DISREGARDING KOMI

Bill has convinced me that currently we cannot be sure that komi equals the first move's value. Therefore let me forget about komi here but speak about other aspects of values of early moves on the 19x19.

CONCEPTS

Since the board is almost empty, there is only little positional context information. This makes it already hard to understand which kinds of values are being studied. Nevertheless, it is some or all of such values that need to be understood when trying to assess early move values. The following terms or concepts to one's mind:

1) the value of gote and the value of sente
2) miai value and deiri value
3) local per move value
4) local temperature, ambient temperature, global temperature
5) the local loss when playing elsewhere
6) the gain elsewhere when playing elsewhere there

What do these concepts mean?

GOTE AND SENTE

The value of gote assumes that a player starts and ends a local sequence and makes 1 local play more than the opponent while otherwise the opponent could start and end a local sequence and make 1 local play more than the player. In the simplest case, which is useful for early moves of the game, either sequence consists of exactly one play, which might be occupying an empty corner, making an approach move to a previously existing first corne stone or forming a corner enclosure to a previously existing first corne stone.

The value of sente assumes that a player starts and the opponent ends a local sequence and the player makes 0 local plays more than the opponent while otherwise the opponent could start and end a local sequence and make 1 local play more than the player. In the simplest case, which is useful for early moves of the game, the sente sequence consists of exactly two plays while the gote sequence consists of exactly one play.

The difference of plays is 2 in a gote situation but 1 in a sente situation. A sente achieves something with only half the number of excess moves. Therefore usually it is considered to be worth twice as much as a gote. Now this tells us something about relative values of gote versus sente. Does it tell us anything about absolute values of an early play or of early plays in the game? Bill claims that yes when relating sente to temperature (I have deleted his references to komi):



However, this also does not provide an absolute value for an early sente play yet because sente is defined to depend on temperature and we do not know the (local?) temperature yet.

There is actually another major problem with sente and gote: We do not easily know whether an early move in the game is sente or gote. It could also be ambiguous - neither clearly sente nor gote. Players can choose to answer a first stone in a corner or to answer an approach play. A player does not need to answer either locally though because afterwards josekis can develop. Not continuing a shimari locally is even more likely so when a player forms a shimari, then quite likely that is gote. My claim therefore is: Each (ordinary) early move in a corner is gote.

If indeed each early move in a corner is gote, then we know (or assume) that it is worth half as much as a sente play somewhere else. Again this tells us only something relative - nothing absolute yet.

MIAI VALUE AND DEIRI VALUE

For a gote to be worth only half as much as a sente, we need to be careful about which values we are speaking of. The miai value is the value per excess play. The deiri value is the difference of comparing the positional value after a sequence with Black playing first with the positional value after a sequence with White playing first. Miai value does the same but then divides by the sum of the numbers of played excess stones. If we assume that early plays in the game are gote, then the sum of the numbers of excess stones is 1 + 1 = 2. So if we get a deiri value D, then we calculate the miai value as M = D/2. Since we are interested in values of early moves, we should be interested in the per move value, which is the miai value. Let us forget about deiri values and use per move values aka miai values only.

Now we have yet more relative value information but still nothing absolute yet. The relative sizes we want are per move values of gote moves.

LOCAL PER MOVE VALUE

So "per move value" is a different phrase for "miai value". There is an additional aspect though: A play can have a local effect or a global effect. Rather a play has both effects but, when there are both players' stones on the board, there is a tendency that the effect (or influence) decreases with increasing distance up to immaterial, small values. So, in a simplifying approximation, the local value is the global value while ignoring the global (far distant) impact. It is like in a game where the players conquer the corners and transform the opening via a boring middle game into an endgame without ever giving the center any significant value; the center remains about neutral. With this assumption, the global value of an early move in a corner is about (just slightly greater than) the local value. So, in such a first approximation, we can assume an early move in the game to be played in a corner and to have an only local value. A value relevant within only one quarter of the board while the other three quarters behave like a neutral area with respect to the local play.

