Ladders are a rare method of attacking the opponent's dots. A ladder attack is possible when both players' dots are positioned in a certain way. Consider the situation of an endless attack by the blue dots on the red dots (Fig. 1). This attack can continue to the edge of the field. The blue dots are always one dot short of encircling the red dots. Figure 1 – Endless attack situation (gif animation) Blue dots, when attacking endlessly, will ultimately fail to encircle. Conversely, red dots can create forks against blue chains in several places (Fig. 2). Figure 2 - Options for creating forks against blue chains Conditions for successful ladder construction However, if a blue dot stands in the path of the endless attack, the blue dots will be able to encircle the red chain. This dot, toward which the ladder is directed, is called the target dot. The range within which the blue dot must be is limited (Fig. 3). If the ladder is directed toward the dot pointed to by one of the red arrows, the ladder will miss and will not be able to complete the encirclement. The ladder will also miss if the blue dot is even further from the ladder's direction of travel. Figure 3 - Successful (green arrows) and unsuccessful (red arrows) ways to create a ladder If you lead the ladder to the dot indicated by one of the green arrows, the ladder will end surrounded by a red chain (Fig. 4). You can also lead the ladder not only to individual dots, but also to chains of related dots. Figure 4 - Example of a ladder (gif animation) An obstacle from a red dot on the ladder's construction path will prevent it from being built (Fig. 5). Similarly, the presence of a red dot in a cross will prevent the ladder from being built (Fig. 6). Figure 5 - Successful (green lines) and unsuccessful (red lines) options for creating a ladder in the presence of an obstacle Figure 6 - Successful (green arrow) and unsuccessful (red arrow) variant of creating a ladder in the presence of a red dot Adjusting the direction of the ladder Let's consider a situation where the blue dot isn't in the ladder's path, meaning the ladder will miss and not end in encirclement (Fig. 7). However, there's another blue dot behind the blue dot. Then, the first blue dot can be used to adjust the ladder's direction, and the ladder should be directed toward the second blue dot (Fig. 8). Then, the ladder will end in encirclement. Figure 7 - The ladder will miss the blue dot Figure 8 – Adjusting the direction of the ladder (gif animation) Using the ladder for a different encirclement It's possible to create a ladder against your opponent's dots, which will fail (effectively resulting in an endless attack), but you can use one of your chains to create another encirclement against other opponent's dots (Figs. 9, 10). However, your encirclement chain must not have more than one gap, meaning your other encirclement will be built one turn after you create the ladder. This is because attacking ladder chains are easily broken by forks. Figure 9 - The ladder attack on the red dot will fail, but one of the blue chains will be used to build another blue encirclement Figure 10 - Using the ladder for another encirclement (gif animation) Strengthening a branch with the ability to create a ladder Instead of the usual strengthening of a branch during a branch struggle, you can strengthen the place where the opponent might pass by placing a dot away from the branch, but along the path of the ladder (Fig. 11). Figure 11 - Strengthening a branch using the ladder feature Protecting a branch with a ladder The ladder can be used to protect your branches (Fig. 12). Figure 12 - Examples of protecting a blue branch using a ladder (gif animation) One-sided ladder Consider the situation of a one-sided ladder, similar to a regular ladder, where a red and blue chain are formed, but a second blue chain is missing (Figure 13). This situation allows one blue dot to attack the red chain, thus forming a second blue chain (Figure 14). The two blue chains ultimately surround the red chain, and the surrounding area is shaped like a regular ladder. Figure 13 - Situation for using a one-sided ladder Figure 14 – One-sided ladder (gif animation) The ladder is against you If you get caught on a ladder, don't continue it, quit immediately, otherwise you'll lose a lot of dots.
