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Estimating The Score
Path: GoodHabits   · Prev: ApproachingALifeAndDeathProblemTheRightWay   · Next: Practice
  Difficulty: Beginner   Keywords: MiddleGame, Strategy

Matt Noonan: A lot of players at about 10 kyu and weaker (some stronger players, too!) seem never to count the score during the game. Counting is very important in a game of Go; in almost every game, strategies must be adjusted to take the score into account.

My guess is that some players think that counting a game-in-progress takes too long or is too inaccurate. But practice makes perfect!

Here are some techniques I use. Please extend the list!


Brute-Force Method

The most obvious way to count is to simply look at what appears to be "territory-like" and count it up, counting two points for each stone that appears dead as it stands, and then one more point per capture. Of course, the trick is deciding what is and is not likely to stay dead or remain territory. The other main drawback of this method is speed -- it's about as slow as counting up a finished game.


Comparative Method

Another good technique is to compare territories directly. First, mentally pick up the captured stones from the lids of the bowls and place them inside your opponent's territory. The idea is to use the captures to neutralize a territory of roughly the same size, so you won't need to count it manually. Next, do the same for the dead stones on the board. Finally, compare the territories by sight: "White's upper left is about the same as Black's lower left, White's center is about 10 points smaller than Black's right" and so forth. This method is very fast and can give quite accurate results, especially with some practice.

[Diagram]
'Group Rengo' : Moves 151-158

This is a position from an OngoingGame. The dead black stones (marked) roughly fill up the black territory in the upper and lower right, with a few stones left over. The extra stones are pretty much cancelled by some of the marked dead white stones. The other dead white stones essentially cancel White's small area of influence on the left side. Now, White's bottom side plus White's little blob at the top right are roughly equal to Black's right side up to about the fifth line plus some of Black's area on the top right, since White has big endgame plays on the right side. Comparing the remaining black center area with White's top shows that White seems to be ahead by a small lead -- maybe 5 or 10 points.

This is a lot of description, but the actual mental calculation is very quick, especially at a physical board.



I've just added some short tricks that can make it easier (or not) --MortenPahle:

Count in twos

You can often save time by counting in two's instead of each point individually. This way you count pairs of territory, or one dead stone inside territory as 'one, two' etc. Visualising pairs of points is normally quite easy.

Count in fives

This may sound tricky, but if you wasted numerous hours you should have been studying by playing some form of tetris, this can actually come quite naturally if you think of filling the inside of territory with "blocks" and can be very fast. Just be careful how you count up dead stones.

Deebster: Aren't the Tetris shapes made up of four blocks/points?

Count individual territories

If you have the memory for it, you can save time by counting and remembering each territory individually, not just the overall score. This way, next time you count, you only have to recount those territories which have changed.

Memorisation trick

This was recommended by Steve Fawthrop on rec.games.go some time ago. (This method cannot be used if you have remembered all the individual territories).
After counting your opponent's territory, don't remember the actual value, but the next large number up. (E.g., for a count of 73, remember 100). Start to count your own territory not on 0 , but on (large number - actual count) - in the example above, start counting on 27. This way, you only have to remember 100, and compare the count of your territory with 100, not with the actual score (which you've forgotten).

Andrew Grant: A variant of this which I was taught many years ago is: Count your territory, then count your opponent's territory backwards starting from whatever total you reached. If you run out of opponent territory before you reach zero, you're winning, and the number you finish on tells you how far ahead you are. Don't forget to adjust this for komi.

Extend territories 'straight' to the board edge.

When you first start counting, the borders of the territories are not very well defined and are subject to change. As a first assumption, you can extend the territories straight to the edge in a 'neutral' manner.

Don't count territory in the centre

Normally there is very little territory in the centre. Unless this territory is really well defined (I.e. completely certain), do not include it in your count. Often the result of a count is that someone is behind (duh:-) and one way of looking at it is that means that I have to gain 15 points in the centre or that means he must gain 15 points in the centre - I can relax a little and play solid moves.

I think there is no territory in the center is a controversial statement, so I have added it there. --DieterVerhofstadt


Use Area Scoring

A refinement of the Comparative Method is to use area scoring.

Since TerritoryAndAreaScoring are equivalent, I currently find it easiest to ignore all dead stones, and try to mentally identify which areas are Black's and which are White's, including all live stones and surrounded points. Then I can compare the areas visually. It's not accurate, but it's quick, and +/- 10-20 pts is good enough at my level. Note that you can't do this with territory scoring, because large groups of captured stones count double, which is hard for my brain to do visually. -- DougRidgway (20k)


Use half counting

Instead of counting both black and white territory, it is possible to count just one of them, using area counting. Especially in online games this is convenient, since you have to know the number of moves already played.

  1. Select the color which looks easiest to count.
  2. Count the empty intersections, dead opponent stones and include not yet played border stones of the selected color (normally you do not count the latter, but only the expected empty points). Dead opponent stones count for only one point in this method.
  3. Add the number of board moves played/2 (round up for black, down for white). When counting for black, add the number of handicap stones minus one. Subtract this when counting for white.
  4. Subtract the number of dead stones of the selected color including the already captured ones
  5. Subtract the total board intersection/2. Multiply this result by 2.
  6. Add or subtract komi

An alternative for step 3+4 is to count and add the number of living stones of the selected color currently on the board (if you don't know the number of board moves played)

Example

-- Araldo (8k)


Adjust lines to make squares

You can try to adjust lines to the inner territory to make squares in the same way as you adjust lines to approximate in a mathematical diagram. Since the inner edge is often somewhat smoother this works pretty well.

[Diagram]
Squares that count

In the UL white has some 15 points if you count the empty intersections. By approximating the area with the marked stones you get three times six and and by subtracting one for the white stone you get 17 points. In the LR you can count the empty intersections and you will get 26 points. By approximating it with the marked stone and the marked intersection you get four times seven and by subtracting one for the black stone you end up at 27.

I have found this method to be quick and accurate enough to help me in at least my games. -- Joorin (18k)



One hand is 50 points

Have you ever noticed your opponent placing his hand over large territories? He is probably using the "one hand is 50 points" technique for estimating large territories. --Bob Myers

Old saying: "if you can put your hand in the territory, you have won". -- Charles Matthews

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Computer Training

The free TANGO go client software has a very nice function which uses GNUGO's score estimating function to form a progress chart. The chart gives an estimate of the score as the game progresses.

It is a wonderful post game analysis tool. Simply import an .sgf file; index the game to the second to last move; and engage the progress chart function. After about 10 min, a chart is formed giving the score vs. the move.

Come to think about it, this may be a great way to train on counting. Simply move a game to a position, try to estimate the score, the check the chart.

(the progress chart needs windows NT to function- it will estimate the score in non-chart format with other operating systems)

[ext] http://www.amourtan.com/feature/progress.html

kritz

AshleyF: SmartGo 1.3 now has this nifty feature as well: [ext] http://www.smartgo.com/t_score.htm

Gernotti: Same is true for The Many Faces of Go v11 ([ext] http://www.smart-games.com/manyfaces.html). I agree with crux's objections in principle, but especially to beginners it can give you a clue, where in the game something really went wrong.

crux: Of course, that assumes that the computer knows what it is doing. I'd hesitate to recommend this kind of thing; computers don't really understand the game. Beginners could easily pick up wrong ideas this way.



Path: GoodHabits   · Prev: ApproachingALifeAndDeathProblemTheRightWay   · Next: Practice
This is a copy of the living page "Estimating The Score" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.