In the US, people are starving, if not actually starving to death. Which is why we are seeing long lines at food banks. At least temporarily we are living under Depression conditions, because a lot of people are not working or are producing less than normal. As we are able to reopen economic activity, people have to have money so they can buy goods and services, pay rent, pay debts, pay taxes, avoid bankruptcy and foreclosure, and so on. I think that the US is doing pretty well in that regard.

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

Visualize whirled peas.

Everything with love. Stay safe.

Back to go stuff.

Recently moha has, IIUC, raised the question of board parity under Button Go. Most of my readers will know that I am an advocate of button go as a hybrid of area and territory scoring. Button go has already been used in international competition, not by using a physical button, but by having special pass rules. For simplicity, let's assume that there is a button, worth ½ pt. under area scoring, that a player may take instead of playing a stone on the board. The normal effect of the button is to make who gets the last dame irrelevant. OC, kos can complicate things.

It turns out that there is no interaction between the button and board parity, except perhaps under unusual circumstances involving ko. For instance, suppose that the territory score on the board is 7 for Black. With odd parity, White will get the last dame and so Black will take the button, for a button score of 7½. With even parity, Black will get the last dame and White will take the button, for a button score of 7 + 1 - ½ = 7½. Now let's suppose that the territory score is an even number, like 6. With odd parity Black will get the last dame and White will take the button, for a button score of 6 + 1 - ½ = 6½. With even parity White will get the last dame and Black will take the button, for a button score of 6½. All same same.

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

Visualize whirled peas.

Everything with love. Stay safe.

Like Cheating on an Exam

Recently I watched this talk by Yasser Seirawan on an endgame ( https://www.youtube.com/watch?v=YI5CQL_ ... 3&frags=wn ). At about 5 min. in he asks his audience how many people spend 10% of their time devoted to chess, both play and study, studying endgames? 25%? 50%? We don't see the audience, but Seirawan notes that a lot of them spend 25% of their time studying endgames. (OC, this was an endgame lecture, so that's probably high for the chess playing population as a whole.) He goes on to relate something that Michael J. Franett, Washington State Champion in the early 1970s, told him early in his career. "Yasser," he said, "studying endgames is like cheating on an exam. because you know you're going to be asked the questions down the road."

OC, the endgame at go is not as consequential as the endgame at chess, but there are many predictable situations in go, such as standard corner life and death positions, common endgames, and ladders. I have stated that I think that dan players should be able to play the late endgame almost perfectly. Not that unfamiliar positions don't arise, but they are usually easy to analyze in a matter of seconds. Even 5 kyus are A+ at filling dame, where the shortage of liberties can potentially lead to big swings. Playing the last 30 moves correctly is not too difficult, if you have put in a little study. But who does?

Recently I was surprised to find that one of my endgame problems has an 8 dan rating on goproblems.com. Here it is.

Click Here To Show Diagram Code

[go]$$Wc White to play and win. No komi.
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O . . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O . X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . . X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]

Now, reading the solution out may take a little time, but an SDK who has studied chilled go infinitesimals should see the first few plays almost instantaneously. This really should not be an 8 dan problem. Mathematical Go came out in 1994, and the SL material on go infinitesimals has been available for many years.

As for smaller plays, the prototypes for them are corridors. True, complicated positoins can arise, but usually they are easy to calculate. For instance,

Click Here To Show Diagram Code

[go]$$Wc Corridors
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O W O . . . X , . |
$$ | . . O . O X X B X . . |
$$ | . . O . X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . . X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]

I have add a Black stone and a White stone to the position, so that the plays in the center each gain less than 1 pt. of territory. Everybody knows that the 2 space White corridor is worth -½ pt. from Black's point of view. The 3 space Black corridor is worth 1¼ pt. for Black. To see that, Black to play closes the corridor for 2 pts. and White to play advances into the corridor for a position worth ½ pt. Both of these plays are gote, so we take their average to get the territorial value of 1¼. The White shape in the center is not a corridor, but it is not hard to calculate its value.

Hint:


----

Speaking of corridors, there is a kind of diagram that appears in nearly every endgame book, of corridors of increasing length, side by side. Like so.



As everybody learns, the correct play is in the longest corridor. And we learn that the territorial value of each corridor is the length of the corridor minus 2 plus a fraction. The value of a length 2 corridor is ½, the value of a length 3 corridor is 1¼, the value of a length 4 corridor is 2⅛, etc. What the textbooks don't teach, not the ones I have seen, anyway, is that after White enters the longest corridor, the result is a kind of miai. That is, the corridors taken together have a territorial score which is the same, no matter who plays first in the combination. This SGF file illustrates that fact. This fact has been discovered independently, it seems, by Antti Tormanen, David Wolfe, myself, and, I am sure, many others. I discovered that fact by considering the miai of the two longest corridors, which, when played, yield another miai in the two longest corridors, and so on. From David's Theorem 8 in Mathematical Go, I suspect that David figured it out by noting that the fractions all add up to 1. David went even further and noticed that if the fractions add up to more than 1, then there will be some number of corridors whose fractions add up to exactly 1, and form this kind of miai. Well done, sir!

