According to the official rules, the size of the field is 39 dots in width and 32 dots in height, which is equal to the size of a standard notebook sheet (a tribute to tradition). Starting position At the beginning of the game, there are several dots on the board, called the starting position. Most often, there are four dots on the board at the beginning of the game; this starting position is called the initial cross and is usually denoted by an X (Fig. 1). A starting position can have four initial crosses, spaced apart, called 4Xs (Fig. 2). Figure 1 - Starting position initial cross (X) Figure 2 - Starting position four initial crosses (4X) Progress and end of the game You play with red or blue dots against one opponent. Players take turns making moves. A dot is placed at the intersection of lines, called a point. Once placed, dots can no longer be moved. In the game, you must surround your opponent's dots and prevent them from surrounding yours. The player who captures the most dots wins. A tie for the same number of captured dots results in a draw. Figure 3 - Example of the start of the game, when the dots are surrounded, the encirclement region is painted (gif animation) The game ends in the following cases:
To construct an encirclement, you need to arrange a sequence of dots in which the distance between adjacent dots must be equal to one cell. Dots can be adjacent horizontally, vertically, or diagonally (Fig. 1). Figure 1 - Adjacent dots with a distance of one cell between them If the distance between two dots in a sequence of dots is greater than one cell, then it is impossible to draw an encirclement through such a sequence (Fig. 2). Figure 2 - Dots with a distance of two cells between them Encirclement When your sequence of dots becomes closed and contains your opponent's dots, an encirclement is formed (Fig. 3). This encirclement may contain empty points and your own dots. For each captured dot of your opponent's, you receive one score. If your opponent has created their own encirclement, he will receive scores for your captured dots. Figure 3 - Example of an encirclement (gif animation) Captured dots can no longer be used in the game (Fig. 4). Figure 4 - Red dots cannot create their own encirclement because the red dot is inside the blue encirclement region and cannot be used You can capture not only individual dots but also entire groups of dots and your opponent's encirclement regions (Fig. 5). If you capture your opponent's encirclement region, your dots within the opponent's encirclement region are vacated, and your opponent loses scores for those dots. Figure 5 - Example of a simple and complex encirclement Encirclement trajectory According to the rules, if there are alternative trajectories, the encirclement is designed to fill the smallest possible area. You should strive to design encircles that follow a longer path (Fig. 6). This will improve the positions of your dots. Figure 6 - Improving the position of dots when surrounded (gif animation) Encirclement at the edge of the field Individual dots, groups of dots and encirclement regions cannot be captured if they are on the edge of the field (Fig. 7). Figure 7: The blue dots are located on the edge of the field and cannot be captured, even though they are surrounded by red dots on three sides. A red dot cannot be placed on the fourth side, as the position does not belong to the field. Houses If your closed sequence of dots contains no opponent's dots, a house is created (Fig. 8). Your house contains empty dots and may contain your dots. A house cannot be considered an encirclement. Figure 8 - Examples of houses Surroundings through houses Your opponent can move encirclement through your house. You can also move encirclement through your opponent's house. To do this, you need to place one missing dot of your encirclement in your opponent's house (Fig. 9). Figure 9 - Blue encirclement is built through the red house (gif animation) If you place a dot in your opponent's house but don't have enough dots to create your new encirclement, your dot is surrounded by your opponent (Fig. 10). Then, your opponent's house becomes your opponent's encirclement region. Figure 10 - The blue dot is placed in the red house and is automatically surrounded (gif animation) Unfinished encirclements There are often cases where you surround your opponent's dots, but the encirclement isn't complete yet (Fig. 11). If the opponent can't escape, it's better not to complete the encirclement and save it for later. This is because while you're completing the encirclement, the opponent will be placing his dots elsewhere on the field. This means the opponent can create a threat to you elsewhere if you don't react in time. Figure 11 - Examples of unfinished encirclements where the opponent cannot escape from the encirclement
