Think and Grow Old

Bill Spight · Post by **Bill Spight** » Thu Jul 26, 2018 11:25 pm

jlt · Post by **jlt** » Fri Jul 27, 2018 1:18 am

@Ed, Bill, Tryss:

Bill Spight · Post by **Bill Spight** » Fri Jul 27, 2018 1:40 am

EdLee · Post by **EdLee** » Fri Jul 27, 2018 1:58 am

Hi jlt,

Tryss · Post by **Tryss** » Fri Jul 27, 2018 2:31 am

EdLee wrote:Hi jlt,
The value of a position is the expected value of (( pts ) - ( pts )).
Thanks. This magic (very human) definition is what I didn't know and was looking for.
Who came up with this definition ?
( Who picked (B-W) and not (W-B), etc. ? )

EdLee · Post by **EdLee** » Fri Jul 27, 2018 4:30 am

Hi Tryss,

Bill Spight · Post by **Bill Spight** » Fri Jul 27, 2018 8:27 am

EdLee wrote:Hi Tryss,
You can also decide to chose W-B, that doesn't really change anything (but you need to stay consistant).
Thanks. Yes, that part is clear, no problem.

My problem was I knew almost nothing about formal end game theory, and when the question "what's the value of this position?" came up, everyone else who was familiar with the basics of end game theory knew the established magic convention (B-W), whereas I had no clue what the term meant. jlt was very helpful to provide the definition and other fundamentals.

You may have noticed that I did not assume that White's territory was negative in these notes. I did assume that the stones surrounding the corridor are alive.

Bill Spight · Post by **Bill Spight** » Fri Jul 27, 2018 8:29 am

@ Tami

This discussion has grown quite a bit. I didn't mean to hijack your thread. If you'd like, we can move this discussion elsewhere.

Tami · Post by **Tami** » Fri Jul 27, 2018 1:56 pm

Bill Spight wrote:@ Tami

This discussion has grown quite a bit. I didn't mean to hijack your thread. If you'd like, we can move this discussion elsewhere.

I don't mind. It was my own fault for asking the question

I'm just trying to make sense of your reply, mathematics not being my thing. Thank you very much for taking the time. It might take me some time to understand fully.

Bill Spight · Post by **Bill Spight** » Fri Jul 27, 2018 2:31 pm

Tami wrote:
Bill Spight wrote:@ Tami

This discussion has grown quite a bit. I didn't mean to hijack your thread. If you'd like, we can move this discussion elsewhere.
I don't mind. It was my own fault for asking the question I'm just trying to make sense of your reply, mathematics not being my thing. Thank you very much for taking the time. It might take me some time to understand fully.

Thanks.

The math is easy: count, add, subtract, divide by 2.

The first example is about gote. Next comes sente, and that's it.

jlt · Post by **jlt** » Fri Jul 27, 2018 10:07 pm

@Bill,

Bill Spight · Post by **Bill Spight** » Sat Jul 28, 2018 2:05 am

I'm off to bed soon, but let me just make a quick clarification or two.

First, the evaluation of go positions and plays does not produce a general theory of the endgame. Far from it. But it is a good place to start your analysis.

Doing so gives you information that will usually tell you where to play. But not always.

Second, you can use probabilities to understand this kind of evaluation. The go books do not teach that, and it is not necessary, but it is one way of looking at it. You can think of the value of a position as a kind of expected value. But you can also think of finding the average value of a position as a form of defuzzification. Historically, however, go players figured out how to evaluate positions and plays without reference to either probability or fuzzy logic.

Third, you can view the evaluation of go positions in minimax terms. I redefined go evaluation in such terms 20 years ago in my paper on the evaluation of multiple kos, which I presented at a computers and games conference in Japan. But that definition depends upon concepts that you do not need for these evaluations. That definition is algebraic. As I mentioned to Tami, all we need here is arithmetic.

In any event, we do not need to know perfect play in any sense to evaluate positions. We can use every possible line of play in a position, alternating or not. For instance, instead of playing first at the mouth of a corridor, we could start at the other end. We would then eliminate such lines of play from consideration. It makes our job easier if we know that they are wrong in the first place, but it is not necessary. We can use evaluation to find lines of play that are in some sense, correct. We do not have to assume perfect play.

Elom · Post by **Elom** » Sat Jul 28, 2018 3:03 am

EdLee wrote:...Seems the 0.5 probability is a huge assumption ? (I'm OK with it being a magic number, just to simplify this example; I'm OK if the exact probability is not very relevant at this stage of learning... )...

Maybe probabilities are assumptions by definition. With no evidence to favour the likelihood of either side having turn, no assumption tops equal distribution of chance.

Extra explanation for go beginners:

The isolated board configuration of the endgame in analysis consists of multiple variables. 18 of them are board-state variables with three possible permutations: black, white or blank. However, there is one more variable, which may be thought of as 'time', having only the two permutations, black's turn or white's turn.

Strictly speaking, endgame study might be about deriving the score of a position when the variable for time is not known. Making copies of position is common, with probabilities a shorthand, I guess.

If we know black plays first and colours alternate, corridor a is nine points for black, zero points for white. If players don't alternate, and we've no way to know who plays after black, it's still nine points (so this position is 'solved'?). If we know white plays first and colours alternate, corridor a is six points for black, zero points for white (white connects, black blocks). If players don't alternate and we've no way to know who plays after white, more calculation is necessary until the score of the position doesn't change depending upon who's turn it is (making some assumptions here).

We could know the time variable's state, and not know a board variable's state. Here:

Click Here To Show Diagram Code: [go]$$ $$ |--------------- $$ | A X . X O . . $$ | X X X X O . . $$ | O O O O O . . $$ | . . . . . . .[/go]

Let us say we know it is white to play and the colours alternate, so we'll know what state the time variable's in every configuration from here on. A Schrödinger's cat situation in which we don't know if the corner consists of a black stone or a blank space occurs. There's a 50% probability of a score of two points for black, zero points for white, and an equal chance of zero points for black, and 15 points for white. So the score of the position is one point for black, seven-and-a-half points for white.

jlt · Post by **jlt** » Sat Jul 28, 2018 4:11 am

@Bill:

I am still under the impression that using minimax is equivalent to assuming perfect play, but let's not worry too much about that minor point. I am more interested in what you have in mind about sente; so far we only had gote examples.

EdLee · Post by **EdLee** » Sat Jul 28, 2018 10:26 pm

Hi Bill,

Life In 19x19

Think and Grow Old

Re:

Re: Think and Grow Old

Re: Think and Grow Old

Re:

Re:

Re: Think and Grow Old

Re: Think and Grow Old

Re: Think and Grow Old

Re: Think and Grow Old

Re: Think and Grow Old

Re: Think and Grow Old

Re: Think and Grow Old