Renju is one of the sports varieties of tic-tac-toe up to five in a row. It is believed that the game originated in ancient China in the Yellow River valley, but the modern rules of the game took shape in Japan about a hundred years ago.

Renju has only three differences from the usual tic-tac-toe:
1. Purely visual differences
2. Presence of fouls
3. Opening regulations

If the game of tic-tac-toe usually takes place on a sheet of paper, and the tic-tac-toe is inscribed in squares, then the game of renju takes place on a 15 * 15 board, black and white stones or checkers are used instead of tic-tac-toe, and the moves are not set in cells, but at the intersection of lines. The purely visual differences end there.

300px-Renju

An example of a renju game

We will dwell on the other two differences separately, but now we will consider the main definitions and concepts that will be useful to us in the future.

Five – a continuous row of five stones of the same color. The five can be located both horizontally, vertically and diagonally.

five

Five examples

Is it possible that there would be more than 5 stones in the line? Of course, such structures also have their own name – a long row.
Long row – a continuous row of six or more stones of the same color. Like the five, it can be arranged in different ways, vertically, horizontally and diagonally. It is easy to guess that the maximum size of a long row can be equal to 9.

long row

Long row examples

So, remember that the goal of each of the players is to build a five of their color. It is logical to suggest that in order to build a five, you must first build a four.
Four – a construction of 4 stones of the same color, which can be completed up to five in one move.

four

Quartet examples

Note: the quad does not necessarily make up a continuous row, as seen in the image above.

Among all fours, it is especially worth highlighting the open four. Open four – a design of four stones of the same color, which can be completed to five in two ways.
It can also be defined as a continuous row of four stones of the same color.

open four

Open Four Examples

How does an open four differ qualitatively from a regular one, that it was decided to single out a separate definition for it? If you have an ordinary four on the board, which can be completed to five in one move, then your opponent can close it by making a move to a point that completes your four to five. But if you have an open four on the board, then your opponent, even with his move, will not be able to close it in any way, which is not difficult to verify, since there are two ways to complete the open four to five, and both of these methods cannot be closed in one move. So, the one who puts an open four first – he will win. Thus, the original goal to build a five is reduced to another – to build an open four before your opponent.

But to build a four, you first need to build a three.
A triple is a construction of three stones of the same color, which can be completed with one allowed move to an open four.

troika

Three examples

Note: the triple does not have to be a continuous row, triples are usually divided into two types: solid (diagonal in the figure) and discontinuous (horizontal and vertical in the figure)
Important! Note the italicized words in the definition of the triple “legal move” and “open four”. We will talk about forbidden and allowed moves a little later, but now we will deal with other constructions:

non-troikas

Are these constructions triples? At first glance, it seems that yes, because each of them consists of exactly three stones of the same color and each can be completed to four by going to the point marked “X”. However, looking again at the definition of a triple, we will see that there is an important requirement for a triple – it must necessarily be completed not to the usual four, but to the open four. And since none of the constructions above can be completed in one move to an open four, we cannot call any of them a three.

The next question that worries us is what to do if a triple appears on the board? Should I respond to it? It turns out yes. After all, if you do not close the three on one of the sides, the next move it will turn into an open four, and we already know that the one who first builds an open four wins. Thus, we can classify the three, as well as the four, as threats that need to be responded to, i.e. close them. It is also worth remembering that the four to the five lack only one stone, which means that as a threat it is older than the three. We will talk about other structures that, although they are not threats, are of interest to us in the next part.

In this thread, you learned:
What is a five
What is a long line
What is a four and how does an open four differ from it
What is a triple and what types of triples exist
What constructions are intuitively similar to a triple and why they should not be classified as triples.