LOCAL, GLOBAL, AMBIENT TEMPERATURE

Temperature is a concept expressing value per move. So it is sort of yet another name for the same thing: the per move value or, using the other name, the miai value. Temperature is overloaded with formal meaning in game theory though. To avoid confusion here and avoid pretending usage of more meaning than we apply, we can stick to the name "per move value". Temperature is interesting for another reason though: there are three different kinds, the local, the global and the ambient temperature. The local temperature is the per move value only within a local region. The global temperature is the per move value of the best next move in the whole board position. The ambient temperature is the per move value of the best next move in that rest of the board that excludes a currently considered local region. So if we consider a particular, say the upper left, corner / quarter of the board, then that is our local region for the local move value. The remaining three quarters of the board are for the ambient temperature. The entire board is for the global temperature, which is, I think, the maximum of the local and the ambient temperatures.

Since, in our simplification, we are assuming local influence only, by symmetry all the four corners have the same value. Hence we can make the assumed simplification implication for the early moves in the game that

local temperature = ambient temperature = global temperature.

LOCAL LOSS WHEN PLAYING ELSEWHERE

How great is the local loss when playing elsewhere from our local corner? Expressed as an absolute, positive value, surely this must equal the local per move value because one does not get what otherwise one could get by means of making a local move: its value.

Note that I still speak of a miai value of a gote here. Of course, if the player does not make his local play, then instead the opponent could make a local gote play of his. Such would have the same absolute value. We would be considering 2 plays difference with twice the difference value, but, since we are not using deiri counting, we might as well forget about multiplying by 2 and dividing by 2 and continue to use only the per move value of only the player (i.e. not his opponent's other play).

GAIN ELSEWHERE WHEN PLAYING ELSEWHERE FROM THE LOCAL REGION

Since the corners have equal values, a play elsewhere has the same local per move value there as the local per move value in our particular (upper left) corner.

Now we know everything about relative sizes of values. Please correct all mistakes I might have made thus far!

ABSOLUTE VALUE

The most difficult aspect for me to understand is the order of magnitude of an absolute value of an early play in the game. Recall that I want to know the local per move value. Must such a value be about 4, about 8 or about 16? These possible factors of 2 scare me. I believe that about 8 is the right order of magnitude. I think so because this is about the value I get in the following examples:

Click Here To Show Diagram Code

[go]$$
$$ -----------------
$$ |C C . . . . . . .
$$ |C C . . . . . . .
$$ |C C . . . . . . .
$$ |. . X . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .[/go]

The first play has gained about 6 points of territory and (I guess) about 2 points of influence.

Click Here To Show Diagram Code

[go]$$W
$$ -----------------
$$ |. . 6 5 . . . . .
$$ |. . 4 3 . . . . .
$$ |. . 2 1 . . . . .
$$ |. 8 X . . . . . .
$$ |. 7 . . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .[/go]

The 6 points are explained by assuming a most peaceful sente endgame reduction sequence like this.

Click Here To Show Diagram Code

[go]$$
$$ -----------------
$$ |C C C C . . . . .
$$ |C C C C . . . . .
$$ |C C C . X . . . .
$$ |. . X . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .
$$ |. . . . . . . . .[/go]

The second play has gained about 5 points of additional territory and (I guess) about 3 points of additional influence.

So, on average, each of the first two corner plays has gained about 5.5 points of territory and 2.5 points of (territorial value of) influence. Thus I assume that the per move value of an early move in the game is about 8 points.

Apart from minor variation of the exact size of a value like 8, have I chosen the right order of magnitude for the local per move value of an early move in the game or am I wrong by a factor 2 in either direction and would 4 or 16 be correct? Why is the order of magnitude right or wrong?

