A little vignette on thickness

[Tami]

Hi everybody, I've written a little piece about on old idea of mine ("deadweight value of thickness"). Maybe you will find it interesting or contentious.

[emeraldemon]

A minor point, but if you're going to count Chinese points, you should maybe add a few points to white's territory also (O19,P19,T17).

[Tami]

A minor point, but if you're going to count Chinese points, you should maybe add a few points to white's territory also (O19,P19,T17).

Yes, you're right. It slipped my attention, but I trust it does not greatly affect the thrust of the argument. But thanks for pointing it out to me anyway.

[tj86430]

Perhaps this will get you more readers:

(;GM[1]FF[4]CA[UTF-8]AP[CGoban:3]ST[2]
RU[Japanese]SZ[19]KM[0.00]
PW[白]PB[黒]C[Tami: Let's start with a classic example of an influence versus territory trade.]
;B[pd]
;W[qc]C[Tami: Everybody knows this invasion is bad when played prematurely, except some players do it anyway, and others simply cannot believe that Black comes off better.

This is an attempt to show why Black's side of the deal is much better.]
;B[qd]
;W[pc]
;B[oc]
;W[ob]
;B[nc]
;W[nb]
;B[mc]
;W[rd]
;B[re]
;W[rc]
;B[qf]LB[pa:1][qa:4][ra:6][sa:7][pb:2][qb:3][rb:5][sb:8]C[Tami: The classic joseki.

White has about 8 points of real profit.

Black has only got a wall, and no points of profit. Yet on an open board Black is already doing much better.]
;W[qk]LB[jc:17][kc:9][lc:1][md:2][nd:3][od:4][me:11][pe:5][of:13][pf:6][rf:8][qg:7][qh:15][qi:19][as:10][bs:12][cs:14][ds:16][es:18]C[Tami: It might be easier to grasp if you think about Chinese rules. In Chinese rules, the game is basically decided by how many living stones you can place on the board.

So, in this diagram I assume Black will certainly be able to place 1 more stone next to each stone in the wall, no matter how much White attempted to reduce the wall's influence.

After that, it seems reasonable to assume Black will be able to place about half as many stones on the board at an interval of two spaces, and to reduce that allowance by half again at three spaces.

In the end, Black gets about 19 or 20 certain points, no matter what. Clearly this is better than the 8 or 10 further points White can count in the corner.

This "no matter what" value is what I can "deadweight value of thickness". Even without an active attempt to attack and use the thickness actively, the thickness will generate points simply by being there.

There are occasions when walls are sacrificed. Even then, the deadweight value must have some meaning - to capture a wall cleanly requires a lot of expenditure, which is offset by the opponent making profitable plays elsewhere.

Deadweight value might also explain why it is a mistake to surround territory using walls. That only assures you of the deadweight value (here around 20 points), but does nothing to prevent the opponent making points in other areas.

The full value of a wall is only seen when you attack and use the influence actively. At least, however, deadweight value should show you that it's generally very promising to be able to take influence for territory on an open board.])

[Tami]

Perhaps this will get you more readers:

Thank you...I feel a bit guilty now for not reading up on how to use the inline game viewer.

[RobertJasiek]

What you seem to be looking for is "current territory" and the "count" (see my books). There is no need to introduce an ambiguous alternative concept "deadweight value".

(;SZ[19]FF[4]AP[GOWrite:2.3.44]ST[2]GM[1]KM[0.00]PM[2]FG[259:]GN[ ]
;B[pd]
;W[qc]
;B[qd]
;W[pc]
;B[oc]
;W[ob]
;B[nc]
;W[nb]
;B[mc]
;W[rd]
;B[re]
;W[rc]
;B[qf]
;W[qk]
;MN[1]PM[2]FG[259:]
(
;B[mb]
;W[na]
;B[ma]
;W[qb]
;B[se]
;MA[sc][sb][sa][rb][ra][qa][pa][pb][oa]W[sd]C[White has 9 points of 'current territory'.]
)
(
;PM[2]C[The count is Black's minus White's 'current territory' ~= 14.5 - 9 = 5.5 points. Note the peaceful sente reductions.]FG[259:]
;B[tt]
;W[ph]
;B[og]
;W[oh]
;B[ng]
;W[pg]
;B[pf]
(
;W[rg]
;B[qg]
;W[qh]
;B[rf]
;W[rh]
;B[jd]
;W[jf]C[This is peaceful enough to be a sente endgame reduction. A deeper move would be an invasion and attacked.]
;B[kf]
;W[kg]
;B[lf]
;W[je]
;B[kd]
;W[mb]
;B[lb]
;W[la]
;B[kb]
;W[mg]
;B[mf]
;W[hc]
;B[ib]
;W[ic]
;B[jc]
;W[hb]
;B[ia]
;W[ma]
;B[ka]
;W[ke]
;MA[qe][pe][of][nf][oe][od][nd][ne][me][md][ld][lc][kc][jb][ja]B[le]C[Black has roughly 15 points of 'current territory'.]
)
(
;PM[2]FG[259:]
;W[mf]C[overplay]
;B[rh]C[mistake, must attack White 8]
;W[ri]
;B[rg]
;W[ne]
;B[oe]
)

(
;PM[2]FG[259:]
;W[lg]
;B[lf]
;W[kf]
;B[le]
;W[ke]
;B[kd]
;W[jd]
;B[kc]
;W[mb]
;B[lb]
;W[ic]
;B[jb]
;W[mg]
;B[mf]
;W[ib]
;B[ja]
;W[ma]
;B[la]
;W[rg]
;B[qg]
;W[qh]
;B[rf]
;MA[qe][pe][of][oe][od][nd][nf][ne][me][md][ld][lc][kb][ka]W[rh]C[Black has roughly 14 points of 'current territory'.]
)

)

)

(The move numbers in the SGF start recounting after the first 14 moves. The L19 SGF interpretation does not handle this correctly. To see correct relation of comments and move numbers, save as SGF and view locally.)

