The super tris, or tris in the trioUltimate Tic Tac Toe, Fractal Tic Tac Toe, are some of the names with which this is known variant of the game of the trio where Each box contains a mini trio And whoever manages to conquer 3 in a row wins by creating a trio of mini tris. We explain the rules of the game and see how with an additional special rule this game can become a real fractal.
Why this game is not the simple trio?
The Game of the Tris it is very popular and it is easy to play practically everywhere, but it has a defect: The tie is too frequent and you know, everyone likes to play to win. In fact, there are strategies to play “perfect games” and if two good players challenge each other without making mistakes end up for draw all games. For the game of Super trisInstead, A winning strategy is not known And the games do not end as easily in a tie, not even those among the most experienced players. Let’s see how it works.
How to play the super tris
We start by drawing the scoreboard, a Great Tris with many mini trioone in each box: the purpose of the game will be conquering Three mini tris lined up In order to make a trio in the large scoreboard, let’s see how it proceeds.

The first player makes his move by putting X or OR, where he prefers, within a mini trio to his choice, but be careful because the Rule of the obligatory move illustrated in the image below:
Each move indicates to the next player who will be the mini trio in which he will have to play during the following round.

In this case the first player occupied, with an X, the box at the top right of mini trio left center from which he chose to leave. The second player is therefore mandatory to play in the correspondent Mini tris at the top right.
From this moment on, each player will have to play in the mini trio indicated by the last move of the opponent. This rule adds an important strategic element to the game because At any time it is possible to choose in which mini tris the opponent will have to play the next move. Continue until a player conquers a mini trio:
When a mini tris is conquered, it is marked with one x or an or and from this moment it will no longer be possible to use it.

From this moment on, it will no longer be possible to play in the mini tris that has been conquered, the same applies to any mini trio that have been completed in a tie (without any player having conquered them) for which it is worth the rule:
If a player is sent to play in an already complete mini trio then he can choose to play where he wants.
The first player who realizes a great trio, a trio of mini tris, wins, as in the figure below where the game was won the player with the X.

If no player manages to create a big trio, the game can be considered even, or you can proceed with the account of how many mini tris has conquered Each player so that those who have the most he will win. In this way, given that the number of mini tris is odd, if they are all conquered by at least one player, the game will certainly have a winner, but in the case of an odd number of draws the game can also end up in a tie.
The real tris fractal: the trio in the trio in the trio
The Trio in the trio that we explained to you remember the Structure of the frattals as it consists of many mini tris inside a trio, but to make a real fractal one would have to continue to draw other three -troos smaller inside the mini trio and continue like this infinite. With these rules it is not possible, but if we add the following rule, things change:
When a mini trio ends in a tie is replaced with a trio in the trio (see figure) in which it will be played with the same rules above and which can be conquered by one of the players

From a practical point of view every new Trio in the trio You can draw on another smaller sheet and place above the mini trio which replaces, obtaining a scoreboard like the one in the figure below (be careful: if a new one Trio in the trio He risks being too small we can draw him on a large sheet taking note of his position in Trio in the trio original).

With this rule, no mini trio will end in a tie but, on the other hand, the game could also last infinity by creating a real fractal like that of the cover image: if you were looking for a game to play with someone for life this is the game for you!
Sources
B. Orlin (2022): “Math Games with Bad Drawings”, Black Dog & Levenhal Publishers, ISBN 978-0-7624-9986-1
