page modified: 25-July-1998, 30-June-2000, 13-May-2005, 03-Jan-2006

A very well-written catalog of various Go variants, none of which (at this time -- there are several, of which QuantumGo is one -- I have asked him to start a new section -- which I doubt he will do -- Quantum Go, as well as other randomness-adding systems -- could be considered a form of "Jokergo".) involve randomness (modulo theories of mind, and groups of minds, cooperation, negotiation, etc) is the World Of Abstract Games section on Go variations, maintained by Joćo Pedro Neto.

Following the format of the summaries on that page, I must report that Quantum Go as described below takes far too long on a full size board, but a ten-by-ten is small enough to be interesting, and good for teaching beginning fighting, as the situations are small enough to be effectively read and explained by the stronger player, and they must be re-read whenever a mutation occurs.

There has been at least one person who has contacted me concerning purchasing quantum go software -- there is none at this time, but i suppose if someone were to fund the venture I could write some.

David NicolDavid Nicol presents his latest weird idea:
Quantum Go
A tool to teach principles of Fault-Tolerant Design, based on the ancient Chinese game of Wei-Chi, also known as Go or Baduk.

Quantum Go differs from normal Wei-Chi in this way: every turn, each position on the board has a small chance of "mutating" as if it was a memory element struck by a gamma ray, or some other normally dependable component of a system that has inexplicably failed.  Mutated positions randomly become open, white or black.  Due to the mutations, the Ko rule is not needed in quantum Go.

What you need:
a Go board, two twenty-sided dice, one six-sided die.

Mutations are modeled, on a 19x19 go board, with two uniquely colored marked twenty-sided dice (0-19), called the "position dice," and one six-sided die called the "control die." All three dice are thrown until a Stop Mutating condition appears.  Each dice throw causes one mutation or a stop-mutations event.

Stop mutating events are, a 0 on either d20, or a 6 on the d6, which provides a 4/15 chance at each throw of the dice that there will be no more mutations that phase.

Otherwise, the 2d20 indicate a random position on the 19x19 board and the d6 controls how it mutates, according to this chart:
d6 shows
remove stone from position
white stone
black stone
white stone
black stone
stop mutating

On smaller boards, or if the above-described scheme results in too many mutations, 4 and 5 also stop muitations.  Or experiment, using a d4, a d8, or a d12 for the control die with your own chart. Put your results on a web page, tell me about it, and I will gladly link to it from here. Bonus points for anyone who provides an accurate statistical description of the model related to current physics theory about spontaneous particle appearance in complete vacuum. Hint: try to determine how large a 1x19x19 block of interstellar vacuum, in meters, is required for the particle appearance rate to match the above dice scheme, at one mutation phase per second.

The mutations phase occurs between piece placement and piece removal.

Normal go consists of two players taking turns, each turn having two phases, place a piece and remove captures if any. For a discussion of normal go, I reccommend Bob Sloane's Go Lessons. Quantum go introduces the mutation phase, which occurs after a piece is played, before captured stones are removed.

End of Game

The game ends by agreement, or one player can definitively win by pointing out that greater than half of the points on the board (181 on a 19x19 board) are occupied by stones of their color.  Stones removed from the board are returned to their bowls, as in Chinese rules.

How does all this relate to Fault-Tolerant Design?
The mutation phase represents faults.

Go has been praised as 100% deterministic. Quantum Go adds a random element to the play.  Go serves well as a metaphor for complex systems (such as computer programs) which are 100% deterministic, in which everything works right, provided that everything works right.  As the saying goes, "if houses were constructed like computer programs, one woodpecker could end civilisation.."  In Go as well, stable structures often become precariously complex. The winner of the game is often the one who can correctly read the complexity.  Redundancy and back-up systems are not required because of the 100% deterministicity.  The flock of woodpeckers released by the mutation phase ends all that.

It is my belief that Quantum Go provides a conceptual framework for designing fault-tolerant systems, as go-stone structures able to remain on the board even with mutations happening must tolerate, or co-exist with, faults, or situations which do not occur in normal "faultless" Go.

Artificial Intelligence?

Another possible application of this variant is in the field of computer go: By providing a new dimension to the game, that of stability, a more general case of game is defined, in which normal Go is the degenerate case of zero instability. Writing artificial intelligence programs that can play good Quantum Go may lead to AIs that can play better normal go.

Copyright and Licensing

the name "Quantum Go" and the game described on this page are copyright 1998 David Nicol, computer programmer in Kansas City. All applicable intellectual property laws apply. Anyone may link to this page. Reprinting the rules described here on paper or electronicly requires licensing and prior agreement, so e-mail me first. Evaluating Quantum Go for more than thirty days or use in a classroom setting requires purchase of a license for each player/student. Nontransferable permanent licenses to play this copyrighted game cost USD $1.00 each and can be obtained with this form:

Your e-mail address user@host.domain:
Number of licenses required:

a list of go variants

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This page last updated on July 26, 1998.

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