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

Visualize whirled peas.

Everything with love. Stay safe.

Corner L&D, endgame

There is a myth that in the endgame life and death are settled, that the endgame is just about points. Not so. In fact, there are frequently unsettled positions, especially in the corner, especially involving ko, that are the right size to play in the early and middle endgame. And life and death battles can occur, particularly with mutual damage positions.

Here is a simple endgame corner position. Per convention, the outside White stones are alive. Territory scoring, counting territory in seki.

Click Here To Show Diagram Code

[go]$$Bc Endgame corner
$$ -------------
$$ | . . . X O . .
$$ | O X X X O . .
$$ | . . X O O . .
$$ | X . X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]

Easy questions.

1) What is the usual territorial value of the corner?

2) How much does a gote or reverse sente gain?

Maybe not so easy questions. Usually, Black cannot afford to fight a ko in such corners because she has too much at stake. However, assume that Black is komaster, and can win a ko in this corner. (Assume that the komaster has just enough large enough ko threats to win the ko without ignoring the opponent's threat.)

3) When Black is komaster, what is the territorial value of the corner?

4) How much does each play in the ko gain, on average?

5) How much does Black gain by winning the ko versus the territorial value of the corner?

6) How should White play this corner?

Enjoy!

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

Visualize whirled peas.

Everything with love. Stay safe.

Attempt:

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

Visualize whirled peas.

Everything with love. Stay safe.

OK I failed.



Let me try something else.

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

Visualize whirled peas.

Everything with love. Stay safe.

Well done!

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

Visualize whirled peas.

Everything with love. Stay safe.

I am not very familiar with the terminology and endgame value calculations, so I will probably get some answers wrong but let me try anyway. I'll start with the easy questions.

If Black plays first, then Black can make two eyes and live with 7 points.

Click Here To Show Diagram Code

[go]$$Bc Black plays first. Score=7.
$$ -------------
$$ | . 1 . X O . .
$$ | O X X X O . .
$$ | . . X O O . .
$$ | X . X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]

If White plays first and Black doesn't play the ko, then White gets a seki. White has 1 point and Black has 0 point.

Click Here To Show Diagram Code

[go]$$Wc White plays first. Score=-1.
$$ -------------
$$ | . 3 . X O . .
$$ | O X X X O . .
$$ | 1 . X O O . .
$$ | X 2 X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]

So the usual territorial value of the corner is the average (7-1)/2 = 3 points.

in the first diagram, or in the second diagram, gain 4 points.

I find that I'm becoming a fan of Yasser Seirawan's lectures. Here is a nice one on learning from your mistakes. https://www.youtube.com/watch?v=rgUQBYO ... gs=pl%2Cwn

He also talks about how copycat chess is bad. Mirror go is not obviously bad, and we know that in some cases it is obviously correct. Such cases are specific instances of miai, which is a powerful concept in go.

BTW, miai does not seem to be a concept that Elf learned. It does make miai plays, but not always. This is something that I have believed for a while, first through observation and second through reflecting on the nature of neural networks. It seems to me that the concept of miai is at a level of abstraction that is beyond the capability of today's bots. It a bot may be said to have that concept at all, I think that it would be in the ability, in certain cases of miai, when one of the miai points is taken, the other one is the top choice in reply.

One place that this occurs is at the dame stage of a review when the human players are filling in the dame, but not playing in either of a miai pair of ⅓ pt. kos. In area scoring, which is what Elf and nearly all other top bots are trained on, there is a danger to filling one of a miai pair of ⅓ pt. kos. If the opponent is able to delay filling the other ko until all the dame have been filled, i.e., to be the komonster of that ko, she may be able to gain from that delay. The safe thing to do is to leave the miai on the board until all the dame have been filled. In effect, the miai pair has a temperature of zero at area scoring.

In one example in a game between Chinese pros, with about 20 dame moves left, Elf recommended taking one of the miai pair of kos instead of making a protective play. Taking the ko got 8918 rollouts, while the human protective play got only 594 rollouts. The human, OC, saw that the protective play would eventually be necessary and so played it instead of waiting for the opponent's atari. Elf does not apparently have the concept of sente at the same level of abstraction as humans do, either. OC, taking the other ko was Elf's top choice in the mainline variation, but it got only 8436 rollouts. Not really a surprise, but a human would have expected taking the other ko to be a sure thing, even if the opponent were an SDK, because SDKs have learned the concept of miai. Elf does not regard this miai as a sure thing, only as a 95% thing. The kicker is this. Despite the protective play being correct Elf gives it a loss of 6% by comparison with taking the first ko, given its choice to fill the first ko after the protective play.

For years I have been asking about the margin of error of bot winrate estimates. One answer is here in the endgame, where humans can work out correct play. In this case a correct play got an estimated winrate loss of 6% to par. OC, that does not mean that a play that gets an estimated loss of 6% is not an error, but it may well not be. Margin of error.

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

Visualize whirled peas.

Everything with love. Stay safe.

Click Here To Show Diagram Code

[go]$$Bc Only one ko threat
$$ -------------
$$ | . . . X O . .
$$ | O X X X O . .
$$ | 1 . X O O . .
$$ | X . X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]

The second diagram is slightly preferable, because White has only one possible ko threat instead of two.

