Zendo, play by forum

[Silken Healer]

AKHTBN iff it is three letters long, and starts with the fifth to the fourteenth letter of the alphabet.

[Proxima]

None disproved Proxima's guess at the time of posting though, so it's still in the rules you need to provide a counter-example.

No, it isn't. NNN is a valid counterexample to my rule guess.

[Simon]

You're both right. Yes, Ramond has to provide a counterexample, and he chose NNN, which is a valid counterexample. I wanted to test NNN anyway, but there's no rule that prevents Ramond from looking at future posts. He could have chosen something else to help us more, but it's still early in the round and he wants to give as little away as possible.

CD
CED
CH
E
HHH
I
U
EXD

-- Simon

[Ramon]

None disproved Proxmia's guess at the time of posting though, so it's still in the rules you need to provide a counter-example.

Since there's an actual turn order in live Zendo but playing by forum allows multiple guesses in one go before marking koans, I just resolved the guesses in my own particular order. We could add a "turn order" rule if you like.

Once again with the new batch of guesses there exist counterexamples to the last rule guess (and even before that the koan NDE is a counterexample).

White koans:
* E    * HHH
  EEE  * I
  END  * NEE
  ENE  * NEN
* ENN    NNN
* EXD  * U

Black koans:
  BEGIN    FINISH
* CD       LEMMING
* CED      NDE
* CH       STA
  DDD      STAR
  DNE      START
  EAGLE

[Proxima]

CDE
N
NED

[Simon]

This is about the shape of the letters.

AKHTBN iff (first shoving the letters together to remove the gaps between them, then taking the convex hull of the entire koan) is the same set as (first taking the convex hull of each letter individually, and only then shoving the hulls together to remove the gaps between them).

Examples:

• The convex hull of H is a filled rectangle. Three such filled rectangles next to each other can be shoved together to make a long rectangle, which is already convex and thus identical to the convex hull of HHH.
  
• All 26 single-letter koans will be white.
  
• You can insert EHEXIHHX in the center (but not necessarily at either end) of a white koan, keeping it white.
  
• The letters D and B can appear at the end, but not anywhere earlier.
  
• The letter C has a little dent in the top-right, which the convex hull of CH fills, therefore CH is black.
  

-- Simon

[Ramon]

Wow, that's a really interesting guess Simon. But a counterexample is AAA which does not have matching sets as per your rule, but is marked white.

White koans:
* AAA    I
  E    * N
  EEE  * NED
  END    NEE
  ENE    NEN
  ENN    NNN
  EXD    U
  HHH

Black koans:
  BEGIN    EAGLE
  CD       FINISH
* CDE      LEMMING
  CED      NDE
  CH       STA
  DDD      STAR
  DNE      START

[WillLem]

E(*)D, where (*) represents each of the 26 letters of the alphabet (e.g. EAD, EBD, ECD, etc.).

EDIT: In addition, please test every letter of the alphabet individually (*), as a string of length 2 (**), as a string of length 3 (***), and as a string of length 4 (****).

Please by all means express the results of this guess as a statement rather than adding each string to the list of koans.

[Simon]

OQ
QO
WV
VYT
LEM

-- Simon

[Ramon]

EDIT: In addition, please test every letter of the alphabet individually (*), as a string of length 2 (**), as a string of length 3 (***), and as a string of length 4 (****).

Apart from the single letter koans, I don't think there is a general statement that can correctly mark all your wildcard guesses without listing them each individually, so please consider submitting only a smaller subset of guesses.
(Honestly I also feel like it's a bit of a dirty trick, since you could just submit those guesses at the beginning of every new rule without regard to the starting koans, which makes the early game kind of uninteresting and isn't usually possible in a live game of Zendo.)

White koans:
  AAA    NED
  E      NEE
  EEE    NEN
  END    NNN
  ENE  * OQ
  ENN  * QO
  EXD    U
  HHH  * VYT
  I    * WV
  N

Black koans:
  BEGIN    FINISH
  CD     * LEM
  CDE      LEMMING
  CED      NDE
  CH       STA
  DDD      STAR
  DNE      START
  EAGLE

All single letter koans are white.
E*D is white for: E H I K M N X Z

[Proxima]

I think it would be good if we agreed on a rule in future to avoid wildcard guesses getting out of hand. I suggest:

On your turn, you may guess a wildcard pattern, such as X*A or ***E, which is understood as a set of 26 koan guesses, replacing all wildcards with each letter in turn (all wildcards must be replaced by the same letter). Only one wildcard pattern may be guessed at a time.