A substitute dot is one or more dots you give up to your opponent to quickly gain a positional or game-score advantage (Fig. 1). Substitute dots are used in both attack and defense. Figure 1 - The general principle of using substitute dots: the blue branch gives the substitute dot to the red branch, which is forced to take it into the net and in doing so slows down When you give your opponent a substitute dot, he shouldn't have a choice. He must take it, otherwise his position will worsen even further (Fig. 2). If you miscalculate the execution of the substitute dot, your opponent won't take the dot, and you'll lose it without any benefit to yourself. Figure 2 - Examples of using substitute dots (gif animation) Provoking an opponent to a substitute point Often, in a struggle between branches, it's difficult for the attacking branch to encircle the defending branch. If the score is tied, the defending branch can be forced to give up the dot to improve its defensive position. However, the attacking branch can capture the substitute dot, take the lead, and then go on defense (Fig. 3). The defending branch will interpret this as a substitute dot being taken for defensive purposes. But that's exactly what the attacking branch wanted. Figure 3 - The red branch makes a substitute dot to improve defense, the blue branch takes this dot into a net and goes on the defensive (gif animation) Substitute tails in the struggle of branches Often, attempts to break through an opponent's branch fail, and your tail ends up caught in the net and not completely surrounded (Fig. 4, 5). When attacking further with another of your branches, you can use the threat of connecting with your tail in the net to improve your attacking position. Figure 4 - The blue branch takes the red tail that has broken through into the net (left), the main red branch tries to bypass from the outside and uses the threat of connecting with the red tail that has been captured into the net to improve its attack position (right) Figure 5 - An example where the attacking red branch uses a substitute tail to capture blue dots. The blue branch is forced to capture the substitute tail's dots. Without the substitute tail, the red branch would not have surrounded the blue branch in this situation (gif animation)
Often, during branch struggle, situations of mutual encirclement arise, when both players attempt to surround each other on the same section of the board (Fig. 1). Often, a single-dot advantage can be decisive, meaning one player will encircle the other one move earlier. Figure 1 - Examples of situations of mutual encirclement during the struggle of branches An example of a mutual encirclement situation Let's consider an example of a branch battle situation in which mutual encirclement will develop (Fig. 2). The emergence and development of mutual encirclement depends on the actions of the players. Figure 2 - An example of a situation in which mutual encirclement will develop. The blue branch is trying to encircle the red branch. The red branch defends itself, and the blue branch penetrates the gaps in the red branch. The red branch attempts to encircle the penetrated blue dots. The blue branch has many moves left before encirclement, so it must defend itself and prevent encirclement (Fig. 3). Figure 3 - The emergence of a mutual encirclement situation. The red branch attempts to encircle the blue dots that pass through it. The red branch takes the infiltrating blue tail into the net. The blue tail must try to break the red branch before the blue tail is completely surrounded. The blue tail has two moves to break and surround part of the red branch. The red branch has three moves left to surround the infiltrating blue tail. Therefore, the red branch begins to defend itself (Fig. 4). Figure 4 - Blue tail tries to break the red branch, which is defending itself from breaking But the red branch defends itself against the break attempt and can encircle the blue tail one move earlier. Then the main blue branch resumes its attack on the red branch (Fig. 5). Figure 5 - The red branch defends itself from the break, the main blue branch continues the attack Next, the red branch breaks another blue branch. The main blue branch continues its attack and attempts to connect with the third blue branch (Fig. 6). The struggle continues... Figure 6 - The red branch breaks the second blue branch. The main blue branch continues its attack towards the third blue branch.
