Zendo

Summary: In this Death Match, deduce the secret patterns faster than your opponent. (Original design by Kory Heath)

Designer(s): Non-original Game

Featured in: DM Colosseum, Blooming Genius: The Elder Tree, The Genius: PnP

Match Type: DM (for 2 players)

Rules:

Credits:

This game was created created by Kory Heath.

It has appeared previously in Death Match Colleseum 1 and Blooming Genius, both hosted by chaotic_iak.

--- Koans and Patterns ---

The goal of the game is to deduce the secret patterns that govern arrangements of dice.

The player to guess 2 out of the 3 patterns in the game wins the DM.

- Koans -

A koan is an arrangement of Up, Down, Left and Right arrows on a square grid.

A koan must contain at least 1 arrow.

Here are some examples of possible koans:

Two koans that only differ by translation are the same koan.

In other words, only the bounding box of koans is considered, which can be defined as the smallest rectangle that can fit all of the arrows.

An example of the above can be seen below. As you can see, the only thing that varies is the empty space around them, so they are treated as identical for all purposes of the game.

For sanity reasons, the bounding box of a koan is restricted to be at most 6x6.

However, rotations of a single arrow or the koan as a whole will result in a completely different koan.

- Patterns -

A pattern is an objective statement about a koan.

Any koan will either follow the pattern or not.

Here are some examples of patterns:

A: There is at least 1 arrow pointing up.

B: There are at most 3 arrows.

C: There are no arrows pointing left.

These patterns will be used for the examples in the rules.

For the actual DM, I have prepared 3 patterns, which are different from the 3 patterns used here. Your goal is to discover them during the game.

To make it fair, each pattern has been described in 10 words or fewer. You don't have to guess it in 10 words, this is specifically a host limitation.

--- Gameplay ---

The game begins with 2 koans shown to the players. One koan will follow all the patterns, the other will not follow all of the patterns.

Here is an example starting position using the 3 example patterns:

Dems, as the DMO will decide the starting player, then turns alternate.

On your turn, you may do one or both of the following steps:

1: Make a koan and declare either "grade" or "challenge". 2: Spend guessing stones to guess a pattern.

Step 1.

First, you may make a valid koan. (koan is valid if it has at least 1 arrow and fits into 6x6 bounding box.)

You need to also declare "grade" or "challenge", as well as which patterns you want to be graded / challenged.

You may also skip this step and proceed to step 2.

If you declare grade, I will state whether your koan follows the declared patterns.

As an example, if you provide the koan shown in the image below, and ask to grade for patterns A and B, this will be my response:

If you declare challenge, both you and your opponent will guess whether the koan follows the chosen patterns. Each player submits for this in private.

After both players have submitted, I will reveal the correct answers.

For each pattern guessed correctly, a player who made the guess will get 1 guessing stone. It's entirely possible for you to get no stones while your opponent gets 2 or 3.

Step 2.

After you've made your koan and gotten a response (or skipped the step), you may spend a guessing stone to guess one of the patterns. If you have no guessing stones, you may not guess.

You can also skip this step if you want to.

State which pattern you want to guess and what your guess is.

If your guess is ambiguous, I and the opponent may ask clarifying question until we all agree on the meaning. Your guess isn't finalized until then and you can take it back at any time.

After you have made your guess, I will take 1 guessing stone and then give a counterexample if possible. That means that I will either...

make a koan that follows the hidden pattern but doesn't follow your pattern.
make a koan that doesn't follow the hidden pattern but follows yours.

After providing the counterexample you are free to spend another guessing stone to make another guess. This means you can repeat step 2 until you run out of guessing stones or until you guess the pattern.

If I am unable to provide a counterexample, that means you have successfully guessed the pattern. All future koans may no longer ask for this pattern to be graded or challenged.

🔍 For example, you can attempt to guess pattern C and state "There are only arrows that point up or down in the koan". A counterexample I may give is show below, as it follows pattern C but doesn't follow the proposed pattern.

You then may spend another guessing stone to state "There are only arrows pointing up, right or down in the koan". As I can not give a counterexample, you have successfully guessed the pattern.

It is left as an exercise to the reader to prove the two rules are equivalent.

<:ToL:1140773480728629398> The player to guess two out of the three patterns wins the DM and advances to final 3.

```

Administration

```

Post your koans in the game room.

You may use any method of submission, as long as it's understandable.

If you don't want to use image submissions, I suggest the following approach: use . for empty spaces, use <v^> or LDUR for Left, Down, Up and Right arrows respectively. Surround your submission with ``` to make your submission monospace, making it a lot easier to parse.

Here is an example koan written this way and what it will look like after processing:

```

.U.

L.R

.D.

```

However, you can also use image submissions if you want to.

Excel / Google Sheets are particularly useful, as they have a square grid.

Additionally, you may use Figma Prototypes that craw has made.

Both DM participants have been sent their own copy of a 6x6 grid which they are free to share around.

Note, however, that making changes to a prototype will reflect that change to everyone with the same prototype link. You making a koan on it will be visible to everyone who has the same link as you.

For this reason both players will be given an additional copy of a prototype at DM start, which they should not share with anyone.

Post your challenge guesses in your submission channel.

Post your pattern guesses in the game room. Your opponent will be able to hear your theories.

After each turn, I will publicly reveal the latest koan played and the response to it, guessing stone count. This game has no secret information. You are allowed to take notes during this game.

Players get 3 minutes for their whole turn. If you run out of time, the remaining steps are skipped.

When you challenge, your timer is paused. Instead a separate 60s timer starts after I post the challenge image, during which both players guess the result. You may change your answer during this time

When clarifying a guess the timer continues to run.

When I'm constructing a counter-example, the timer is extended by 30 seconds and paused for the duration of the construction.

If the game lasts over 2 hours, the game is stopped immediately.

Instead we host a challenge quiz, where both players answer challenges to koans that I create. The player to answer more challenges correctly will be considered to have solved the rule. The game should never reach this point.

Challenge quiz rules

I will give players 10 koans to judge on all unguessed rules, identical to regular Challenge rules.

For each pattern, the player who gets more successful challenges wins that pattern.

In case of a tie, 5 more koans of increased difficulty will be provided.

This will repeat as many times as necessary until the winner is decided