Zendo — The Game of Science

Zendo is a great game. It’s a really, really, great game. It’s one of those perfect examples of a game mechanism distilled to its finest and packaged into a game that really works. Kory Heath, the game’s designer, really hit on a genius idea. It’s also a very general game. You can play Zendo with Looney Pyramids, designed by Looney Labs, one of my favourite game companies, or almost any other set of things that are plentiful and can be assembled into a large number of configurations. I’ve played Zendo with pictures on a chalkboard, and with words over e-mail. As an illustration I’ve included below a game played with strings of zeros and ones.

The only thing that bothers me about Zendo is the theme. As Nick Bentley points out, Zendo is about science. I feel like the Zen theme distracts one from the core lesson that the game can teach and might put some anti-religion folks off of the game. I’ve re-written the rules below, in part to see how well the science theme fits the game. The original Looney Labs version is, of course, the best. The write up of the game in Playing With Pyramids is beautiful, with lots of great examples.

Players: Any number greater than two.

Equipment:

  • Success tokens
  • Failure tokens
  • Grant tokens
  • Anything else

Goal: Players, imitating scientists, try to experimentally discover a secret law which a distinguished player, the universe, has formulated. The players perform experiments by assembling bits into configurations to see if their guess at the law holds experimentally.

Rules:

One player is chosen by the others to be the universe. The universe formulates and writes down a secret law which configurations of the pieces available must satisfy. The law must satisfy the following:

  • The law must be a success/fail-valued function on experiments. That is, the law must say that any experiment either succeeds or fails. According to the law, an experiment cannot “half succeed” or “kinda fail”.
  • The law must only refer to the pieces in an experiment, their relative positions, and the surface they are played on as considered as an abstract, infinite, featureless plane. In this sense the law must be local concerning a single experiment. It cannot refer to previously existing experiments, players of the game, directions, things going on while the experiment is being assembled, or a myriad of other things.

Once the universe has selected a law, they produce an example of an experiment which succeeds and an experiment which fails by placing two experiments on the table and putting success or failure tokens beside the experiments.

The scientists proceed to attempt to experimentally determined the law.

On a scientist’s turn they may:

  • Organize an experiment. When a scientist organizes an experiment, they can either immediately perform it or collaborate. If the scientist chooses to immediately perform the experiment, the universe will then say whether the experiment is a success or a failure by placing a token marking it as such beside the experiment. If the player chooses to collaborate, all the scientists will make a conjecture as to whether the experiment will succeed or fail. The universe announces the success or failure of the experiment. All the scientists who correctly conjectured whether the experiment would succeed or fail receive a grant token.
  • Publish a theory. If a scientist has a grant token to spend, they can formulate a theory to publish. The scientist then formulates, as precisely as possible, their hypothesis about the law. If they correctly formulate the law, they win. If their formulation is incorrect, the universe has to provide an example showing such. (Perhaps this corresponds to independent verification of published results.)

Note that the two options are non-exclusive. A scientist can organize an experiment, collaborate on it, receive a grant, and publish a theory all in one turn.

It’s important for the universe to formulate their rule as accurately as possible before play begins. Here are some examples of inadmissible laws:

  1. An experiment looks pretty.
  2. An experiment has a piece pointing at the CN-tower.
  3. An experiment has more pieces in it than the last experiment.
  4. Bob organized the experiment.

Here are some examples of admissible laws:

  1. An experiment contains a red piece.
  2. An experiment contains only one piece.

Is the following an admissible rule?

An experiment has a group of pieces which is bigger than the others.

Well — At first glance, it’s not clear what “bigger” means. There are lots of ways to measure bigness. We can measure it by counting the total number of pieces in an experiment, or the total amount of space that the experiment occupies, or the height that the experiment extends off the table, etc. So — There’s that, suppose we mean that “bigness” means the number of pieces in an experiment. So — Is the rule now admissible?

You have to be careful about what is really going on here. Would the rule above say that experiment with a single group of pieces succeeds? What about if the experiment has three groups of pieces?

4a) An experiment contains a group which is bigger than every other group that the experiment contains.

4b) The experiment has more than one group, and there is a group which is bigger than every other group that the experiment contains.

Both of these are possible interpretations of rule 4.

An example.

Suppose we want to play Zendo online. We say that our set of pieces is going to be strings zeros and ones. There are going to be two scientists, Alice and Bob, and the universe, Hugh.

Hugh exhibits two experiments:

Success 0011
Failure 01010

Alice organizes and performs and experiment: 101

Hugh marks it as a failure.

The following are now on the table:

Success 0011
Failure 01010
Failure 101

Bob thinks that maybe being a palindrome matters. He organizes and performs: 110

Hugh marks it as a failure.

Success 0011
Failure 01010
Failure 101
Failure 110

Alice notices that every failure has either: more ones than zeros or zeros than ones. She organizes and performs the following experiment: 01

Hugh marks it as a success.

Success 0011
Success 01
Failure 01010
Failure 101
Failure 110

Bob knows that being a palindrome is apparently unimportant since there are palindromes and non-palindromes that both failed. Bob starts to think that having several zeros before several ones, matters. He organizes and performs the following experiment: 000111

Hugh marks it as a success.

Success 000111
Success 0011
Success 01
Failure 01010
Failure 101
Failure 110

Alice starts to think that an experiment having an equal number of zeros and ones is the rule. All the examples confirm this rule although they also fit Bob’s rule.

Alice organizes the following experiment and calls a conference: 0101

Bob conjectures it will fail, since it doesn’t conform to his pet theory. Alice conjectures that it will succeed. It does, so Alice gets a grant token since she conjectured correctly. She now publishes a theory: “An experiment succeeds if it has an equal number of zeros and ones.” Hugh knows that this is not the law and so present the following failed experiment: 1111

Bob is no stymied, since this sort of conforms to his theory, now he’s thinking that “An experiment succeeds if it some number of zeros, possible none, before a string of consecutive ones.”

Play proceeds.

For the curious, the law Hugh has in mind is: (ROT13 spoiler) Na rkcrevzrag fhpprrqf vs naq bayl vs vg unf na rira ahzore bs qvtvgf va vg.

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One thought on “Zendo — The Game of Science

  1. Pingback: An Asynchronous Zendo Variant | Playing with Games

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