Torigo — the Go game revolution

Our next challenge against AI, and for AI. Could it beat humans in an updated Go game?

2016 — Match of master Lee Sedol vs AlphaGo

Note that, in the following article, AI stands for Artificial Intelligence and the Goban is the name of the board in Go.
We will mainly discuss about Go game and asks questions on AI mechanisms that had been used to build AlphaGo and even more on AlphaGo Zero that now beats AlphaGo (see “Mastering the game of Go without human knowledge” for more details). will stand for both AlphaGo and AlphaGo Zero for simpler reading.
Finally, note that I am not an AI expert, neither a Data Scientist, so feel free to share your thoughts after reading 🙂

Introduction

Artificial Intelligence has made a lot of noise in the last years and as its use spreads in the society it may not stop. Videos of robots performing flips, dystopian series like “Black Mirror” or articles explaining that our jobs are being replaced at high speed by machines are there to convey both fear and bliss in front of our technological progress.

In 2016, Lee Sedol 9 Dan in Go, a true master, was beaten by AlphaGo, the Go artificial intelligence acquired by Google (the Deepmind company).

Approaching the 10⁶⁰⁰ playable games, the game of Go is so deep and intuitive that we thought impossible to build one day an engine able to beat best human players. To get some comparison, there would be 10⁸⁰ atoms in the universe, and 10¹²⁰ playable games in Chess game (see Shannon number for more details).

Lee Sedol’s defeat has touched me as a player and as a human being. This game is so deep that it was part of the last to hold the upper hand on machines. The feeling that the game was “solved” added to my frustration and put me behind a form of ambient fatalism on AI that would dominate us on every games. In the other hand, as a developer and computer science lover, I was also amazed to see how this field has enhanced with the computation ressources available. We must remember and reassure ourselves that it is humans and not robots who build the subtle mechanisms of Artificial Intelligence.

2016 - Sophia, a humanoid robot saying it will detroy humans

The rise in power of AI and its generalized use brings new questions concerning the distinction of the human in the domains where he is competing, and his future place in society. How are we logically different from AI and on what parameters could we play to regain our ascendancy over it? It is a question of studying the limits of human intelligence and those of the machine.

Are intuition and imagination the prowess of humans while memory capacity and computation power are those of machines?

I ) Computation versus intuition

How to reduce the efficiency of predictive computation in the game?
How can we promote intuition and imagination in the game of Go?

Before going further, here is a useful knowledge about the game:

In the game of Go, edges and corners are areas where well studied and standardized sequences of moves, known as , are played. After millennia of games, both studies and experiences has allowed to learn that some sequences of move are better than others. Moves close to the edges are actually called “territory oriented”, i.e. you will win points quickly and efficiently. Moves closer to the center of the board are called “influence-oriented” because they are more intuitive moves, or even longer-term bets. Josekis are paths that offer positive outcomes in the balance between confirmed points and influence on the future of the game.

The specific Josekis of game openings, on corners and edges, are called . They allow maximizing the winning probability from the start of the game.

Starting with AI mechanics:

In AlphaGo, reinforcement learning seem to be the main assets to master the game. As we have seen, AI cannot compute all possible games. These technics are ingeniously used to avoid irrelevant moves and ponderate the ones getting more rewards to win. It improves playing itself by selecting the best root moves and explore new sequences. But, tabula rasa, what could be the first quick wins and rewards that would allow AlphaGo to learn its first patterns?

Capturing moves would be the ones to get quick rewards, sooner before the goban is filled. It is easier to capture against an edge. Moreover, rewards can be gained surrounding territory in fewer moves on corners than elsewhere. Over self playing frames, it seems that the machine feels attracted somewhere like gravity attracts us to the ground, where it becomes ponderated with more rewards: on corners and edges!
Until gradually the seeds (stones) move away from the ground (edges), and generate some fusekis (relevant opening moves)? The robot grows and stands up.