Move reduction is forcing your opponent to spend his moves closing gaps in his branches, while you also close gaps in your branches (Fig. 1). Forcing means that your opponent has no other choice, otherwise they will worsen the position of his dots (Fig. 2). The goal of move reduction is to increase the chances of encircling your opponent. By reducing moves in remote areas of your branch, you can improve your position at the end of the branch. Figure 1 - During a branch struggle, gaps are formed in the branches (left), the attacking red branch makes a reduction in moves and the blue branch is forced to close the gap (center), the attacking red branch has fewer moves left before encircling the blue branch (right) Figure 2 - During the struggle between branches, gaps are formed in the branches (left), the attacking red branch performs a reduction of moves, but the blue branch does not close the gap, but strengthens the end of the branch (in the center), the red branch passes through the blue one and surrounds it, the blue branch saves the end of the branch from being surrounded (right) Since both players are closing gaps in their branches, you should reduce your moves when you have a better chance of encircling your opponent first in a mutual encirclement situation. If you are fewer moves away from encirclement than your opponent, you need to focus on protecting your points from encirclement (Fig. 3). Figure 3 - In a mutual encirclement situation, the blue branch has fewer moves before completing the encirclement (left), the red branch makes a reduction in moves, but this is in the hands of the blue branch, which will complete the encirclement faster (center), the correct choice for the red branch is to try to break the blue branch at its weakest point and escape from the encirclement before it is too late (right) Methods for reducing moves Moves can be reduced by creating a threat of breaking through the opponent's branch or encircling part of it. This can be done through standard attacking situations: forks, nets, and sacrifices (Figs. 4-5). Figure 4: The blue branch shortens its path by threatening a fork, forcing the red branch to strengthen. The blue branch's number of gaps decreases by one, while the red branch's number of gaps remains the same (gif animation) Figure 5: The red branch shortens its path using the threat of encirclement through the potential net on the blue branch, forcing the blue branch to strengthen. The number of gaps on the red branch decreases by one, while on the blue branch, it remains the same (gif animation)
Forecasting the situation on the field is one of the most important components of the game. The ability to make accurate predictions many moves ahead will greatly improve your performance. Forecasting involves calculating moves in local situations and predicting how the situation will develop across the entire field. Determining the best position in a local situation In local situations (situations within a small area of the board), you must calculate the situation several moves ahead—every move you make and every move your opponent makes. You need to calculate the most likely scenarios for how the situation will unfold. After you or your opponent makes a move, you need to adjust your forecast. If the game moves to another part of the field, you need to remember your prediction for the current part of the field so that you don’t have to recalculate it later. After forecasting a situation, you need to connect it with forecasts for other local situations related to the current situation. You also need to connect the local situation forecast with the overall field forecast and your goals for the game. Determining the best position on the field Let's consider the position of branches on the board as an example. Draw paths between adjacent branches of the same color and calculate their length in cells (Fig. 1). It's best to attack the opponent's branch that requires fewer dots to encircle than the same opponent's branch requires to connect to another adjacent opponent's branch (Fig. 2). Figure 1 - Branch struggle situation in the field (left) and assessment of the position of branches (right) Figure 2 - The best places for the blue and red players to attack each other You won't have time to calculate which position is better or worse in a game, so you have to judge the quality of a position by eye and experience. When determining a position, you should also consider the proximity to the edge of the field. Correctly determining the best position doesn't guarantee a successful attack or defense. Opponent's mistakes Every player makes mistakes in the game, ranging from serious to innocuous. Serious mistakes can impact the outcome of the game. The better you play, the fewer mistakes you make. Innocuous mistakes are often not considered mistakes, and only strong players notice them. In every situation, you must choose the best move; the others will be incorrect. However, there are often several equally good moves, and any of these moves can be considered inconsequential. It's worth taking advantage of your opponent's mistakes, but you can't expect them to unless you've exhausted all the options in the game. When you move in the hopes of your opponent making a mistake, it's usually obvious, and the likelihood of your opponent making a mistake is minimal. Therefore, for you, this move will be a mistake. Mistakes often affect the outcome of a game to the disadvantage of a weaker player, as they are less likely to take advantage of an opponent's mistake and more likely to make one themselves. But even stronger players often lose to weaker players because of their own mistakes.
The game often presents a choice between gaining a better position and capturing dots. The player who gives up dots assumes they will gain a better position and later regain their lead. The other player is given the option of capturing dots but worsening the position of their branches, or not capturing dots and improving their position. The choice depends on the prediction and the players' abilities (Fig. 1). Figure 1: The red branch sacrifices a dot to the blue branch and gains a good position to attack the blue branch. But the situation is difficult to predict (gif animation) The influence of forecast on actions in situations If a player is defending and his dots are predicted to be surrounded, then it is permissible to sacrifice these dots to the opponent in order to protect most of the dots. If a player is attacking and is predicted to surround the opponent's branch, then it is permissible to sacrifice individual dots to the opponent. If sacrificing dots isn't necessary for a successful defense or attack, then it shouldn't be done. If sacrifices won't help attack or defend, then they shouldn't be made either. The influence of players' abilities on actions in situations If your opponent defends well and attacks poorly, then don’t give him dots, but if he gives you an opportunity to capture them, take advantage of it. If your opponent is a good attacker (such players are also good defenders), then give him dots only when you are ahead, and if he gives you an opportunity to capture, don’t take them, but improve your defense. If you have a good defense and a weak attack, then take this dot. If you need a win and the opponent is strong, then take it. Many players play this way: they force the opponent to lose the dot and then switch to defense. Move on time Some moves can be made earlier than necessary, others later. But some moves must be made at the right time—not earlier and not later, but precisely when they are needed. When considering a move, consider whether to make it now or postpone it. If a move doesn't bring significant benefits at this point in the game, it's better to postpone it.