IMO, it must be right because a few moves later, with a slightly dropped local per move value, one can find an example of the value 6:

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------
$$ |. . . . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . . X X O . . . O .
$$ |. . X . O O . . . . .
$$ |. . . . . . . . . . .
$$ |C C X . . . . . . . .
$$ |C C . . . . . . . . .
$$ |C C . . . . . . . . .
$$ |. . 1 . . . . . . . .
$$ |. . . . . . . . . . .[/go]

Black 1 adds the 6 marked points of territory and shifts influence of a previously existing black stone downwards rather than creating any noteworthy additional influence. (White can force from the outside.) These 6 points are slightly less than 8 but neither slightly less than 4 nor slightly less than 16. Thus I uphold my claim that about 8 is the right order of magnitude for the estimated local per move value of an early move in the game like a first stone in a corner or an approach move to a first corner stone.

EDIT

[replaced all "deire" by correct spelling "deiri"]

14kyu rewriting go theory...


Temperature of a "move" confuses me.... Forgive me if there is a formal "go" definition of temperature but in physics temperature is a measure of the distribution of energy of particles. You can define the energy of a particle (=one move I guess) and you could define the temperatures of a group of particles (= many moves). But you can't define temperature for a single particle/move/event..

Additionally, in order to define a temperature you need a "normal distribution" of particles which are in equilibrium. To my mind this can't happen on a go board certainly at the early stages and clearly not at the end (you have a winner).

To win a normal distribution and produce a temperature usually requires "scattering and randomizing" collisions. In go, there tends to be more "action at a distance" (go players speak about influence) - which in turn doesn't tend to randomise distributions so rapidly (so temperature becomes less accurate as a description).

I'm not sure that statistical descriptions - such as those drawn from thermodynamics help in go...on the other hand I'm not sure what will. There's probably more "helpful" ideas in chaos theory - the patterns that emerge certain have chaotic properties (e.g local organisation) but my knowledge of chaos is only at undergraduate level so I can't really comment.

I'll go back to Tygem now and get thrashed by an 18 kyu......

The temperature that Robert is referring to is indeed go and not physics related. It is a mathematically derived way of expressing the urgency of making a play in a certain area of the board. You can look it up on Sensei's Library for more information.

_________________
Patience, grasshopper.

see previous threads about physicists getting involved in threads like this...

from Senseis library:

Re temperature:

"It is typically more urgent[1] to make a play in a hotter game than in a cooler one.

Temperature is not equal to heat: for the statistical reasons outlined above. e.g The temperature of electrons in a fluorescent tube is 11000 degrees centigrade (ish). - but the tube doesn't melt because there is a difference between temperature and heat.

Superficially, it's just interesting semantics. People got a very long way believing the Earth was flat, it was only when better models were introduce (round Earth) that more understanding was won.

Combinational game theory seems to have taken and misinterpreted some basic physics ideas.. it happens....

Looking around the net there doesn't seem to be much on go theory using chaos, collective effects, energy treatments etc.. Looks like some understanding might be won using this sort of thing:

http://en.wikipedia.org/wiki/Lattice_Boltzmann_methods

Go games become "fluid like" and a particle approach would be favored. Computer are dealing in four dimensions with big grids.. 19x19 should be straightforward BUT..... I'm not convinced that after a stack of modelling and pain.. much more understanding would be won..

but on the other hand unless you want a PhD in go.... just play it

er before I get banned for trolling/being off topic I am minded of the third law of physicists:

viewtopic.php?f=8&t=3532&start=60


did anyone see Pippa Middleton yesterday... she was "hot" in a temperature kind of way

Some scattered comments:

1. It is deiri, not deire.

2. You are assuming that opening moves are countable by miai or deiri methods. This may be too impractical. A completely new way of counting may be needed, the same way that chemists may use moles instead of grams. Ultimately it may not even be possible to count in a practical way even with a new measure, because groups interfere with each other. We may therefore need a more pragmatic way of assessing values, for example measuring the inter-relationship of groups with something like Hansen solubility parameters.