[Tami]

Thank you for sharing you example. It looks like we are talking about the same issue, although our ways of tackling it are different.

BTW, I first wrote a page on SL about "deadweight value of thickness" ten years ago. I would certainly concede that your word "count" is more compact than mine, but possibly mine has its own advantage in expressing the inherent ability of thickness to generate points without any particular further effort.

Anyway, I`m not trying to compete with you; I only thought I would share my own thoughts with the readers here. If by some chance they were to go on to prefer using a Tamiism to one of your terms, that would be beyond your control and mine. Just as we are free to introduce our ideas, others are free to reject them or modify them as they please.

[RobertJasiek]

"count" is a well known term in endgame theory; I have just applied it less strictly to opening and middle game. You can also find a definition of "current territory" here:

http://senseis.xmp.net/?CurrentTerritory

I`m not trying to compete with you; I only thought I would share my own thoughts with the readers here.

You should be trying to compete because you will have difficulties to justify your values 8 points for White and 19-20 points for Black:)

[Tami]

As emeraldemon pointed out, I probably undercounted White's score, and I accept that. I would up it to 10 in light of his comment. I think 19-20 remains a reasonable assessment of Black's deadweight value on an open board.

A problem I have with your example is that in order to make the "count", you have to surround the wall with white approach moves, but you are not including their value in your calculation. My method seems simpler and not affected by that complication.

[Bill Spight]

(;AP[GOWrite:2.2.21]SZ[19]ST[2]FF[4]GM[1]CA[ISO8859-1]FG[259:]PB[ ]PM[2]PW[ ]GN[ ]
;C[We estimate the value of this stone as around 14 points.]B[pd]
;W[qc]
;B[qd]
;W[pc]
;B[oc]
;W[ob]
;B[nc]
;W[nb]
;B[mc]
;W[rd]
;B[re]
;W[rc]
;C[The premature invasion is bad for White. Black still hase one more stone on the board than White. That means that the value of the Black wall minus the value of the White corner is greater than 14 points. My guess is that the difference is around 18 points.]B[qf]
)

[RobertJasiek]

The problem I have with your example is that in order to make the "count", you have to surround the wall with white approach moves, but you are not including their value in your calculation.

The purpose of "current territory" is to assess ONLY territory of ONLY one player - not to assess newly gained influence of reduction stones.

My method seems simpler and not affected by that complication.

My method is simpler because the complication of trying to assess influence of newly played reduction stones is not considered at all. Consider your rough idea of extensions and checking extensions. The opposing checking extensions can have a lot of influence. If you wanted to include that, then Bill's objection applies: easily you can get NEGATIVE total values.

Applying n-territory (0-territory is the current territory), the black wall can get a slightly higher territory value; if we determined also its 1- and 2-territory (1-territory: 1 extra black play, extra intersections count 50%, 2-territory: then second extra black play, then extra intersections count 25%), then we enter about your intuitive 19-20 points range (if we still ignore all the white reduction plays / checking extensions). And we get such values due to a clear definition while "deadweight value" remains ambiguous.

[Tami]

Thanks for your input, too, Bill.

I suppose I have come up with a primitive method for assessing wall vs territory exchanges.

Basically, fill in the territory leaving two eyes and that will be the score for the territory side.

As for the influence side, add one for every outward-facing liberty. The influence side should expect to keep control of those points if nothing else. Add half the value again, and then add half the value once more. This is to acknowledge the wall`s affect radiating over the board.

Anyway, maybe estimates produced this way are somewhat conservative, but that's about the size of it: assume a wall will definitely gain profit equivalent to the number of points immediately next door, and then add some more to account for its long-range effect.

In any case, this method shows that influence versus territory exchanges on open boards tend to favour the influence side.

To Robert - your latest post appeared while I was writing this. Please don`t think that I am ignoring you - let me think about your remarks and respond later if I can think of something to add or question.

[RobertJasiek]

Bill, you better add that the 14 points value refer to the average local move value aka miai value:) Otherwise people wonder: "Which kind of value?" Your guessed 18 points refer to a different kind of value than the one I have calculated; the two values are not comparable.

What you are saying with "about 18 points" is that Black has gained 4 points by replacing his initial one excess stone worth 14 points by the guessed 18 points miai value. The exact size of "18" is unknown so far and I cannot provide a method yet with which a rather accurate miai value could be determined for the excess stone at the end of the 3-3 under 4-4 invasion.

I can determine current territory, with some more effort probably also n-territory (2 steps iteration) and an approximative territory efficiency. For the miai value, however, more research is necessary, I think.

[RobertJasiek]

To Robert - your latest post appeared while I was writing this.

I have noticed our simultaneous writing and so also edited my post again. No problem:)

[Bill Spight]

Bill, you better add that the 14 points value refer to the average local move value aka miai value:) Otherwise people wonder: "Which kind of value?"

I am not referring to move value but the value of the position. True, it is an estimated value.