70. Zendo (Comprehensive Rules)
DR. LORXUS'S UNOFFICIALLY OFFICIAL COMPREHENSIVE RULES OF ZENDO (v1.0)
Zendo is an inferential game for 2 or more players, with technically no upper limit on players. One of the players is Nature, and comes up with a secret rule which determines whether an arbitrary arrangement of pyramids fits or doesn't fit their rule. The rest of the players are all Scientists/Seekers, trying to figure out the secret rule. The Seekers need not be in competition with each other, nor is it required that they cooperate; whichever they do, they will learn good research habits and can enjoy play. It's not even necessary that the players agree on whether they're competing.
In order to play Zendo as I define it here, you will need numerous plastic Icehouse pyramids in several colors (my set has red, yellow, green, blue, white, and black, and I keep toying with getting at least one more color) and sizes as sold by Looney Labs, go/baduk stones in both white and black, and some kind of token to use as a counter for Guessing Gems. (In the past, Guessing Gems have taken the form of other go stones, business cards, and tiny flexible magnetic whiteboard cards; I keep meaning to buy some nice chonky synthetic rubies for the purpose.)
[picture of my set to go here]
SETUP, GAME ACTIONS, and WINNING THE GAME
At the beginning of the game, Nature comes up with a fair rule (see below) regarding arrangements of pyramids and keeps it secret. They may want to write down a canonical wording of their rule, for memory, legibility, or proof purposes later. Then, they set up and label an Example (white stone) and a Non-Example (black stone) of arrangements that fit their secret rule. All of the Seekers should take a white stone and a black stone, for Prophecy/Prediction purposes.
Only Seekers get turns, and should decide in advance on a fair ordering of Seekers. Clockwise and counterclockwise around a table are canonical choices.
On a Seeker's turn, they may take one of two free actions, or they may cash in a Guessing Gem to makes a guess at the rule.
First, they can make any arrangement of pyramids (even the empty arrangement) and ask Nature to Grade it as Example (white stone) or Non-Example as at the start of the game.
Second, they can ask Nature to generate an Event for the Seekers to Prophecy about - or if you prefer, the Scientists to Pre-Register/Predict. Nature then sets up an arrangement of pyramids of their own design, and after giving the Seekers some time to come to conclusions, counts down, and everyone reveals their guesses; all the Seekers who predicted Nature correctly get a Guessing Gem.
If a Seeker has a Guessing Gem, then they may spend their turn to cash it in. They give the Gem to Nature and clearly state their guess at Nature's secret rule. Nature should work with the Seeker here to clearly define and state the rule that the Seeker wants to test. Then, one of three things happens:
First, Nature can point to an on-board arrangement of pyramids to refute the Seeker's rule. In that case, the Seeker is refunded the Gem and may try again.
Second, Nature can refute the Seeker's guessed rule and keep the Gem. They do this in one of two ways: by constructing an arrangement of pyramids that fits Nature's rule but not the Seeker's proposed one, or else by constructing an arrangement of pyramids that fits the Seeker's proposed rule but not Nature's. All Nature needs to do is provide any counterexample that separates the two rules.
Finally, if Nature believes that the Seeker has their rule correct or has stated a rule that is differently phrased but logically equivalent (e.g., "All pyramids are red" vs "No non-red pyramids"), or else simply can't construct a counterexample of either type, then Nature should say so and congratulate the Seeker on winning the round of Zendo. At this point, the Seeker may Ascend to become Nature if they so choose, and if they decline, the players should decide among themselves who the next Nature will be.
RULES
Different rules make for different play experiences. As Nature, err on the side of making a simple rule. If you can express your rule in 10 reasonable words/tokens or less after "An arrangement of pyramids [fits my rule]/[doesn't fit my rule] if..." then you're probably doing OK. Adding extra conditions is always risky: then, you need to think about which conditions are local (tinkering with some subset of pyramids can tell you about the rule) or global (touching any pyramid meaningfully could affect whether the rule is satisfied) and also what kinds of logical connectives are OK to use (IF-THEN/SUBSET is often OK, as is AND; OR is fraught, and XOR is brutal.)
Example rules I have used or seen used:
(Quick/0.5 star) "...fits my rule if there's at least one red pyramid."; "...fits my rule if one pyramid points to another."
