How to play sea battle on paper. The optimal algorithm for playing sea battle

In Game "sea ​​battle" the game is played by two people who take turns naming the coordinates of the ships on the opponent's map. If the coordinates are occupied, then the ship or part of it "sinks", and the one that has fallen has the right to make one more move.

The game takes place on a field of 10x10 cells of each player, on which a fleet of ships is located. Horizontals are usually numbered from top to bottom, and verticals are marked with letters from left to right. In this case, letters of the Russian alphabet are used from “a” to “k” (letters “ё” and “й” are usually omitted) or from “a” to “i” (using the letter “ё”), or letters of the Latin alphabet from “ a" to "j". Sometimes the word "republic" or "snow maiden" is used, since not a single letter is repeated in these 10-letter words. Since there are various options for setting the coordinate system, it is better to agree on this in advance.

The fleet consists of

* 1 ship - a row of 4 "four-deck" cells

* 2 ships - a row of 3 "three-ball" cells

* 3 ships - a row of 2 "two-deck" cells

* 4 ships - a row of 1 cell "single-deck".

When placed, ships cannot touch each other at the corners.

Ship decks should be built "in a line", and not with bends. The main thing: you cannot build the decks of one ship diagonally.

Before the start of hostilities, players cast lots or agree on who will go first.

The player making the move makes a shot - he calls aloud the coordinates of the cell in which, in his opinion, the enemy ship is located, for example, "K1!" .
If the shot hit a cell that was not occupied by any enemy ship, then the answer “Miss!” and the shooting player puts a dot on someone else's square in this place. The right to move passes to the opponent.
If the shot hit the cell where the multi-deck ship is located (larger than 1 cell in size), then the answer is “Wounded!”. The shooting player puts a cross in this cell on a foreign field, and his opponent puts a cross on his field also in this cell. The player who shoots gets the right to one more shot.
If the shot hit the cell where the single-deck ship or the last undamaged cell of the multi-deck ship is located, then the answer “Sunk!” or "Killed!" Both players mark the sunken ship on the sheet. The player who shoots gets the right to one more shot.

The winner is the one who first sinks all 10 enemy ships. The loser has the right to ask to study the opponent's playing field after the end of the game.

Violations

The player has his field drawn incorrectly: the number of ships does not comply with the rules; ships touch each other; incorrect field sizes and incorrect coordinate system.

The player made changes on his playing field that were not provided for by the rules of the game (during the game, you can only put dots and crosses and only according to the rules), for example, completed the missing ship, the player peeped at the location of the enemy ships or missed his move.

A couple of days ago I was surprised to learn that some of my friends do not know how to play sea battle. Those. Of course, they know the rules, but they play somehow haphazardly and as a result often lose. In this post, I will try to outline the main ideas that will help you level up your game.

Rules of the game

There are many options for naval combat, but we will consider the most common option with the following set of ships:

All listed ships must be placed on a 10 by 10 square field, and the ships cannot touch either corners or sides. The playing field itself is numbered from top to bottom, and the verticals are marked with Russian letters from "A" to "K" (the letters "Yo" and "Y" are skipped).

An enemy field of the same size is drawn nearby. In case of a successful shot at the enemy ship, a cross is placed on the corresponding cell of the enemy field and a second shot is fired;

Optimal Strategy

There is always an element of randomness in the game of naval combat, but it can be minimized. Before proceeding directly to the search for the optimal strategy, it is necessary to voice one obvious thing: the probability of hitting an enemy ship is higher, the fewer unchecked cells are left on its field, similarly, the probability of hitting your ships is the lower, the more unchecked cells are left on your field. That. to play effectively, you need to learn two things at once: optimal shooting at the enemy and optimal placement of your ships.

In the following explanation, the following notation will be used:

Optimal Shooting

The first and most obvious rule for optimal shooting is the following rule: do not shoot at the cells directly surrounding the destroyed enemy ship.

In accordance with the notation adopted above, in the figure, those cells on which unsuccessful shots have already been fired are marked in yellow, the cells on which the shots ended in a hit are marked in red, and the cells that were not fired on are marked in green, but it can be guaranteed that the ships there are no ships in them (ships cannot be there, because according to the rules of the game, ships cannot touch each other).

The second rule immediately follows from the first rule: if you managed to knock out an enemy ship, you must immediately finish it off in order to get a list of guaranteed free cells as soon as possible.

The third rule follows from the first two: you must first try to knock out the largest enemy ships. Perhaps this rule is not obvious to you, but if you think a little, you can easily notice that by destroying an enemy battleship, at best, we will immediately receive information about 14 guaranteed free cells, and by destroying a cruiser, only about 12.

That. the optimal firing strategy can be reduced to a targeted search and destruction of the largest enemy ships. Unfortunately, it is not enough to formulate a strategy, it is necessary to propose a way to implement it.