3. Ishida Yoshio may have done something like this for us already. At any rate, his book "Kono te, nanmoku" (How much is this move worth?) uses diagrams very similar to Robert's, and discusses gote and sente in very like terms, but the fundamental difference (apart from him being a 9-dan) seems to be that he counts differently. Despite the book's title, the first chapter is headed "The empty corner is worth 20 points", i.e. putting a value on an area rather than a move. By using this approach, he is able to relate his numbers also to traditional concepts such as corner-side-centre and also to traditional heuristics such as a ponnuki capture being worth 30 points (though this seems to be for the audience's benefit rather than his own). This all leads him to conclude that a big point, for example, is worth usually about 30 points, and an ikken tobi towards the centre from a side group is worth about 20 points. Indeed, he is prepared to go to finer estimates, with certain fuseki moves being labelled 32 points, or 18 points, and he comes up with new heuristics such as "a normal attack is worth 20+ points" (maybe this is where Rob van Zeijst's QART system orignated), or "a forced invasion is worth 20 points".

I don't pretend to understand Ishida's system. I haven't even done more than riffled through the book. But what did strike me was that the values given by him seemed to bear a close relationship to the average size of an area at the end of a game. What I mean by that, is that if you look at a shape such as a two-move shimari and count the average of the territories made around it over a large number of games you come up with a figure of just under 20 points. A two-space extension on the side seems to come in at a little over 5 points. In practical terms, this means that when you make a shimari you are saying, "I expect on average to make a final 20 points in this area". These values seem to relate to Ishida's statements of the type "the empty corner is worth 20 points". So, I think he is measuring in a subtly different way, but the mental leap required may simply be of the order of remembering to specify you mean a mole of molecules and not a mole of atoms. (At the pro level, though, I imagine there is indeed some equivalent of solubility parameters.)

Whether or not I've twigged Ishida myself doesn't, of course, alter the requirement for researchers to take account of his theories. The ISBN is 4-537-01563-2.

Indeed I do want to assume that early moves or stones can be measured by a per move method. My motivation is that such can help in judging joseki plays in comparison to playing elsewhere. For that purpose, a per move value is much more useful than anticipating a statistical average a la Ishida because it is essential to recognize the good moments of tenuki.



Certainly this is another valid and presumably also very useful approach (even if using partly symbolic numbers so far). It is, however, not a kind of approach I am interested in for a better understanding in this thread. Symbolic appraoches can be useful indeed; in my book I will present some such approach where I assess instability by small symbolic numbers. I think small is good: Counting beyond 2 won't hardly be necessary:)

Assessing values of early moves should be rather precise though because comparing values allows 1) move decisions and 2) assessment of territorial values of influence-creating stones. I need to be sure of the fundamentals though (see my first message).

It very seldom does.



Let me try to clear something up. "Sente" has more than one meaning. One meaning is simply having the move, of playing first. "The value of sente" means the value of playing first. At the start of the game, the value of sente is the theoretical value of komi. The value of a sente play is something else. It is how much the reverse sente play gains.



Thanks for clearing that up.

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

Visualize whirled peas.

Everything with love. Stay safe.

Well, it turns out that Ishida means that a play in an empty corner is worth 20 points. And he is using deiri counting. So he is using the traditional values, whereby a handicap stone is worth 10 points and komi is worth approximately 5 points.

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

Visualize whirled peas.

Everything with love. Stay safe.

As Bill has mentioned the value of the first move is more likely to be near twice the komi value, rather than near the komi value. If I recall correctly, pro versus pro winning rates suggest that in practice, fair komi lies somewhere around 6 to 7 points, and is almost certainly greater than 4 or 5 points. This suggests that the per-move or miai value of the first few moves is closer to 12-14 points, and is probably more than 8-10 points.

In fact, a heuristic argument shows that 8 points is very likely too low. Consider a game where you play second as white in an even game but receive 7.5 komi. Empirically, this gives white close to a 50% winning chance, despite playing second. Now, assume that the value of an opening move in the corner is worth about 8 points (per-move, or miai value). So heuristically, if you pay 8 points to add a stone to one of the corners before the game begins, you should not gain any significant advantage.