[WillLem]

Apart from the single letter koans, I don't think there is a general statement that can correctly mark all your wildcard guesses without listing them each individually

The way you've done it above is fine. Example:

(*) is white for: (list of letters)

(**) is white for: (list of letters)

(***) etc.

I also feel like it's a bit of a dirty trick, since you could just submit those guesses at the beginning of every new rule without regard to the starting koans, which makes the early game kind of uninteresting

As soon as strings like "EEE" and "NNN" are assigned a white koan, the logical next step is to guess the other letters of the alphabet in the same pattern. I probably wouldn't arbitrarily guess (*), (**), (***), etc unless "EEE", "NNN" or any other such string had first been guessed and assigned*.

Besides, if players guess "AAA, BBB, CCC, DDD, EEE..." individually across several posts, I'm fairly sure that won't make the early game any more interesting for either the player or the rulemaster!

*EDIT: My first set of guesses was mostly full words, but only "EEE" gained a white koan. The full-alphabet guesses then seemed appropriate and necessary.

and isn't usually possible in a live game of Zendo.

OK, but we aren't playing a live game of Zendo. The format means that players might only be able to post one set of guesses per day, so the tendency is to want to optimize guesses.

The above guesses are intended to determine if any letter allows a string of (< 3), and which letters are not allowed in a string of (< 3). Of course, some letters may be allowed in the presence of other letters, but not by themselves. Hopefully my guess also turns up a few of those as well.

To be fair, I should probably have explained that so the guesses didn't seem perhaps so arbitrary.

On your turn, you may guess a wildcard pattern, such as X*A or ***E, which is understood as a set of 26 koan guesses, replacing all wildcards with each letter in turn (all wildcards must be replaced by the same letter). Only one wildcard pattern may be guessed at a time.

Fair enough, this is a good idea. One question that occurs, though: what determines a "turn"? Another user posting guesses after you? The rulemaster posting a reply to your initial guess?

[Ramon]

The way you've done it above is fine. Example:

(*) is white for: (list of letters)

(**) is white for: (list of letters)

(***) etc.

(*) was pretty simple to mark, but everything above wasn't feasible for this particular round. Those are 676 guesses for (**) alone, and if roughly half of them are white without an easily explainable pattern, that still leaves over 300 koans to be manually marked or entered.

BUT in hindsight, reading your previous post again I realize I misunderstood what exactly you were guessing. I interpreted it as having each wildcard icon go through each letter individually, not just the same letter up to length 4. I will include those in the general patterns below the koans.

Fair enough, this is a good idea. One question that occurs, though: what determines a "turn"? Another user posting guesses after you? The rulemaster posting a reply to your initial guess?

Personally I think a turn should be considered the time between two rulemaster markings (once you put in a set of guesses, you can't add any more until the rulemaster has marked your last guesses). I'd also advocate for a limit of guesses per turn, but that's probably a bit harder to justify and a matter of personal taste. In the end it's just for fun though so I don't mind.

White koans:
  AAA    NED
  E      NEE
  EEE    NEN
  END    NNN
  ENE    OQ
  ENN    QO
  EXD    U
  HHH    VYT
  I      WV
  N

Black koans:
  BEGIN    FINISH
  CD       LEM
  CDE      LEMMING
  CED      NDE
  CH       STA
  DDD      STAR
  DNE      START
  EAGLE

All single letter koans are white.
E*D is white for: E H I K M N X Z (and black for every other letter)
(**), (***) and (****) is black for: B D F J L P R (and white for every other letter)

[Simon]

I'd be reluctant to introduce a hard limit per day, or a hard limit between posts.

I see why you would want that though. It would lose some of the spirit if every game begun with:
foreach (1 ≤ len ≤ 10), foreach ('A' ≤ x ≤ 'Z'), test xxx...x of length len.

People haven't done it so far, therefore I'm hesitant to enforce anything.

I've tested one batch of 26 in Proxima's round, and even made the choice of batch dependant on single instances of the batch that I predicted. If you really want to enforce a limit, such prediction seems like the better way. But then you'll be hung if you see no pattern to predict, but know that you want the batch tested. I still advise against any kind of limit.

Another argument that's weakly against introducing a limit: I conjectured that all single-letter koans were going to be white in Ramond's round here even after Ramond broke my theory about convex hulls. But I wanted to keep that for myself. I wouldn't have mass-tested the singles.

-- Simon

[Simon]

MEL
AE
FJ
AJ

zendofmt should support a free-form notes section that gets printed below black and white lists. namida's tool supports that, and here we need it again.

-- Simon