To begin with, let's consider a 4 by 4 cell area of ​​the playing field. If there is an enemy battleship in the area under consideration, then it is guaranteed to be knocked out in no more than 4 shots. To do this, you need to shoot in such a way that there is exactly one checked cell on each horizontal and vertical. below are all options for such shooting (excluding reflections and turns).

Among all these options, only the first two options are optimal on a field of 10 by 10 cells, guaranteeing a hit in a battleship in a maximum of 24 shots.

After the enemy battleship is destroyed, it is necessary to start searching for cruisers, and then destroyers. In this case, as you may have guessed, you can use a similar technique. Only now it is necessary to divide the field into squares with a side of 3 and 2 cells, respectively.

If you used the second strategy when searching for a battleship, then to search for cruisers and destroyers you need to shoot at the following fields (green indicates the fields that you have already fired at when searching for a battleship):

There is no optimal strategy for finding boats, so at the end of the game you have to rely mainly on luck.

Optimal ship placement

The optimal strategy for placing ships is in some sense the reverse of the optimal strategy for firing. When shooting, we tried to find the largest ships in order to reduce the number of cells that need to be checked at the expense of guaranteed free cells. This means that when placing ships, they must be placed in such a way that, in case of their loss, the number of guaranteed free cells is minimized. As you remember, the battleship in the center of the field opens 14 fields for the enemy at once, but the battleship standing in the corner opens only 6 fields for the enemy:

Similarly, a cruiser standing in a corner opens only 6 fields instead of 12. Thus, by placing large ships along the field boundary, you leave more room for boats. Because there is no strategy for finding boats, the enemy will have to shoot at random, and the more free fields you have left by the time you catch the boats, the harder it will be for the enemy to win.

Below are three ways to place capital ships that leave a lot of room for boats (marked in blue):

Each of the above arrangements leaves exactly 60 free cells for boats, which means that the probability of accidentally hitting a boat is 0.066. For comparison, it is worth giving a random arrangement of ships:

With this arrangement, only 21 cells remain for boats, which means that the probability of hitting a boat is already 0.19, i.e. almost 3 times higher.

In conclusion, I want to say that you should not spend too much time playing sea battle. I especially want to warn you against playing in lectures. When I was sitting in Wabi Sabi and playing sea battle with my girlfriend, a waitress walked by and said that she plays quite well, because. I practiced a lot in pairs. Who knows what she would have worked for if she had listened to lectures at one time?

P.S. The comments absolutely correctly indicate that there were already similar publications on Habré, it would be wrong not to put links to them.

Incredible popular game on the paper. And although now there are special game sets for " Naval battle”, as well as a lot of computer implementations, the classic version on a piece of paper remains the most popular.

The goal of the game is to sink the enemy's ships before they can sink yours.

Rules of the game " sea ​​battle»

Two players play. Each of them needs a piece of paper (preferably in a cage), a pencil or a pen. The game begins with the preparation of the field. Two squares of 10 × 10 cells are drawn on the sheet. On one of them, their ships will be placed, in the other, "fire" will be fired at enemy ships. The sides of the squares are signed with letters horizontally and numbers vertically. It is necessary to agree in advance which letters will be written (the main disputes arise whether or not to use the letter “Yo”). By the way, in some schools, instead of the boring alphabet, they write the word " REPUBLIC"- it just contains 10 non-repeating letters. This is especially useful for those who have not mastered the alphabet.

Arrangement of ships

Next, the deployment of fleets begins. Classic Rules sea ​​battle they say that there should be 4 ships in one cell (“ single-deck" or " single-pipe”), 3 ships of 2 cells, 2 - of 3 cells and one - four-deck. All ships must be straight, no curved or "diagonal" allowed. The ships are placed on the playing field in such a way that there is always a gap of one cell between them, that is, they should not touch each other either by the sides or by the corners. In this case, ships can touch the edges of the field and occupy corners.

The game

When the ships are placed, the players take turns making "shots", naming the squares according to their "coordinates": "A1", "B6", etc. If the cell is occupied by a ship or part of it, the enemy must answer "wounded" or "killed "("sunk"). This cell is crossed out with a cross and you can make one more shot. If there is no ship in the named cell, a dot is placed in the cell and the turn passes to the opponent.

The game is played until the complete victory of one of the players, that is, until all the ships are sunk. At the end of the game, the loser can ask the winner to look at his ship placement.