But you have gained a large advantage. Effectively, you have become the first player, and you have gone from receiving 7.5 komi to giving 0.5 komi to the opponent, so the opponent is receiving almost no compensation. This suggests that actually, the value of the opening move is much more than 8 points. It should be closer to twice komi, so that when you pay that amount for the privilege of starting with an extra stone on the board, you go from receiving +komi to receiving -komi.

Also, considering the miai values of moves in the macroendgame, >=12 points for an opening move also seems about right. Certain monkey jumps, or moves like the one in the following diagram can have miai values as high as 7-8 points considering territory alone:

Click Here To Show Diagram Code

[go]$$W
$$ ---------------------
$$ |. . . . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. 1 X . . . . X . X .
$$ |. O . X . X . . . . .
$$ |. . . . . . . . . . .
$$ |. . O . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . O X . . . . . . .
$$ |. . O . . . . . . . .
$$ |. . . . . . . . . . .[/go]

Yet they are generally too small to play until the endgame, UNLESS they have additional benefits, such as stealing or gaining a base for a group, which makes them much more valuable. If groups on both sides are strong and stable, you typically don't see these moves until the endgame, which is not what you would expect if they had values as just about as high as big opening moves.

You say that you calculate the miai value but I think what you actually calculate here is the deiri value.

You also add komi to your consideration but 1) komi is just a constant shift of the whole board scoring and 2) komi compensates for all moves of the game instead of compensating only the first move of the game. Therefore embedding the first move value's analysis in an environment of one additional komi playing card does not add useful extra information.

Ignoring the superfluous komi card environment, the normal case is: Black starts by making a first play worth X.

Now you change that to become: White starts by making a first play worth -X.

To compare both cases, we determine a count X - (-X) = 2X. This is deiri counting. To get miai counting, we need to divide by the move number difference 2 and get the miai value X. (Say, X is 8.)

When studying the miai value of a local play (in an almost empty corner), I do not care whether Black or White started the game. Either player might be the one to play first in a particular corner.



I am not convinced by these kinds of examples because a high macroendgame value can be the result of several previous (necessary but) below-average plays.

Click Here To Show Diagram Code

[go]$$
$$ ---------------------
$$ |. . . . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . X . . X . . . . .
$$ |. O . X . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . O . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . O . . . . . . . .
$$ |. . . . . . . . . . .[/go]

Either player has made on average 6 points (Black 5 vs. White 7) with 3 plays or 2 points per play. The black and white influences roughly neutralise each other. Now you would not conclude that 2 were the average value of an early play in the game.

Click Here To Show Diagram Code

[go]$$
$$ ---------------------
$$ |. . . . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . X . . X . . . . .
$$ |. O . X . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . O . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . . . . . . . . . .[/go]

White's territory is 0. If White makes one play, then White gains 7 points of territory. Besides White gets additional influence that neutralises the previous black play's additional influence. However, White's previous two stones have much less influence value than the next white play's stone. It is more useful to speak of influence on average per invested stone.

This goes back to my consideration above: In the finished joseki, the simplified average player has made 6 points with 3 stones and a so far unknown territorial value of influence of Y points with 3 stones. I claim that Y is about 3 points.

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------
$$ |C C C . . . . . . . .
$$ |C C C . . . . . . . .
$$ |. 1 X . . X . . . . .
$$ |. O . X . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . O . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . O . . . . . . . .
$$ |. . . . . . . . . . .[/go]

Black 1 adds 6 points of territory. Let us assume that the play is Black's usage of his earlier influence. Before that play, Black making versus White denying the additional black territory each has a 50% likelihood. So the expected addition of black territory is worth only 50% * 6 = 3 = Y points.

