# The digital method and the number of method?-- -- -- -- -- - go in the beauty of mathematics

just learn chess a lot of friends asked me, go inside to determine the outcome, the number of rules and son, Japan and South Korea, then the method of these two species?If the three countries play different go?Even have a friend for years under the chess have the impression, is the number of children and number come out the result is not the same.Some I have great respect for professional master JiangQi also said: "because this dish chess is South Korea rule number method, so the children died in vain in somebody else's empty lost" and so on.Under number method actually died in the somebody else is lost in the air, but under several sub method is also lost, because it might at least be a single officer.It should be said that the number of the son and number method is substantially the same, let me explain below.

first of all, Chinese rules and should's rule number of method is not a pure number method, a more accurate statement is "son empty all ground" (the ancient pure number method does not need the concept of "empty", not table).Black and white is the final score is calculated by counting their son and surround the empty.And the number of the method is to calculate their own around the empty minus the death of their son (or their surrounding empty and the other side of the dead child).Shown in the following table.

 black white number method black son live + black empty child in + white empty number method black empty - the black death child white empty - white dead child

the two columns of table do subtraction, respectively the number of the method is based on the method of minus (+ dead son live).Under the living child + death is actually a total number of hand in hand on the board.That is to say, the number of children the results and the number of if and only if both black and white as the total number of hands.Because the game is one of his, so both sides of the total number of hand should be the same, so I should say that this two kinds method is substantially the same, so you generally don't have to worry about because the law changed a few results are different.Due to the smaller number method figures, so the game when the situation judgment are generally the number method.

so what cases both sides hand number will be different?Here are several kinds of common situations.

1) the charge after the first.

black charge after the first one of the most common causes of both hands several different situations, on average every two sets will occur.As the black go first, if the final step in single officer is also a black out, black hand number will be more than white hand.So if not stick mesh/child, black and a little cheaper.It is said that in the tang and song dynasties is not admitted to the interests of the black charge after the first, then to the Ming and qing dynasties in order to avoid the frequent draw gives admit again.

let's talk about why Japan and South Korea rules as long as the black stick to six and a half, while China rules to black stick son 3 and 3/4.Board a total of 361 points, is a singular, so if after the dish of what number is the number that black, on the other hand is white after closed.If black disk 7 orders, is black in the rules of Japan and South Korea won, but in China the rule black lost, because after the disk is white, 7 orders.China rules need to be black disk 8 orders didn't win, that's why we sometimes ShuiTie 3 and a half and 3/4 equivalent to stick son 7 orders, of course black's pressure is bigger than stick to 6 orders and a half.However, if the Chinese rules to stick a 3 and a quarter of the son, they won the black as long as the disk 6 orders, that is only about five and a half orders, black and too easily.So although generally reflect the post 3 and 3/4 of black stressful, but under the digital method also can saying is a kind of helpless, because the digital method can't realize the black stick to 6 orders and a half.

 disk after , Japan and China black five orders white Bai Sheng half 1 Bai Sheng 1 1/4 child black more than 6 orders black Bai Sheng half an eye Bai Sheng 1/4 child black more than 7 orders white black - half an eye Bai Sheng 1/4 child black more than 8 orders black black wins and 1 half black - 3/4 child

also need special attention is, if the board appears a eye double live such special circumstances, there is a point both sides cannot be accounted for, so they became dual board.Then stick 3 and a half and 3/4 and to stick son 6 orders.That is to say, a (singular) any eye double living situation, black is cheap, 1 or white lost game 1.

2) to connect

let connect several different obviously also leads to both sides of the hand, because black first on board who posed a few child and then a hand start.But owing to generally let connect both sides is a big gap between the strength, and to connect the result is not important, the results generally so this influence often ignored.In fact, to connect the white if using digital method is harder to win than number method, it is easy to understand.There is a solution: if n is connect, then black should stick son also n / 2 white, such as basic and number is consistent with that method.But we also can think that the digital method truly reflect who won and who lost, this is not right or wrong.But we need to know is that this number and the number of results is not the same.

3) stick after takeover

in just a few rules, is a special kind of method is called after the takeover.That is, when the board is left in my hand of plunder and several single officer, I didn't stick, first and charge sheet first officer, in the process that the advantage of material has walked with the bullet.When I closed my last a single officer, to mention again, forcing each other because there is no hook material and stop, and then I stick hook.Is called special means, because it need we have a lot of bullet material (more than half the number of single officer and the other side of the number of materials), and the number of single officer must be singular.Game, though, rely on the stick after the takeover reversal wins examples also occur frequently.

stick after the takeover from the point of view of "eye" no cheap, so under the rules of Japan and South Korea have no this kind of means.But, when each other because there is no time of material and stop, both the number of hand balance is broken, that is to say by this means can get cheap "son", special circumstances can even cheaper for child.

several method to go here more change, and the number of rules is relatively stable.

4) plate angular four

"plate angular four, rob is dead", this sentence will go should all know (if you don't know, now know that).Disk angular four this chess particularity lies in the fact that plate angular four although itself is rob, but kill chess party can choose to open the timing of the hook, and dirt.This means that he can wait until all the other side of the hook material to fill out, and then open again, let the other side did not fight back.But, when you fill in your empty of material, the other party may recruit not stopped, it's also the hand count the difference of both sides.The son, in his empty for several method has no effect, but for number method go a loss 1 eye.In order to make the result like number method, rules are Japan and South Korea, once appear, plate Angle of four piece of chess, dies as a net, that is to say, don't need to fill material and then eat it.Things here and even settled satisfactorily originally, but didn't expect unexpectedly some of material is also not to drop the tonic, such as double work.You can't in order to fill material of the first double living to die?Since you won't, so each other are likely to put their own double live to die when the bullet.That is to say, in accordance with the rules of China plate angular four combat decision, if you have any double living on board, plate angular four side is possible to obtain certain compensatory, even do work.The number of the method to determine the plate angular four could solutions on these problems are too rigid.Fortunately, almost did not appear in the professional game there are both plate angular four and double living situation.

to summarize, the number of method with digital method is largely the result of the same, you can safely use exchange.But to say the two identical words need to have a very tough conditions, is the same number of black and white on both sides, that is to say, can't is black, also cannot stop for any one party.Along the way of thinking, we can rationalize some subtle differences between the game rules and the reasons behind.Of course, there are a lot of there is no discussion, such as eye double live mesh decision problem, but it was a pure concept different problems, rather than the digital and the number of the intrinsic nature of the problem.

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Date：2016-12-13