qubic — A whole new way to play Tic Tac Toe.
You probably got bored of tic tac toe a long time ago. You were playing it wrong.
Qubic is the tic tac toe experience you've been waiting for. It takes one of civilization's oldest games and lets you play like you never have before. 3D tic tac toe doesn't just have more lines to worry about; advanced wins demand unparalleled spatial planning and strategy. 4x4x4 is a first player win game, provided one moves perfectly. But no human has ever mastered the insanely complicated strategy required. Now you can try for yourself.
4x4x4 tic tac toe can be played on a sheet of paper or on a computer. But 2D projections make play annoying and learning difficult. An interactive board is essential for playing the game and building new strategies. Qubic gives you that and more—it can play against you, from easy to unbeatable difficulty, showing you what it takes to win. The app provides analysis as you play and lets you play against other players over the internet. Beat others and rise in the ranks to prove your skill.
Recent Progress:
3D sketch of current 4Play design
High-level circuit diagram for the motherboard
How 4Play (the previous physical board) works
Patent Pending Design
Since XNO is still designing and prototyping 4Play, the final design isn't settled yet. This section describes the current design.
From the outside, 4Play is a relatively simple device. It's composed of a plastic case that houses some circuit boards and batteries. As with many designs, this simplicity was the product of many redesigns and prototypes, and is one of the key features of the device. Including batteries, 4Play only includes 5 unique components; this simplicity makes both assembly and maintenance easier. The device can be assembled from scratch in a few minutes by anyone with a screwdriver. Since this process is entirely reversible, repair also takes just a few minutes and a screwdriver—a huge improvement over your other electronic devices.
The parts themselves aren't too complicated either. As you can see in the 3D mockup on the left, the 16 vertical circuit boards (columns) each have a button on top and 4 LEDs on them to display the game board. The LEDs are tiny RBG LEDs that can display 7 distinct colors. The buttons allow for interaction with the board, like choosing moves and selecting between menus. All of these columns are mounted on the motherboard. This larger horizontal circuit board is the backbone of the device. It connects and supports the columns and batteries, and contains the power switch and selector button. It regulates voltage coming from the batteries and houses the processor that controls all of the input and output to and from the device. A sketch of this circuit is shown to the left. Note that all of the columns are entirely modular, able to be swapped in and out in any order. These simple designs make manufacturing and testing significantly more straightforward than they could otherwise be.
But how does the board connect to your iPhone? The same processor that handles all input and output data for the device is also a Bluetooth® transceiver. Since all the data is in the same place, it's easy to communicate information about your moves (or even the state of your device) to your iPhone, and take in data about another player's moves or even (potentially) firmware updates cleanly and remotely. This design allows for features like cloud-based single- and multi-player games, live gameplay tips, or strategy analysis to be implemented without adding complexity to the product.
How To Play 4x4x4 Tic Tac Toe
4x4x4 tic tac toe has the same basic rules as 3x3. Both players want to get 4 in a row (instead of 3), and take turns placing moves anywhere on the board. The biggest difference is that players now have 76 lines they can win on instead of 8. These lines can go any which way—up, down, left, right, and diagonally. You can see a few examples in the picture on the right. That picture doesn't show a fully diagonal line, which moves across all 3 axes—those totally count too!
The normal end of the game in 4x4x4 is different from 3x3. Since the other player could just block any 3 moves in a line, one rarely wins by actually getting four in a row. Instead most wins are checkmates, moves that require the other player to make two blocks at once; they create two 3-in-a-row's with a single move. When one player gets a checkmate, it's treated as a win; they aren't required to get one of the two literal 4-in-a-row's. As players get more advanced (especially when playing on a physical board), they start to see and block these checkmates before they are set up. This is when wins get increasingly complicated.