Image 1: 1–1 point, a move in the corner with the least liberties from start. Image 2: a famous joseki on the corner. From AlphaGo Zero in “Mastering the game of Go without human knowledge”

These images from AlphaGo show some learning process: AI first learns to avoid irrelevant moves on the corners the stone is directly in a dangerous position (stone 1 image 1), while the opponent would be rewarded by capturing the stone. Later (image 2) we see AI has learned to play good sequences on corners but finally even reduces those uses over time to prefer even better patterns.

Before reaching a deterministic stage of the game, the moves are predicted based on probability computations allowed by finite sequences of moves that provide the best winning rewards. The deterministic sequences with less depth are based on edges, that’s why the first sequences learned are Josekis. Edges allow highlighting deterministic patterns while the center remains a dark non-derteministic area.

AlphaGo against Lee Sedol — Classic opening

Those strategy locations are heuristics, also known as openings, that last from years of games which reduce to known and studied sequences of moves (Josekis you got it) at a stage the game’s breadth is the highest: all the goban is free to play!

What if these traditions prevent us from discovering other styles of play? How would a machine be able to reduce the game’s breadth allowing it to select a move if we can no longer rely on such sequences made available by edges and corners?

Josekis are indeed an advantage for both humans and AI, but they cause the AI to emerge with even more efficient moves, then how could we remove Josekis? A radical but still serious answer came to me: let’s remove the corners and edges from the goban!

II ) An edgeless goban

So .. how can a goban look like with no edges?

Well yes … and no. Here it may depend on how you imagine the shape of the universe 🙂. But if we want to make a game with a decent length so we could still be able to drink our tea while playing, let’s consider that the official Go grid of 19x19 rows and columns should be respected. So, how to remove the edges and keep a finished grid?

Let’s join the edges of the goban! What do we get?

Why not! But we must not forget that the game board is a grid at all points, otherwise the rules of the game would be invalid!
To check if the Sphere respects the condition of a grid at any point, let’s draw a grid on it:

The grid seems to work.. except at the 2 poles! Indeed, we can notice it is no longer a grid at those places but rather a multitudes of lines that joined in a unique point. Triangles are getting formed in place of squares.

The sphere is therefore not a possible shape for a goban with no edges.

But then, isn’t there a shape for the edges to meet and play Go?

Let’s try a last thing for our new game board. If we twist this board in the middle (not to be done at home!), to make two opposite edges merge, what do we get?

A solid of revolution: the Cylinder!

Yes, now our grid is valid with two edges less, but there are still two circular edges.. What if we repeated the experiment by merging this time the two remaining edges, the two circles of the Cylinder obtained?

BinGo ! We now have Torus: what a revolution!

Torus or “doughnut”, where grid is respected in all points: a circular grid.

Now we have a shape to play Go with no edges and it is 3-dimensional. But well, it is not very practical.

III ) A playable board

With this desire to get out of the collective resignation in front of the machines and to discover the game of Go with a new vision, I have implemented a platform to play the game of Go without corners nor edges:

The « Torigo »! ➡ https://torigo.io

As you may have noticed, it is the concatenation of :

  • « Torus » , the shape where the circular grid is possible (the math donut)
  • and « igo » which is the name of Go in Japan.

As mentioned before, it is not easy to play on a donut. It would be better to see the whole board and the stage of the game without turning an object. So here are the tricks I found to make Torigo playable:

In the same way as in classic Go on a 2-dimensional board, the whole goban is displayed but now, there is the extension of the dotted lines at the ends. If a stone is played at one end, it will appear transparent on the opposite end to view its presence: so we could understand it’s where the torus would join in the real world.

However, since there are no more corners or edges, there is no center either! This is why you can change the reference and, thus, the perspective of the game by clicking on the arrows, to make the board shift step by step. You can either click and move directly on the goban just as you were deplacing yourself on a virtual world map.

Images 1, 2: same 9x9 game with a different perspective. Dotted lines and mirror stones on sides. Image 3: capture.

During the games it is fun to know that you may look at the game from a different perspective than our opponent.