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------
$$ |. . . . . C C C . . .
$$ |. . . . . C C C . . .
$$ |. . X . . X . . 1 . .
$$ |. O . X . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . O . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . . . . . . . . . .
$$ |. . O . . . . . . . .
$$ |. . . . . . . . . . .[/go]

Black can use his prior influence also for making these additional 6 points or White can prevent that. Same as before. Y = 3. (Actually Y is a tiny bit larger, say it is 4, because the four black stones work better together to the outside than previously only the three black stones.)

As you notice, I count only the player's territory and his territory's increment while I ignore the additional negative territory impact on the opponent's values. So maybe this explains the factor 2 gap? What I determine would then not be the miai value but half the miai value, namely that part of it that increases the playing player's territory and territorial value of influence. So it is "the value per move per player". EDIT: This makes the idealised assumption that the opponent would get unrelated and elsewhere on the board good plays of equal size for himself.

Have I identified the source of our discrepancy correctly now?

So maybe Bill and you are right when also considering the komi playing card environment. I would like to see your better explanation of that though!

Of course, the first move's value does not depend on what komi is. However, the point is that one expects the "fair" komi value to have a relationship with the value of the first move. If by other means, such as observing pro v pro winning statistics, we are able determine what likely values of the "fair" komi are, then that gives evidence for certain values of the first move.

What is this relationship? Well, first we observe that in general, given a game situation (position + current player to move), let the value of that position be V (from the current player's perspective). If you assert that a certain move for the current player has miai value X, then heuristically, you expect that if you give the current player that move for free, so that it's still the current player's turn afterwards, the value of the new position will be V+X.

This assumes that there is a rich environment with lots of plays of different values, and only a gradually decreasing global temperature. For example, imagine a simplified game where there are a series of tokens worth 10, 9.5, 9, 8.5, ..., 1, 0.5, and the players alternate turns taking a token of their choice on their turn and gaining that many points. The miai value of taking a token is the value of the token, because the difference between taking it and the opponent taking it is twice the value of the token, and we divide by two because there are two moves difference between these outcomes. Additionally, from the perspective of the first player, the value of the game is V = +5 (under optimal play, he will get the tokens 10, 9, 8, ..., 1 and his opponent will get the token 9.5, 8.5, 7.5, ..., 0.5, for a score of 55 versus 50).

Now, if we allow the first player to pick up the "10" token without costing his turn, which has a miai value of X = 10, then the new game has a value of +15 (the first player will get the tokens 10, 9.5, 8.5, .... 0.5 and the second player will get the tokens 9, 8, 7, ..., for a score of 60 versus 45). Voila, changing the game to allow the first player to get a move of miai value X for free raised the value of the game from V to V+X.

Similarly, if we allow the second player to pick up the "10" token for free before the game begins (but thereafter the other player moves first as usual), then from the first perspective, the value of the game changes to -5 (the first player will get the tokens 9.5, 8.5, ..., 0.5 and the second player will get the tokens 10, 9, 8, ..., 1). As expected, the value of the game has changed from V = 5 to V-X = -5.

This only breaks down if the sum of the even differences between the values of the tokens is very large and the sum of the odd differences is very small (such as if the tokens are 10, 9.9, 9, 8.9, 8, 7.9, 7, ..., 1, 0.9) or vice versa (such as if the tokens are 10, 9.1, 9, 8.1, 8, 7.1, 7, ..., 1, 0.1). However, if there are lots of tokens and they are distributed "randomly enough", then we expect this not to be the case. That is, so long as the total drop in temperature on the even steps and the total drop in temperature on the odd steps throughout the game are comparable, then getting a move of miai value X at the beginning of the game for free changes the value of the game from V to about V+X.

So let's apply this to Go. It is not an unreasonable assumption to assume that the total drops in temperature on the even and odd moves of Go will be comparable, on average - it would be strange if strong play consistently led to one player or the other always getting tedomari throughout the entire game. From the observation that komi around 7 gives roughly equal winning chances to both sides in pro games, (and significantly higher or lower values do not), we guess that that the value of the opening position with black to play is close to +7 for black.