Your dots on the board had to be connected. Just as a single dot is no match for another, so a single dot is useless without connections to other dots. You need to build your game based not on individual dots, but on entire groups of dots. Your dots can be located either close or far from each other. The general term for dots connected by a common tactical and/or strategic objective is a branch. Specific manifestations of a branch include tails (small, undeveloped branches), chains, walls, forms, and clusters. Chains (branches without gaps) Adjacent dots of the same color form a chain. The distance between dots is one cell. A chain where all dots are connected only horizontally and/or vertically is called a wall. These are the simplest dot constructions (Fig. 1). Figure 1 - Types of chains Branches with gaps Your branch may have gaps, that is, distances between adjacent dots that exceed one cell (Fig. 2). Figure 2 - Branches with gaps Branch gap sizes When constructing branches, it's advantageous for each branch to allow you to control a large area of the field. To achieve this, you need to increase the gaps in the branches (Fig. 3). Figure 3 - A branch of 10 dots with different gap sizes Abstract branches and clusters When the gaps in a branch are greater than three dots, the connections between the dots remain only in your head; such a branch becomes mental, abstract. If you place dots with large gaps between them and each dot is connected to several others, the resulting branch takes the form of an abstract cluster. Such branches are the most complex dot constructions (Fig. 4). Figure 4 - Abstract constructions Branches construction It's recommended to construct the branch consistently in one direction (Fig. 5). If you don't place the dots sequentially, large gaps will appear that an opponent might try to penetrate. Figure 5 – Branch construction sequence (gif animation)
Through gaps in your branch, an opponent can build their own branch and then surround yours. The fewer gaps in your branch, the more difficult it is for the opponent to pass through it. However, the fewer gaps in a branch, the smaller the area of the field your line controls, meaning the opponent can surround your branch from the outside without passing through it (Fig. 1). Figure 1 - Your branch and your opponent's branch Impassable and difficult to pass connections of dots (forms) Let's consider the clusters of dots (forms) through which the opponent will in most cases be unable to draw their branch. Such clusters cannot be considered completely impassable, as in some cases the opponent can force you into a mistake. Difficult to pass are the connections of dots in branches (chains) in which the gaps between dots are 1-2 cells (Fig. 2). Figure 2 - Examples of difficult connections between dots Therefore, it is recommended to construct difficult-to-pass branches (chains) with gaps of 1-2 dots (Fig. 3). Figure 3 - Main types of difficult to pass branches (chains) When an opponent attempts to penetrate your branch, you need to close the gaps in the branch. This will allow you to surround the opponent's dots as they attempt to break through. Surrounding the opponent's dots on only one side of your branch is sufficient to prevent them from building interconnected tails (Fig. 4). Figure 4 - Examples of branch protection when an opponent attempts to pass it (gif animation)
If the red and blue branches are a few dots apart, they are free. If the branches are close together, they are struggling (Fig. 1). Figure 1 - Example of free and struggling branches The purpose of the struggle of branches The goal of branch struggle is to attack, defend, and gain a better position. During branch struggle, one branch attempts to bypass or bend another branch (Fig. 2). The attacking branch must travel a greater distance to bypass the defending branch. To achieve this, more breaks must be created in the attacking branch. Figure 2 - An example of a branch struggle, the red branch tries to surround the blue one (gif animation) The blue branch's goal when defending is to avoid being encircled and outflanked, then the red and blue branches will each control territory on their respective sides (Fig. 3). The red branch's goal when attacking is to encircle and surround the blue branch, then the red branch will control territory on three or four sides around the blue branch, meaning the red branch will be able to encircle the blue branch or, at a minimum, gain a better position on the field. Figure 3 - Players' goals in the branch struggle When attacking the red branch, the blue branch most often cannot afford to attack the red branch. This is because, if the blue branch is attacked, the red branch will complete its encirclement faster than the blue branch (Figure 4). Figure 4 - The red branch will surround the blue dots faster than the blue branch will surround the red dots. Defense during the struggle between branches Since the attacking branch creates more gaps between dots, the defending branch can try to break the attacking branch (Fig. 5). Figure 5 - Blue branch breaks the attacking red branch The attacking red branch may not allow itself to be broken. Then