Very skilled players win by using forcing sequences. Forces are moves in which one player gets 3 moves in a line, forcing their opponent to move in the last open spot in that line. Even if the other player could make their own forcing move, they are required to respond to the current force, since they would otherwise lose on the very next move. Since the opponent's move is predetermined, this allows a skilled player to maintain control of the board for many moves. These forcing sequences can often include 5-7 forcing moves (and sometimes many more), requiring the player to hold 10-15 future moves in their head. What makes this approachable is that it is wholly deterministic; there’s no guesswork as to what one's opponent might do, because all of their moves are controlled. These wins can be very tricky to see coming and block effectively. One in-plane example (looking at just a single plane of a board) is shown in the gif to the right. This is a fairly standard forcing sequence that I call a 3-move-force, since it takes 3 moves in a plane to set it up. Not any 3 moves in a plane allow for this style of win, but many combinations do! Watching for this setup in all planes (including diagonal and vertical planes) on every move can be very difficult. Once players are good enough at planning out forcing sequences, they are theoretically unbeatable from the first move. The next section explains how computers have been able to reach this level of play, but no human ever has—maybe you could be the first!
Example winning lines in 4x4x4 tic tac toe
3 move force win
Tic Tac Toe Research
Tic tac toe has been the subject of a surprising amount of research. Mathematicians have analyzed its game theory and explored its many symmetries, computer scientists have used it to prove out game playing algorithms, and XNO is working to optimize these algorithms for working on 4Play's processor.
4x4x4 tic tac toe is interesting mathematically. Mathematicians have looked at many different tic tac toe games, with different sizes in different numbers of dimensions. 3x3x3 tic tac toe is quickly won with a forcing sequence from the second move. This makes any 3 or more dimensional 3-wide game of tic tac toe is a first player win game. On the other side, in wider games, it’s easier for the second player to get in the way. That’s why 4x4 tic tac toe is a tie game. 4x4x4 is actually the smallest game that's tie-able but not a draw. This was shown for the first time in 1976 in a theoretical proof that didn't actually demonstrate how the first player could win, but proved that such a strategy existed (I’ve been unable to get ahold of this paper, unfortunately). 4x4x4 is also interesting because of its high number of symmetries. These symmetries are typically called automorphisms: ways of resorting the squares of the board without changing the state of the board. While 3x3 has 8 automorphisms, from rotations and reflections, 4x4x4 has 192. This goes beyond rotations and reflections, and includes switching out the inner and outer parts of the board and switching the order of rows and columns. This paper details the mathematics behind these automorphisms. One important result of these automorphisms is that there are only two possible first moves—read the papers or work on your own to figure out what they are!
These results open the door for interesting computational work. In 1980, Oren Patashnik, an MIT researcher, used 1500 hours of computer time late at night on a then state-of-the-art machine to create the world's first winning dictionary for 4x4x4. This is a full dictionary of moves to take before reaching force-able boards; it's assumed that the computer is able to complete all potential forcing sequences perfectly. While there are nearly a billion different potential games before either player can start forcing a win, the dictionary consists of only 2929 moves. This efficiency is achieved by clever move selection and not repeating automorphic boards. However, as Patashnik explains in his paper, while he produced a winning dictionary, it's not the optimal winning dictionary (p. 215). Another winning program was built in 1992 for the third Computer Olympiad, and detailed in this book. Their algorithm used a much longer (4886 move) dictionary, but a much faster forcing algorithm. It also ran on a computer that was roughly 10-20 times faster than the TX-0 used by Patashnik. 4Play uses a processor roughly 1000 times faster than Patashnik’s, but still about 100 times slower than your computer.
XNO is currently working to advance this research. 4Play is planned to have an unbeatable first-player program, and this will require building a fast and efficient algorithm. Additionally, XNO's top priority is making people love tic tac toe. Part of this work includes making these algorithms simpler for humans to understand and use. No one is going to memorize Patashnik’s winning dictionary and be able to perfectly apply all of the automorphisms needed to make each move in every game. However, a set of understandable rules that still allow for first-player wins would be a huge breakthrough for human play. For these reasons, XNO is currently working to make headway on this research, and will publicly release any new results.
I wanted to give you a quick update from all the progress I've made this summer. In short, everything is coming along really well! Here's an update from each aspect of the project.