So far, so good.

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

Visualize whirled peas.

Everything with love. Stay safe.

Let's continue slowly, since I am confused. If Black is komaster, and if White plays first, a sequence like this can be expected

Click Here To Show Diagram Code

[go]$$Wc ko threat, answers, takes ko
$$ -------------
$$ | a . . X O . .
$$ | O X X X O . .
$$ | 1 2 X O O . .
$$ | X 3 X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]

The corner can be left like this, but eventually Black will need to settle the ko by playing at a. Black has 5 points of territory and 3 captures but White has captured a stone, so Black got 7 points.

If Black plays first, then Black doesn't need to play anything in the corner right now, but because of the preceding sequence, Black will eventually need to add a move.

So I think that the territorial value of the corner is 7 points.

Evaluating kos is tricky, because kos involve the rest of the board. I call everything relevant to the ko fight the ko ensemble. Well, Professor Berlekamp developed a strong theory that makes simplifying assumptions, so that you don't have to know much about the ko ensemble; you can focus on the ko itself. It's the komaster theory.

The first assumption is that the komaster can capture the ko without ignoring any of the opponent's threats. So in this case, White has no effective ko threat to make and plays elsewhere. The second assumption is that at this point the komaster has to go on and settle the ko as soon as possible. IOW, Black cannot afford to leave the corner like that. So wins the ko.

I was working on my own ko theory when I heard Berlekamp speak on the komaster theory in 1994. It solved problems that I had found intractable.



Right. But note that after an even number of plays, White gets a play elsewhere in exchange for losing the ko. This ko exchange is important for evaluating the ko. The exchange is not peculiar to kos. Other plays have exchanges as well. We just don't usually talk about them.

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

Visualize whirled peas.

Everything with love. Stay safe.

I am still confused. To simplify things, I assume that the board only contains

1) the corner position
2) sufficiently many ko threats for Black
3) gote moves of values E₁, E₂, E₃... The sequence is ordered from the largest to the smallest.

For instance

Click Here To Show Diagram Code

[go]$$B Playing at a is a move of value 2
$$ -----------------
$$ . . X O O a O . .
$$ . . X X X X O . .
$$ . . . . . . . . .[/go]

Suppose first that it's White to play, and that White plays in the corner. Then Black has to choose between the seki variation and the ko variation.

If Black chooses the seki variation, then Black gets -1 point in the corner and after the sequence it's Black to play, so Black will play the move of value E₁, etc. so the final score will be -1+2(E₁-E₂+E₃-E₄+...)

If Black chooses the ko variation, then plays the move of value E₁, settles the ko, plays the move of value E₂, etc. so the final score is 7+2(-E₁-E₂+E₃-E₄+...)

The difference between the second and the first is 8-4E₁, so

If E₁<2 then Black chooses the ko variation
If E₁>2 then Black chooses the seki variation
If E₁=2 then Black chooses either one.

These considerations don't help me much.

This is how I built my theory of ko.



1) If Black chooses the seki variation, and if the value of E1 is less than or equal to 4, then White moves to -1 in the corner, and Black plays in the Es. The result will be

-1 + E1 - E2 + ....

plus some constant.



2) If Black chooses the ko variation and E1 is less than the value of a move in the ko, then after White takes the ko, Black plays a threat, and White answers it, and then Black takes the ko back, White plays in E1, Black wins the ko, and then play continues in the Es.

The result is 7 - E1 - E2 + E3 - ....
plus the same constant.

The difference in the results is 8 - 2*E1. But we know that E1 <= 4, so Black should make the ko.

3) But what if E1 > 4? Then if Black chooses the seki option, White does not make a seki but plays in E1.

Now, we do not know the size of the rest of the Es, so we do not know whether the corner will become seki or not. We can estimate the result, however as

3 - E1 + E2/2
plus the same constant.

If we change the result of making the ko to a similar estimate, we get

7 - E1 - E2/2

The difference is 4 - E2.

But if E2 < 4, we do know that if Black does not make ko, White will play in E1 and then Black will make life. So E2 >=4, and Black should choose the seki option.

Berlekamp's theory ignores the differences between the Es and comes to the same conclusion more easily.

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

Visualize whirled peas.

Everything with love. Stay safe.

An Alternating Sum should be abbreviated:

∆E₁ := E₁-E₂+E₃-E₄+...

-∆E₁ := -E₁+E₂-E₃+E₄-...

An elementary question: why do your formulas differ from mine by a factor 2?

For me, E₁=2 corresponds to a move like this

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ . . X O O a O . .
$$ . . X X X X O . .
$$ . . . . . . . . .[/go]

If Black plays there, Black gets 2 points of territory + 2 prisoners = 4 = 2E₁ points, that's why I wrote a factor 2 but you didn't??

You always start, as one of my philosophy profs pointed out to a chorus of boos, from where you are. Before either player plays from this position, what is its territorial value? After either player plays here, how much has she gained (on average)? That's the question. Gains are what add and subtract correctly.

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

Visualize whirled peas.

Everything with love. Stay safe.