the blue branch should also try to create gaps between the dots to prevent being overtaken and push back the red branch (Fig. 6). Figure 6 - The blue branch pushes aside the red branch But if gaps form in the blue branch, the red branch can attempt to penetrate these gaps and connect with another red branch, encircling the blue branch. The blue branch must then contain the invading red dots and encircle them (Fig. 7). If this fails and the red branch prepares to complete the encirclement, then another blue branch can be built to protect its dots (Fig. 8). Figure 7 - The blue branch surrounds the red dots that have penetrated through it Figure 8 - Construction of the second line of defense The red branch can bypass the blue branch. Then, the blue branch can prevent the two red branches from connecting, and the blue branch can counterattack and connect with another blue branch. When the two blue branches connect, they will surround the red branch within the blue dots (Fig. 9). Figure 9 - The blue branch prevents itself from being surrounded, counterattacks, and connects with another blue branch Attack during the struggle between branches If the blue branch's defense fails, the red branch bypasses it and connects with another red branch (Fig. 10). This creates an encirclement, and the blue branch must try to break the red branch if that's still possible. Figure 10 - The red branch surrounds the blue branch and connects to another red branch The red branch can pass through the gaps in the blue branch. The red branch should strive to connect with the other red branch (Fig. 11). Figure 11 - The red branch goes through the blue branch and connects to another red branch Who will surround faster? A common situation is mutual encirclement, where two red branches connect and two blue branches connect during a branch struggle. This results in two incomplete encirclements, as both branches have gaps (Fig. 12). The first player to close the gaps in his branches completes the encirclement. Figure 12 - The player with the fewest gaps in the branches will create the encirclement Success in the struggle of branches Every attack and defense in a branch struggle can end in success or failure. Success depends on the specific situation and the strength of the opponents.
The most common situation in branch struggle is when the attacking branch attempts to outflank and bend the defending branch (Fig. 1). To do this, the attacking branch must travel a greater distance by making more gaps. Figure 1 - The blue branch is trying to bypass the red branch Technique for bypassing an opponent's branch If the blue branch wants to bypass the red one, but will repeat the moves of the red one, then it will not be possible to bypass it (Fig. 2). Figure 2 - The blue branch follows the red branch's movements, so it can't bypass it (gif animation) In order to get ahead of the red branch, the blue branch needs to make gaps (Fig. 3). Figure 3 - The blue branch makes gaps and therefore goes ahead of the red one (gif animation) But to encircle the red branch, you need to do more than just go ahead of it. The blue branch needs to bend the red branch. To do this, you need to block the red branch's path and force it to turn (Fig. 4). Figure 4 - The blue branch blocks the red branch's path and forces it to turn back (gif animation) Size and frequency of gaps when bypassing an opponent's branch The gap sizes in your branch when bypassing your opponent's branch should be 1 or 2 dots (Fig. 5). Figure 5 - Examples of the blue branch making a 1-dot gap (left) and a 2-dot gap (right) (gif animation) If the gap is larger than 2 dots, your branch can be interrupted (Fig. 6). This will make it difficult or even impossible to bypass your opponent's branch. Figure 6 - Blue branch makes a 3-dot break, red branch interrupts blue branch (gif animation) If you make frequent gaps in your branch or sharply bend your opponent's branch, he may break your branch with a fork (Fig. 7). Forks will be discussed in a separate article. Figure 7 - Examples of a blue branch attack that is too sharp and can be broken If your opponent creates gaps in his branch to protect it, you need to respond with gaps of your own. Depending on the situation, your gap should be one dot larger or the same as your opponent's gap (Fig. 8). Figure 8 - Examples of the blue branch's response when the defending red line makes gaps (gif animation) Protecting a branch when it is bypassed When someone tries to bypass your branch, the techniques discussed in the article on branch struggle will come in handy. To choose a defensive option, you need to predict the development of the local situation in your current position on the field and the overall situation on the field. Don't try to break your opponent's branch unless you predict it will work. If you fail to break your opponent's branch, you'll only make their branch stronger with fewer gaps. With fewer gaps, your opponent's branch will have fewer moves to encircle your branch.