Typically, in a local situation, a player can make several moves with nearly equal effectiveness. There are two points to consider here: In a complex situation, several local combinations combine to form a more complex one, making it difficult to find the right move. But often in such situations, there's one obvious move. With experience, you'll be able to quickly find such a move. To learn effectively after your games, watch replays and analyze the moments where you struggled to find the right move. These situations should be memorized so you don't repeat them in future games. Branch complexity Creating simple branches also helps improve your performance. Simple branches reduce the likelihood of you getting confused in your own dots, which an experienced opponent can exploit. With a simple branch, you're in control—you're confident the branch is impassable and don't overthink it. However, many players make mistakes when constructing branches: Therefore, try to make branches that are understandable to you, with maximum simplicity and protection. Correct construction of branches When constructing branches, avoid unnecessary gaps and strive to increase the branch's length and the area covered (Fig. 1). In rare situations, it is permissible to create unnecessary gaps when this improves the defensive position (Fig. 2). Figure 1 - Examples of incorrect (left) and correct (right) branch construction Figure 2 - Examples of justified creation of extra gaps in a branch (gif animation) It's recommended to build branches in a single direction (Fig. 3). If a branch splits into two or more directions, it becomes less effective. Splitting a branch is acceptable when protecting a branch from surrounding enemies, especially if it's possible to sacrifice several dots. Figure 3 - Examples of incorrect (left) and correct (right) branch construction (gif animation)
Pushing back an abstract attacking branch (stretching) is used as an element of abstract defense against an opponent's attacking branch. The goal is to stop the opponent's branch from advancing locally and force them to attack at a larger radius, where you can continue your defense (Fig. 1). The ultimate goal is to make encirclement of your branch impossible. Figure 1 - A blue abstract branch surrounds a red one, the red branch tries to break and push back the blue one (left), the blue player builds a new abstract attacking branch at a larger radius, the red player tries to break it again (right) Let's consider an example of a break in an attacking branch in a local situation on a small area of the field (Fig. 2). Figure 2 - A local situation in which an abstract blue branch attempts to encircle a red one. The distance between the blue dots is 2 moves. The red branch's goal is to increase the number of moves between adjacent blue dots. This doesn't necessarily mean increasing the distance between the two blue dots in question; it could be the distance from the two blue dots in question to other blue dots. This pushes the attacking blue branch toward the edge of the board (Fig. 3). Figure 3 - Examples of the red branch pushing aside the blue one (gif animation) In this area, the situation transforms from an abstract attack into a struggle of branches. As long as you can push back your opponent's branch locally, you must maintain that situation. When your options for pushing back your opponent's branch are exhausted, you must break and push back his branch elsewhere. You must learn to consider such situations not only by considering adjacent dots, but also dots along a larger stretch of your opponent's branch and your own. You should first break your opponent's branch in the easiest places to do so. Blocking an abstract attack branch If an opponent's abstract attack branch attempts to penetrate your branch, it can be blocked. If your line has at least two defensive directions, an opponent's branch entering from one direction is blocked from the second direction (Fig. 4). Figure 4 - Example of a situation (left), the attacking blue branch enters from one direction and is blocked in the second direction (center and right) The defending branch can have large gaps between dots and still block the attacking branch (Fig. 5). When the attacking branch is blocked, no matter which direction it moves, it will be unable to pass (Fig. 6). Figure 5 - An example of the red branch blocking the attacking blue branch (gif animation) Figure 6 - Blue branch is blocked Breaking of an attacking branch during a struggle between branches In a branch struggle, a poorly constructed branch can be torn apart using forks. But the better the branch is constructed, the more difficult it is to tear apart. Some attacking branches cannot be torn apart. Sometimes, well-constructed branches can be torn apart, but not immediately, but after preparation (Fig. 7). However, one must assess the situation and be confident of success. Figure 7 - An example of the red branch breaking the attacking blue branch after 20 moves (gif animation)