(Easy/1 star) "...fits my rule if there's a pyramid that doesn't touch the ground."; "...doesn't fit my rule if any pyramid is lying down."
(Moderate/1.5 star) "...fits my rule if every upright pyramid is green."
(Challenging/2 star) "...fits my rule if it consists of one pyramid of each size, plus an extra yellow."
(Difficult/2.5 star) "...fits my rule if there's an even number of pyramids, or at least one pyramid is red."
[I will not put examples for 3+ star Hard/Hard+ rules here. I have not deployed them in a game. No one has been ready. To attempt such might drive anyone mad. I thus will not put examples of those here. Do not try to use them.]
As a necessarily incomplete list of Niceness/Regularity Conditions that Zendo rules must always satisfy, Zendo rules must always be:
However, as another incomplete list, Zendo rules can totally care about:
A NOTE ON PLAYING AS NATURE
As Nature, there is no "winning" of the game. You set up a rule and arbitrate guesses, but the joy of playing Nature is in watching the Seekers unwrap the (fair) mystery you set them and then setting down your mantle to become a Seeker once again. The Seekers' work is already hard enough: as Nature, be generous and willing to work with the Seekers as much as possible, helping them to firm up their statements of rules, pointing out problems, and maybe even dropping very oblique hints. Keep the game moving: this is still a game, at the end of the day, and we are doing this to enjoy ourselves.
If you're the kind of person who would find it fun to make a very difficult, basically impossible-to-guess rule, and watch a team of Seekers spend hours on hours failing to make progress, you probably should not be playing Nature and should hand that off to someone else. If Lorxus is around the game, they will very likely be willing to take over as Nature and make a pleasantly spicy rule.
As a general note, though: get buy-in from your players before you make a rule on how hard they want it to be. You can cajole them to try a little harder or dream a little bigger, but don't push the Seekers too hard: sometimes people just want a break and to pick apart an easier rule.
Zendo is an inferential game for 2 or more players, with technically no upper limit on players. One of the players is Nature, and comes up with a secret rule which determines whether an arbitrary arrangement of pyramids fits or doesn't fit their rule. The rest of the players are all Scientists/Seekers, trying to figure out the secret rule. The Seekers need not be in competition with each other, nor is it required that they cooperate; whichever they do, they will learn good research habits and can enjoy play. It's not even necessary that the players agree on whether they're competing.
In order to play Zendo as I define it here, you will need numerous plastic Icehouse pyramids in several colors (my set has red, yellow, green, blue, white, and black, and I keep toying with getting at least one more color) and sizes as sold by Looney Labs, go/baduk stones in both white and black, and some kind of token to use as a counter for Guessing Gems. (In the past, Guessing Gems have taken the form of other go stones, business cards, and tiny flexible magnetic whiteboard cards; I keep meaning to buy some nice chonky synthetic rubies for the purpose.)
[picture of my set to go here]
SETUP, GAME ACTIONS, and WINNING THE GAME
At the beginning of the game, Nature comes up with a fair rule (see below) regarding arrangements of pyramids and keeps it secret. They may want to write down a canonical wording of their rule, for memory, legibility, or proof purposes later. Then, they set up and label an Example (white stone) and a Non-Example (black stone) of arrangements that fit their secret rule. All of the Seekers should take a white stone and a black stone, for Prophecy/Prediction purposes.
Only Seekers get turns, and should decide in advance on a fair ordering of Seekers. Clockwise and counterclockwise around a table are canonical choices.
On a Seeker's turn, they may take one of two free actions, or they may cash in a Guessing Gem to makes a guess at the rule.
First, they can make any arrangement of pyramids (even the empty arrangement) and ask Nature to Grade it as Example (white stone) or Non-Example as at the start of the game.
Second, they can ask Nature to generate an Event for the Seekers to Prophecy about - or if you prefer, the Scientists to Pre-Register/Predict. Nature then sets up an arrangement of pyramids of their own design, and after giving the Seekers some time to come to conclusions, counts down, and everyone reveals their guesses; all the Seekers who predicted Nature correctly get a Guessing Gem.
If a Seeker has a Guessing Gem, then they may spend their turn to cash it in. They give the Gem to Nature and clearly state their guess at Nature's secret rule. Nature should work with the Seeker here to clearly define and state the rule that the Seeker wants to test. Then, one of three things happens:
First, Nature can point to an on-board arrangement of pyramids to refute the Seeker's rule. In that case, the Seeker is refunded the Gem and may try again.