Mastery

If you think that sea ​​battle- a game built solely on luck and luck, then you are mistaken. In fact, it has both strategy and tactics, which we will talk about in conclusion. So - about tricks as well as various honest and not very fair methods of playing in sea ​​battle:

• First of all (and this is the most important thing!), it is necessary to keep your sheet of ships in such a way that the enemy couldn't peep your location;
• Be sure to keep a record of your own and other people's moves, marking them dots. So shots on the same cells will be excluded;
• Having sunk an enemy ship, also surround it with dots so as not to shoot at places where there are obviously no ships;
• You should not put ships in the corners of the field: usually beginners shoot at them first of all. However, exceptions will be discussed below;
• It is necessary to develop a strategy for placement. A good result is the uneven distribution of ships: collect all the "large" ships in one or two dense groups, and hide the remaining "one-deck" ships separately in secret places on the playing field. In this case, the enemy will quickly figure out and defeat the grouping of large ships, and then it will take a long time to search for the remaining small ones;
• After killing a large ship, the enemy surrounds it with dots. So, finding four-deck”, the enemy immediately opens (4 + 1 + 1) * 3 = 18 cells (that is, 18% or almost 1/5 of the field). " Three-deck" gives 15 cells (15%), " double decker" - 12%, and " one-deck" - 9%. If you put the “four-deck” against the wall, then it will allow you to open only 12 cells (10 for a three-deck, 8 for a two-deck). If you put the "four-deck" in general in a corner, it will allow you to open only 10 cells (8, 6 and 4, respectively). Of course, if the enemy realizes that all the ships are on the edge, he will quickly sink them. Therefore, it is better to use this advice in combination with the previous one.
• Shooting tactics can also be different. However, the destruction of enemy ships is best to start with the search for a "four-deck". To do this, you can shoot diagonally, or draw a rhombus, or shoot through 3 cells on the fourth. As soon as a four-deck ship is found, we look for three-deck ones, then two ... Of course, in the process of searching, “every little thing” will come across and make adjustments to the plans.
• And here is a dishonest way: to arrange all the ships, except for the last one-deck ship (it will act as the Elusive submarine). And he will be placed (and killed) only in the last remaining cell. Dealing with this is easy enough: let the players arrange the ships in one color, and fire in another. It is possible, for example, for players to have pens or pencils of different colors and, after placing the ships, simply change pens.

Do you play sea battle but don't always win? Then you are probably interested in learning how to significantly increase your chances of winning, how to place ships correctly, how to quickly destroy enemy ships and, of course, how to win in the game sea battle!

Rules of the game "Sea Battle"

There are many options for naval combat, but we will consider the most common option with the following set of ships:

All listed ships must be placed on a 10 by 10 square field, and the ships cannot touch either corners or sides. The playing field itself is numbered from top to bottom, and the verticals are marked with Russian letters from "A" to "K" (the letters "Yo" and "Y" are skipped).

An enemy field of the same size is drawn nearby. In case of a successful shot at the enemy ship, a cross is placed on the corresponding cell of the enemy field and a second shot is fired; Optimal Strategy

How to win in the game Sea Battle

There is always an element of randomness in the game of naval combat, but it can be minimized. Before proceeding directly to the search for the optimal strategy, it is necessary to voice one obvious thing: the probability of hitting an enemy ship is higher, the fewer unchecked cells are left on its field, similarly, the probability of hitting your ships is the lower, the more unchecked cells are left on your field. Thus, for an effective game, you need to learn two things at once: optimal shooting at the enemy and optimal placement of your ships.

In the following explanation, the following notation will be used:

How to shoot at enemy ships

The first and most obvious rule for optimal shooting is the following rule: do not shoot at the cells directly surrounding the destroyed enemy ship.

In accordance with the notation adopted above, in the figure, those cells on which unsuccessful shots have already been fired are marked in yellow, the cells on which the shots ended in a hit are marked in red, and the cells that were not fired on are marked in green, but it can be guaranteed that the ships there are no ships in them (ships cannot be there, because according to the rules of the game, ships cannot touch each other).

The second rule immediately follows from the first rule: if you managed to knock out an enemy ship, you must immediately finish it off in order to get a list of guaranteed free cells as soon as possible.

The third rule follows from the first two: you must first try to knock out the largest enemy ships. Perhaps this rule is not obvious to you, but if you think a little, you can easily notice that by destroying an enemy battleship, at best, we will immediately receive information about 14 guaranteed free cells, and by destroying a cruiser, only about 12.

Optimal shooting strategy

That. the optimal firing strategy can be reduced to a targeted search and destruction of the largest enemy ships. Unfortunately, it is not enough to formulate a strategy, it is necessary to propose a way to implement it.

To begin with, let's consider a 4 by 4 cell area of ​​the playing field. If there is an enemy battleship in the area under consideration, then it is guaranteed to be knocked out in no more than 4 shots. To do this, you need to shoot in such a way that there is exactly one checked cell on each horizontal and vertical. below are all options for such shooting (excluding reflections and turns).

Among all these options, only the first two options are optimal on a field of 10 by 10 cells, guaranteeing a hit in a battleship in a maximum of 24 shots.

After the enemy battleship is destroyed, it is necessary to start searching for cruisers, and then destroyers. In this case, as you may have guessed, you can use a similar technique. Only now it is necessary to divide the field into squares with a side of 3 and 2 cells, respectively.