stretch towards the friendly stone and the second choice the stretch towards the enemy stone. The difference lies in the playouts though, as both get 57,3%

LeelaZero 15-block network (trained by bubblesId/bjiyxo)

Bill Spight · Post by **Bill Spight** » Thu Dec 19, 2019 10:53 am

Knotwilg wrote:
Bill Spight wrote:
Knotwilg wrote:I'll continue and try answering dfan's intermediate question: does LZ like shoulder hitting a 3-3, which should be particularly attractive when combined with a ni ren sei?

{snip}

This means the shoulder hit loses approximately 1,4% to enclosing one of Black's corners with a keima inside or outside. White recovers the loss she incured by playing two 3-3's.
What winrate do you get for White's top response to a) the outside keima, b) the inside keima, and c) the shoulder hit? Thanks.
For outside and inside keima, White's top choice and 2nd choice are the same: approach other corner, 3-3 other corner
The percentages are slightly different for similar playouts: 56,4 and 56,2 for outside keima, 56,1 and 55,9 for inside keima

For the shoulder hit White's top choice is the stretch towards the friendly stone and the second choice the stretch towards the enemy stone. The difference lies in the playouts though, as both get 57,3%

LeelaZero 15-block network (trained by bubblesId/bjiyxo)

So by this comparison Black prefers the outside keima by a small amount, and the winrate difference between the shoulder hit and the outside keima is 0.9% or 1.1%, depending on the number of playouts.

Knotwilg · Post by **Knotwilg** » Thu Dec 19, 2019 3:16 pm

Bill Spight wrote:
So by this comparison Black prefers the outside keima by a small amount, and the winrate difference between the shoulder hit and the outside keima is 0.9% or 1.1%, depending on the number of playouts.

No. I'll explain better. From a starting position with 2 white 3-3 and 3 black 4-4, the following are

Black keima enclosure towards white (outside keima)
- White approaches other corner; White 56,4 Black 43,6
- White 3-3 invades other corner; Whte 56,2 Black 43,8
Black keima enclosure towards black (inside keima)
- White approaches other corner; White 56,1 Black 43,9
- White 3-3 invades other corner; White 55,9 Black 44,1
Black 4-4 shoulder hit
- White stretch towards white corner; White 57,3 Black 42,7
- White stretch towards black corner; White 57,3 Black 42,7

Black minimaxes and chooses the inside keima, upon which White approaches the other corner. White 56,1 Black 43,9

Bill Spight · Post by **Bill Spight** » Thu Dec 19, 2019 3:32 pm

Knotwilg wrote:
Bill Spight wrote:
So by this comparison Black prefers the outside keima by a small amount, and the winrate difference between the shoulder hit and the outside keima is 0.9% or 1.1%, depending on the number of playouts.
No. I'll explain better. From a starting position with 2 white 3-3 and 3 black 4-4, the following are

Black keima enclosure towards white (outside keima)
- White approaches other corner; White 56,4 Black 43,6
- White 3-3 invades other corner; Whte 56,2 Black 43,8
Black keima enclosure towards black (inside keima)
- White approaches other corner; White 56,1 Black 43,9
- White 3-3 invades other corner; White 55,9 Black 44,1
Black 4-4 shoulder hit
- White stretch towards white corner; White 57,3 Black 42,7
- White stretch towards black corner; White 57,3 Black 42,7

Black minimaxes and chooses the inside keima, upon which White approaches the other corner. White 56,1 Black 43,9

Thanks.

So by this comparison Black prefers the inside keima to guarantee an estimated winrate of 43.9%, which is 1.2% better than Black's estimated winrate after the shoulder hit. Right?

Knotwilg · Post by **Knotwilg** » Thu Dec 19, 2019 4:45 pm

Bill Spight wrote:
Knotwilg wrote:
Bill Spight wrote:
So by this comparison Black prefers the outside keima by a small amount, and the winrate difference between the shoulder hit and the outside keima is 0.9% or 1.1%, depending on the number of playouts.
No. I'll explain better. From a starting position with 2 white 3-3 and 3 black 4-4, the following are

Black keima enclosure towards white (outside keima)
- White approaches other corner; White 56,4 Black 43,6
- White 3-3 invades other corner; Whte 56,2 Black 43,8
Black keima enclosure towards black (inside keima)
- White approaches other corner; White 56,1 Black 43,9
- White 3-3 invades other corner; White 55,9 Black 44,1
Black 4-4 shoulder hit
- White stretch towards white corner; White 57,3 Black 42,7
- White stretch towards black corner; White 57,3 Black 42,7

Black minimaxes and chooses the inside keima, upon which White approaches the other corner. White 56,1 Black 43,9
Thanks. So by this comparison Black prefers the inside keima to guarantee an estimated winrate of 43.9%, which is 1.2% better than Black's estimated winrate after the shoulder hit. Right?

Right

sorin · Post by **sorin** » Thu Dec 19, 2019 11:49 pm

Knotwilg wrote:The major paradox (apparent contradiction) in the AI revolution is that the bots like early 3-3 invasions but don't play 3-3 as an opening point.

I don't think there is a paradox: AI plays 3-3 to make a 4-4 stone inefficient, not because the 3-3 point has any special value by itself.

Also: AI actually plays 3-3, see AlphaGo's match with Ke Jie.

Knotwilg · Post by **Knotwilg** » Fri Dec 20, 2019 1:29 am

sorin wrote:
Knotwilg wrote:The major paradox (apparent contradiction) in the AI revolution is that the bots like early 3-3 invasions but don't play 3-3 as an opening point.
I don't think there is a paradox: AI plays 3-3 to make a 4-4 stone inefficient, not because the 3-3 point has any special value by itself.

Also: AI actually plays 3-3, see AlphaGo's match with Ke Jie.

Indeed. It's interesting to see that 3-3 is a way to make 4-4 inefficient, but 3-3 itself is not made inefficient by a local reply, rather it already has some global inefficiency.

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Re: The AI revolution and the 3-3 opening point

Re: The AI revolution and the 3-3 opening point

Re: The AI revolution and the 3-3 opening point

Re: The AI revolution and the 3-3 opening point

Re: The AI revolution and the 3-3 opening point

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Re: The AI revolution and the 3-3 opening point

Re: The AI revolution and the 3-3 opening point

Re: The AI revolution and the 3-3 opening point

Re: The AI revolution and the 3-3 opening point