# Local tally

Keywords: Strategy, Theory

### Meaning of local tally

Local tally is to find out whether there are more black or white stones (in a local position) under 2 scenarios.

The 2 scenarios are:

• if B plays first
• if W plays first

It involves the calculations about the differences between the following in a local board/position:

• the number of black stones played, and
• the number of white stones played

### How to calculate local tally

Now I am going to tell you how to calculate local tally of a position/board.

There are 3 steps.

Local Board (original position)

### Step 1 - Find local tally if B plays first

Local Board - B first

--.
B plays 2 stones; W 1.

So Scenario 1(S1) local tally is:
= no. of B - no. of W
= 2-1 = +1

PS: A reverse order of the subtraction is okay. But it is just the meaning of "+" and "-" is changed. In my case, "+" denotes B has more stones played than W in this local board; "-", B has less. If you reverse the calculation. "+", W has more; "-", W has less.

### Step 2 - Find local tally if W plays first

Local Board - W first

B plays 2 stones; W 2.

So Scenario 2(S2) local tally is:
= no. of B - no. of W
= 2-2 = 0

### Step 3 - Comparing differences in local tally

Local Board Position

Finally we have to find the local tally in the above position overall.

So this position(P) local tally is:
= S1 local tally - S2 local tally = (+1) - (0) = +1

You may wish to read the /old version if you feel this explanation still baffles you.

### Local Tally and Miai Counting

Local tally is used in the calculation of miai counting. Simply speaking, there is a formula

Click on [301] for details of each concept.

### Some Other Use of Local Tally

Local tallies are an accounting device that help to understand the effect of play on sub-boards that is not alternating play. Or, to say it another way, they count tenuki plays, in such a way that, for example, Black's tenuki and White's later tenuki cancel out against each other.

Since the opening few plays of a game usually consists of a number of tenuki plays considered from the point of view of 10x10 corners, 'local tally' is a rather more deeply-rooted idea. If Black makes a corner enclosure with two plays before White intervenes, that counts as tally Black x2, or BB. It may be much later in the game that either player adds to the corner: if there is a sente sequence for Black or for White played out there, the local tally will remain as BB.

That is, both BBWBWBWBWB (means a sequence White then Black, four times, added to a BB position) and BBBWBWBWBWBW reduce to the tally BB for this region of the board. Any sequence of BW or WB leaves the tally unaffected. [1]

On the other hand a gote sequence will change the tally. From BBWBWBW we have White playing in gote against Black's position. In the end the tally reduces to B only. And likewise a black gote sequence here, like BWBWBWB, changes BB into BBB. [2]

[301]

Local tally is related to miai counting and deiri counting. Read the following for details:

[1] This is all watertight mathematics, by the way, as a type of single-entry book-keeping.

kokiri: A question - to my understanding this seems to rely on the idea that the moves are in some way commutative - i.e. BBBWW is equivalent to BWBWB. Is this true, as it seems a bit of a sketchy proposition to my mind? Or is there an implication that if BBBWW can't equate to BWBWB somehow, then white shouldn't have bothered playing in that area (twice)?

Charles The idea here is to evaluate the result in one part of the board (not how you got there) in terms of each players' investment of stones there. When is this a sensible or even useful thing to do? It is plausible in cases where the background on the rest of the board promises 'plenty of big points left' (so the ambient temperature stays pretty well constant), and also the players are jumping about a fair amount rather than settling local fights and only then moving on. For example, a well-played ko fight in the middle game, which isn't game-deciding in itself. Perhaps you can say that in such situations you have to use local tally, to get a grip on a rather fluid 'market' of things to do on the board.

[2] Doesn't this whole section just boil down to: "Local Tally is the difference between B and W moves on a sub-board." Or what am I missing here? -- Sebastian

Yes, you could say it does. Charles

Well, you might wish to start with a position that had unequal numbers, and then play from there, for example in a yose problem. Then the local tally would normally refer only to plays after the starting position. -- Evand

Thomas55?: I don't quite get it : does local tally include tenuki plays and ko threats ? It seems to include tenuki, as said in this page, put not ko threats, since the local tally is 3 : 1 to connect the ko, 2 to take and win the ko IGNORING A THREAT.

Bill: As I understand it, local tally is Charles's term for, as Sebastian put it, the difference between B and W moves on a sub-board (between two positions). Since a tenuki is , by definition, not local, you do not count tenuki. OC, you may have a sequence of play between the two positions you are comparing in which there was a tenuki, but you do not count the tenuki play itself.

As for ko threats, the sub-board does not have to have a single region. The sub-board for a ko along with a ko threat may have two regions, one with the ko and one with the threat. In that case you do count the plays in the region of the threat. So in your ko fight example you are comparing two postions, one after, say, White wins the ko, and one after, say, Black takes the ko, White plays a threat, Black wins the ko, and White completes the threat. We have to include White's last play because it is a sufficiently hot play in the sub-board. (If it were not hot enough, it would not be a threat.) In this case you may verify that the local tally is 1.

OTOH, suppose that White plays tenuki instead of making a ko threat. Then our second position is reached this way: Black takes ko, White tenukis, Black wins ko. Now the local tally is 3.

Es claro?

Local tally last edited by PeterHB on August 6, 2007 - 19:03