When one player's plans fail, he is forced to resort to other actions to achieve a result. Let's consider backup plans when one player fails in the battle of branches. When a blue branch breaks a red branch, the red branch must build an even denser branch over the break (patch the break) with fewer breaks, making it even more difficult to break (Fig. 1). The blue branch must prevent the fragments of the red branch from joining at the break and further breaking it. Figure 1 - Blue branch breaks red branch (left), red branch tries to fix the break (right) If the blue branch doesn't allow the red branch to bypass it and becomes landed, the red player is left to attack the second blue branch (Fig. 2). The second blue branch must defend itself using the known methods. Figure 2 - Blue branch landed (left), red attacking another blue branch (right) If the blue branch doesn't allow itself to be surrounded, connects with another blue branch, and surrounds the red branch, then the red branch must continue moving and surround all of the blue player's dots (Fig. 3). The blue player should continue defending in the easiest spots and the fastest way to land. Figure 3 - Blue branches capture a red branch (left), another red branch continues the attack (right) If a red branch connects to another red branch and captures a blue branch, the blue player is left to attack the red encirclement region from all sides of the field (Fig. 4). The red player needs to land in places where this is easier to do. Figure 4 - Red branches capture blue (left), blue attacks from all sides of the field (right)
At the edge of the field, some techniques don't work, others change, and still others are unique. These techniques apply to both defense and attack. When defending branches, players typically move them to the edge of the field, where the branch is more difficult to surround. The edge is used to stop the opponent's branch by setting up a block, net, or a second line of defense (Fig. 1). Figure 1 - Options for stopping the advancement of the red branch at the edge of the field If you are attacking an opponent's branch that is heading towards the edge of the field, you need to quickly get around that branch so that they cannot successfully use the edge of the field for defense. The struggle of branches to the corner of the field Consider a situation where the red branch is trying to pass the blue branch at the edge of the board. If both branches move without gaps, they will reach the corner of the board and stop, preventing the red branch from passing the blue branch (Figure 2). If the red branch jumps to pass the blue branch, the blue branch will ground itself and be blocked (Figure 3). Figure 2 – Struggle of branches towards the corner of the field (gif animation) Figure 3 - The blue branch is landed after the red branch jumps (gif animation) Defense at the edge of the field If the red branch wants to pass the blue branch near the edge of the field and there's a red dot in the way of the two branches' struggle, the red branch will use it. Then the bypass will be successful (Fig. 4). To prevent this, the blue dots perform a combination specific to the edge of the field (Fig. 5). Figure 4 - The red branch bypasses the blue branch with the help of an additional red dot (gif animation) Figure 5 - The blue branch can stop the red branch in three ways (gif animation) If the red dot is even closer to the red branch, the blue combination won't work (Fig. 6). Then, the blue team has the option of trying to capture the red dots in the net (Fig. 7). If the blue team's dots are poorly positioned and capturing the red dots in the net won't work (this must be predicted before using the net), a second line of defense can be built instead (Fig. 8). Figure 6 - The blue branch can't stop the red branch (gif animation) Figure 7 - Blue branch makes a net of red dots (gif animation) Figure 8 – Blue player builds a second line of defense (gif animation) There are also other defensive combinations at the edge of the field, where the blue branch can stop the red branch from passing (Figs. 9, 10). These combinations often involve substitution dots—the defending player gives up one or more of his dots to prevent the opponent from passing. Figure 9 - Blue branch stops the red branch from passing (gif animation) Figure 10 - Blue branch stops the red branch from passing (gif animation) Attack at the edge of the field In some situations, the attacking branch gains an advantage when attacking at the edge of the board. This is because the defending branch will not have enough space to break the attacking branch (Fig. 11). Therefore, the attacking branch can attack with a gap between dots that is one cell larger (Fig. 12). Figure 11 - The attacking blue branch cannot be broken at the edge of the board, but if the edge of the board were further away (at least one cell), the blue branch could be broken or pushed back with a fork Figure 12 - The difference in attack of a blue branch on a red branch between the edge of the field and a place away from the edge of the field (at least one cell further) (gif animation)