When attacking or defending, gaps form in the branches. These gaps allow the enemy to successfully push their branch through and surround your dots or worsen their position. When the opportunity or need arises, you can spend a move or several moves strengthening your branches. Branches should be strengthened in the most vulnerable areas and in the most dangerous directions for enemy attack. Strengthening the abstract branch to an impassable one Since the gaps in abstract branches are larger than in regular branches, reinforcement should be done at the locations of the largest gaps. At the same time, an effort should be made to make the abstract branch impassable (Fig. 1). Figure 1 - Strengthening an abstract branch to an impassable one (gif animation) If the opponent's moves are made near an abstract branch, then the branch needs to be strengthened in places close to the opponent's moves (Fig. 2). Figure 2 – Strengthening the abstract branch in places close to the opponent’s moves (gif animation) When an opponent penetrates through an abstract branch, the branch's dots must be connected at the penetration point (Fig. 3). The penetrated dots must then be stopped and surrounded. Figure 3 - Surrounding the enemy's dots that penetrated through the abstract branch Strengthening an abstract branch to an abstract cluster The second option for strengthening an abstract branch is to construct an abstract cluster of points (Fig. 4). This will make it difficult for the opponent to pass through the branch. Figure 4 – Strengthening an abstract branch to an abstract cluster (gif animation) Strengthening a branch during branch struggle During a branch struggle, you should also strengthen the branch at the most likely points of enemy breakthrough. You should try to close more than one breakthrough threat with a single move, while maximizing the position of your dots (Fig. 5). When strengthening a branch, you should create conditions that will allow the enemy's dots to be easily surrounded if they break through. Therefore, well-fortified branches are rarely attacked. Figure 5 - Strengthening the blue branch during branch struggle
Landing is the connection of all its dots, which are part of the encirclement regions and branches, to the edge of the field so that they cannot be surrounded (Fig. 1). This means that all branches are transformed into walls (Fig. 2) and all dot connections are made impassable (Fig. 3). Figure 1 - Landing the branch Figure 2 – Landing process (gif animation) Figure 3 - Dot connections are made impassable (gif animation) When one player wishes to end the game, he connect all his dots to the edge of the field and declare "landing" (Fig. 4). If any dots remain unlanded, they are surrounded and the scores for them are given to the second player. Therefore, the first player can lose if he don't land all his dots. Figure 4 - The red player has landed all of his dots, the blue player will no longer be able to surround the red dots and will lose Not all dots must be landed. For example, if you're leading by 10 dots, you don't have to ground 9 dots. These 9 dots will be added to your opponent's score, but he'll still lose by one dot. It's important to be careful with your calculations and land only as many dots as necessary to win. When landing, you should also carefully review all dot connections and remember to make them impassable. Why is landing included in the rules of the game? Many beginners dislike landing, but it's included in the rules of the game. The right to land is a player's right to end the game with a positive result, without waiting for the empty points on the board to run out. The second player, if he want to achieve a positive result, must prevent the first player from landing. If a player is unable to prevent their opponent from landing, he is weaker in the game and must acknowledge this.
Creating a net is the primary technique for attacking enemy dots. The net involves encircling enemy dots or creating an incomplete encirclement from which escape is impossible. Creating a net The simplest net consists of three dots. If an opponent places a dot between these dots, he will be surrounded in one move (Fig. 1). Figure 1 - The simplest net (gif animation) Other simple nets also involve encircling the opponent or creating an incomplete encirclement from which the opponent cannot escape (Figure 2). Figure 2 – Simple nets (gif animation) Remember that your opponent will also make nets against you, so you need to anticipate them and not fall into them. Exiting a poorly prepared net Poor placement of blue dots will prevent the creation of a net for red dots (Fig. 3). Figure 3 – Output of red dots from possible nets (gif animation)
Forks are one of the basic techniques for attacking an opponent's dots. A fork implies that in a single move, a player can attack two or more groups of opponent's dots at once, while the opponent can only defend one group and lose the other. Weak opponents usually buy into simple forks. You need to understand how forks are made to prevent them from being used against you. In the situation where a simple fork is created, a blue dot penetrates between two red dots and can capture either of the red dots (Fig. 1). The red player can only defend one of their dots, so the blue player captures the other red dot. Figure 1 - The simplest fork (gif animation) More complex forks are made in several moves (Fig. 2). Figure 2 - Examples of forks (gif animation) The threat of creating a fork to gain a better position Strong opponents almost always anticipate a possible attack with a fork. Therefore, rather than a fork, they usually use the threat of one to scare off the opponent and gain a more advantageous position for their dots (Fig. 3). Figure 3 - Improving the position of the red dots by threatening to create a fork Fork protection If you're forked, you need to defend a more important group of dots (Fig. 4). Then your opponent will capture a less important group of dots. Figure 4 - The red player has defended a more important group of dots because it is in a cross with another red dot