Images 1, 2: same ending game 13x13 on torigo.io, from different perspectives.

IV ) Implications on the game

For new players, since this game does not yet have the weight of history, it can be an advantage in understanding the game of Torigo and developing brand new ways of playing. I noticed it is as simple to learn Torigo as it is to learn Go. While deep, the game is very simple to play with 2–3 rules, but hard to master. Removing the edges actually removes almost one rule.

If you’re interested in learning Go, also called , you can play a simplified version of the game: the where the aim is to be the first one who capture 5 stones. Feel free to try it on both torigoban or classic one: Capture Bot 🤖

For experienced Go players, this variant can be complementary with classic Go and even reshuffle the cards with your opponents! You may also wonder if all rules and principles are preserved. Well the fact that the grid is respected at all points keeps the rules unchanged.

A question we might wonder is: is the preserved?

The « Shichō », or , is a sequence of moves where a player has locked up his opponent’s stones so that if he tries to escape, he will be sure to capture his stones once the sequence reach the edge. Does the sequence work on Torigo? Well, let’s answer it by yourself and meet on the game 🙂.

For artificial intelligence:

We cannot deny that making territories efficiently towards the center on a classic goban must also be part of AlphaGo ingenuity. However, with respect to its person 😅, we can assume that it wont be that easy to reduce the game’s breadth from the begining of the game and that the improved Tree Search applied (even), might not be so efficient with such a new goban: the outcome of sequences will remain as uncertain as non deterministic.
Also note that we are adding a dimension and are moving from a 2D world to a 3D goban.

Will the machine be disoriented without a frame of reference and its “edges’ gravity” ponderation? Will the robot be able to stand up without a ground to stand on? Even more possibilities for linking groups of stones seem to emerge impacting the whole new circular board: even more relevant moves are possible from the start!

“I Robot” movie, meme.

It makes no sense on a classic goban to play your first stones on the edges because they could directly be captured and would not form territories (3 liberties on the edges, 2 on the corners). On the torigoban, all winning probability of possible moves from the grid are equally distributed at the begining of the game:

Another thing I would discuss learning process is that the authors said that the AI has discovered Shisho surprisingly much later than grand principles. Well, it’s no such a surprise to me since the depth of this sequence can be as long as the biggest diagonal of the goban. On Torigo, it may be one of the first principle that AI needs to discover, and guess what, the diagonal of shishos on torigoban is on average always bigger..!

From “Mastering the game of Go without human knowledge”, AlphaGo Zero

In any cases, it will be necessary for Go players to “put aside” classic strategies when entering this new dimension. The game of Go is thousands of years old and still remains mysterious. But on the Torigo, lots of things are still to be understood and, everything almost to be done!

The game of Go has allowed me to broaden and deepen concepts while having fun and even wonder about philosophic parallels.

I think playing on a torigoban still brings something new: having to rely on our own stones rather than on known limits, recenter our own intuition in this great strategy game.

Conclusion

Main objectives of this reflexion and the implementation of Torigo are to:
- Challenge AI researchers and human players to confront each other in this new dimension;
- Allow new players to discover Go in a new creative way, with no openings!

Further questions remain:
➜ Will this reshuffle the cards between players?
➜ Will AlphaGo and Lee Sedol play again and what might be the outcome on the Torigo?
➜ Could this be the new and last strategy game where human remains unbeaten by AI? For now, it is 😜

Do not hesitate to share your thoughts on the comments section or to contact me directly. I would be pleased to discuss with you and, who knows, to see a first AI try to play Torigo!

Here we Go again?
https://torigo.io

(A quick game: Capture Bot 🤖 )

Thanks to my friends and family, for their support and the nice discussions we had. We may still be arguing but for sure our questions will meet answers sooner or later. I wouldn’t have made it this far without their critical eyes and their kindness.

Support project: Patreon
Contact: vick@torigo.io

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Maxime Goaziou

Software engineer and Go player — Creator of Torigo.io the open game of Go with no edges, unbeaten by AI