Second, Nature can refute the Seeker's guessed rule and keep the Gem. They do this in one of two ways: by constructing an arrangement of pyramids that fits Nature's rule but not the Seeker's proposed one, or else by constructing an arrangement of pyramids that fits the Seeker's proposed rule but not Nature's. All Nature needs to do is provide any counterexample that separates the two rules.
Finally, if Nature believes that the Seeker has their rule correct or has stated a rule that is differently phrased but logically equivalent (e.g., "All pyramids are red" vs "No non-red pyramids"), or else simply can't construct a counterexample of either type, then Nature should say so and congratulate the Seeker on winning the round of Zendo. At this point, the Seeker may Ascend to become Nature if they so choose, and if they decline, the players should decide among themselves who the next Nature will be.
RULES
Different rules make for different play experiences. As Nature, err on the side of making a simple rule. If you can express your rule in 10 reasonable words/tokens or less after "An arrangement of pyramids [fits my rule]/[doesn't fit my rule] if..." then you're probably doing OK. Adding extra conditions is always risky: then, you need to think about which conditions are local (tinkering with some subset of pyramids can tell you about the rule) or global (touching any pyramid meaningfully could affect whether the rule is satisfied) and also what kinds of logical connectives are OK to use (IF-THEN/SUBSET is often OK, as is AND; OR is fraught, and XOR is brutal.)
Example rules I have used or seen used:
(Quick/0.5 star) "...fits my rule if there's at least one red pyramid."; "...fits my rule if one pyramid points to another."
(Easy/1 star) "...fits my rule if there's a pyramid that doesn't touch the ground."; "...doesn't fit my rule if any pyramid is lying down."
(Moderate/1.5 star) "...fits my rule if every upright pyramid is green."
(Challenging/2 star) "...fits my rule if it consists of one pyramid of each size, plus an extra yellow."
(Difficult/2.5 star) "...fits my rule if there's an even number of pyramids, or at least one pyramid is red."
[I will not put examples for 3+ star Hard/Hard+ rules here. I have not deployed them in a game. No one has been ready. To attempt such might drive anyone mad. I thus will not put examples of those here. Do not try to use them.]
As a necessarily incomplete list of Niceness/Regularity Conditions that Zendo rules must always satisfy, Zendo rules must always be:
- Translation-invariant, rotation-invariant, time-invariant, and player-invariant.
- Solely focused on single arrangements of pyramids and saying nothing about pyramids in different arrangements.
- Memoryless and thus independent of previous guesses.
- Topologically-nice and thus not focused on exact angles or distances.
- Generally treated as though each arrangement of pyramids exists in its own timeless pocket universe containing nothing but an infinite featureless plane (and gravity, I guess).
- The added condition that Nature need not be cruel to be challenging and thus that Nature should be nice with respect to conditions that are hard to verify, measure, or check.
However, as another incomplete list, Zendo rules can totally care about:
- Color, size, and upright status of any number of present or lacking pyramids.
- How many pyramids there are.
- Whether pyramids touch the ground and/or how.
- Which pyramids point at or touch or are stacked on or are beneath which.
- Which pyramids point between two other pyramids or which pairs of pyramids point at the same location or different locations...
A NOTE ON PLAYING AS NATURE
As Nature, there is no "winning" of the game. You set up a rule and arbitrate guesses, but the joy of playing Nature is in watching the Seekers unwrap the (fair) mystery you set them and then setting down your mantle to become a Seeker once again. The Seekers' work is already hard enough: as Nature, be generous and willing to work with the Seekers as much as possible, helping them to firm up their statements of rules, pointing out problems, and maybe even dropping very oblique hints. Keep the game moving: this is still a game, at the end of the day, and we are doing this to enjoy ourselves.
If you're the kind of person who would find it fun to make a very difficult, basically impossible-to-guess rule, and watch a team of Seekers spend hours on hours failing to make progress, you probably should not be playing Nature and should hand that off to someone else. If Lorxus is around the game, they will very likely be willing to take over as Nature and make a pleasantly spicy rule.
As a general note, though: get buy-in from your players before you make a rule on how hard they want it to be. You can cajole them to try a little harder or dream a little bigger, but don't push the Seekers too hard: sometimes people just want a break and to pick apart an easier rule.
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