Now, allow white to gain make a move for free before the game begins. If the miai value of such an opening move is X, then we heuristically expect that the value of the new game is about 7-X from black's perspective.

Now we observe that this new game is equivalent to a game in which white moves first on an empty board. By symmetry, if black moving first on an empty board gives a value of +7, then white moving first must give a value of -7. Therefore, 7-X = -7. Therefore, X = 14.




It seems strange to say something like this, if you are talking about miai values. Perhaps you are using a different notion of the value of a move? Perhaps Bill can correct me if I'm wrong, or qualify this better, but miai values should take into account the value of the followups to moves, so if a move enables a large followup that was not possible before, then the move should be worth correspondingly more.

The point I'm trying to make is:

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . b . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . O O X X . . . |
$$ | . . . . . . . O . O . . O X O X . . . |
$$ | . . . . . . . . . . . . O X O X . . . |
$$ | . . . . . . . . . . . . . . a . . . . |
$$ ---------------------------------------[/go]

Consider this position. It doesn't matter how we got to it, all we are concerned about is how much black's next move will gain. Then, is a move like A really worth as much for black than a move at B? Endgamewise, A is quite big, and indeed, territorially its miai value seems to be pushing up at 8 points (maybe more - the possibility of ko when blocking the followup hane confuses me). It doesn't have any other value, because the black and white groups are quite stable.

But at least in my opinion, A is too small to play at this moment, compared to moves like B or other similar moves in the top left. And the (miai) value of moves in the top left should at least be roughly comparable to the value of such moves when the board is empty. If we assert that a move in the top left also have a miai value of 8, we are asserting that on average, a capture like A when both surrounding groups are stable is worth as much as a big opening move, which seems wrong to me. But maybe I'm mistaken.



Possibly. I don't completely understand the rules for what you consider to be gained by a move, or how you weight (or don't weight) followups to moves in the value of moves, and so on. But if you are not considering the loss for the other player, then I think yes, your notion of move value differs somewhat from miai value.

I make the same simplifying assumption of a dense token-like enviroment with only decreasing values. Furthermore I guess I have studied mainly shapes with sudden drops of values after having played the currently interesting moves. So essentially I ignore deeper iteration. Very convenient but might be too simplifying indeed.



I have not found / understood all the "value-related rules" myself for what I am considering. So not surprisingly you neither.



Somewhat or exactly 1/2?

I usually find this stuff very hard to follow, but that might have been the clearest explanation I've encountered, lightvector. For that reason alone, I hope it's right.

_________________
Occupy Babel!

As I understand now, that value does not express the komi but solely the territory value per played stone while it forgets to include the impact on reduction of opposing territory. Now, considering particularly well chosen example positions, I think that 14.22 ~ 14.51 points are good estimates of the per move value of early moves. Finally that is surprisingly close to the token model's result, which furthermore relies on pro game statistics. All methods rely on simplifying axioms though.

Click Here To Show Diagram Code

[go]$$B 7 pt. "komi"
$$ ---------------------------------------
$$ | . . . . . . . . . . . O O X X . X O . |
$$ | . . . . . . . . . . . O . O X . X O . |
$$ | . . . . . . . . . . . O O O X X X O . |
$$ | . . . , . . . . . , . . O . O O a O O |
$$ | . . . . . . . . . . . . O O O O X X X |
$$ | . . . . . . . . . . . . . . X O . X . |
$$ | . . . . . . . . . . . . . . X X X . X |
$$ | . . . . . . . . . . . . . . . . X X X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

The position in the top right is independent of the rest of the board. It has a count of -7 and a local temperature of 14. The negative count is like a komi of 7.

Unfortunately, the thickness may have altered the temperature of the rest of the board. But if not, the question of whether to play at a or elsewhere should be close.

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

Visualize whirled peas.

Everything with love. Stay safe.

Even if 14 is the ambient temperature, I prefer to play elsewhere because there is the psychological, optimistic advantage of superior decision making:)