Zendo-Tao

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Zendo-Tao
Tom Phoenix
Zendo game.jpg
Zendo masters take small steps along the path to discover the one true secret rule.
:Players Players:
:Time Length: unknown
:Complexity Complexity: Medium
Trios per color: 5
Number of colors: 5
Pyramid trios:
Monochr. stashes:
Five-color sets:
- - - - - - Other equipment - - - - - -
Wikipedia:wiki,wiki
Setup time: ten minutes
Playing time:
Strategy depth: Some
Random chance: Some
Game mechanics:
Theme: Zendo variant
BGG Link:
Status: complete? (v1.0), Year released: 2987


Prologue

A group of Zendo masters out on a walk one day came upon an abandoned Zendo game. Each koan had a marking stone next to it, except for one. After studying the assembled koans in a long moment of silence, one master spoke.

"It seems to me," said Albert, "that there's just one possible rule that could apply to these koans. We could mark this last koan."

"No, you can never narrow it down to just a single rule," said Bonita. "You can always add an exception to a rule, like AKHTBN if the number of red pips is a prime number, OR if it's this one crazy exception koan made from a dozen pieces. So there's always more than one possible rule."

"Let us say that there's only one reasonable rule, then. We can all agree on what's reasonable and what's unfair."

"I can disprove that," said a third master, Chris. "Not the agreeing part, the only one rule part. However you mark that last koan, I can give you a fair rule."

Bonita said, "Okay, bear with me for a moment. You're saying that you know two rules that work for these koans, but the unmarked one would be answered differently for your two rules, right?" She paused. "All right. I will say that the rule could have been AKHTBN if it has at least two red pieces." (Somebody groaned.) "Hey, I'm just saying it could have been, but it isn't." She marked the last koan, which didn't have any red pieces, with a white stone to show that it had the Buddha nature, then started arranging some stray pieces. A moment later, a new koan stood on the table. "Either way you choose to mark this new koan, I can still give you a reasonable rule."

More masters began to gather at this point. Nobody knew what rules Bonita was thinking of, but everybody wondered whether it was a bluff. Then Danni stepped forward and, after a moment of hesitation, put a white stone by Bonita's koan. "The rule is not AKHTBN if it has an even number of pieces," she said quietly naming one of Bonita's rules and building another new koan. "There are still at least two possible rules, and two viable ways to mark this koan."

Ethan addressed the group. "I don't know how many possible secret rules there are in all, even if we limit it to just the ones that all of us agree are 'reasonable'. It's a very large number, maybe millions or even trillions. But it's finite, right? Eventually, if you keep adding koans and stones, you'll find that there's just one possible rule left at some point."

"Yeah, but that might take millions of koans, too," said Albert.

"Not so. Every new koan can potentially cut the number of possible rules in half, depending upon how you mark it. It should be quick to run out of possible rules.... Like now, Danni claims there are at least two possible rules remaining, corresponding to the two ways you could mark her last koan, right? Can any master now find a fair rule which holds for all koans until this last one, mark the koan to show that the rule is no longer viable, and produce a new koan that could still be marked in either way, as Bonita and Danni have done?"

And one could, and did so. Thus the game began.

About the game

This game is an attempt at a wiki-playable form of Zendo. Or maybe it's more like Last Master Standing. In this game, every player strives to see the last fair rule that eludes the others.

This is also potentially more difficult than ordinary Zendo. To take a turn in this game, a player normally needs to discover three secret rules that work for everything posted so far, not just one. The more rules you can find, the better you can score.

(Note that there's nothing about this game that requires a wiki. It could translate into a real-world asynchronous game, if you can solve the problem of katsu.)

What's all this about "posting"?

The instructions that follow discuss "posting". Normally, posting on the wiki will be done with the help of template macros. See the page about Zendo-Tao/Wiki for wiki specifics.

Starting a game

To start a new game, simply post a normal pair of marked koans, plus a third, unmarked, koan. (Post in the proper sandbox page, or you could start a new page, if you want more than one game running concurrently.) Posting those three koans constitutes your first turn.

Joining a game

Any new player may join a game at any time before a winner successfully claims victory. (See "Claiming Victory" below.) Bystanders and players are encouraged to post comments freely, as well, but please don't post still-viable secret rules (even in Rot-13). Sore losers (rules invalidated as a side effect of a koan) are encouraged. ("Until Albert's koan, I had AKHTBN unless it has exactly one red and no medium!" -- Bonita     "I had that too." -- Danni)

Leaving a game

Because of the nature of wiki, players may leave the game at any point. More accurately, on a wiki-based game, every player leaves the game, but some will eventually return. In your absence, however, players and bystanders may nullify your moves, since there's no way to know that you had the rules you claimed. You certainly can't "win" without sticking around until the end. But if you're clearly out of the running, you don't need to keep watching the game.... unless you want to make a comeback, of course.

Taking a turn

You may take another turn once someone else has taken a turn since your last turn, or when your last turn was more than 20 hours earlier. (That is, you can take two turns in a row, but not without giving somebody else a chance to play.) A player is never compelled to take a turn, but if you fail to claim victory in a timely manner at the end of the game, another player may jump in to steal the win; see below.

Post a stone and a koan and a rule

On each normal turn, until the endgame, you need to find at least THREE fair rules that are still possible for every koan already marked. The rules must not all give the same response to the unmarked koan on the table. That is, at least one rule would mark the koan with a white stone, and at least one rule would mark it with a black stone. Any third rule must agree with one of the first two, of course. Keep the two agreeing rules secret for now, but do keep them — you may be required to produce them later.

To take your turn, your post must include three items.

  1. You must post one of the rules you've discovered.
  2. You must mark the previous unmarked koan with the proper stone that disproves the rule.
  3. You must post a new koan that distinguishes between your two remaining, viable rules. (One of your secret rules gives your new koan a white stone, one doesn't.)

A turn typically looks something like this:

"The rule is not AKHTBN if whatever, as the stone I've placed at the previous koan now shows. There are still at least two viable fair rules, though, as my new koan could be marked with either kind of stone."

During the turn, a player should also post the necessary judgment calls, if any. See below.

What's going on here?

On a player's turn, he or she is taking on the roles of both the student and the master of ordinary Zendo. As a student, you are "giving the master a guessing stone" and proposing a rule which is valid for each marked koan. As the master, you are to verify this rule against each of the already-marked koans, then to check that the newest koan (the previous player's koan) is a valid counterexample, which you now mark. (For example, if the rule you post would mark the previous koan white, you mark it black. That disproves the rule.) As a student again, you build a new koan, confessing your humility as you know that you do not yet know how to mark it. As a master, finally, you assign the task of marking that new koan as a mondo (challenge) to any player who can show how to do so.

I can't find three good rules!

Sucks, don't it? You can have thirty-three rules that work for everything on the board, but if they all give the same answer for the unmarked koan, you're out of the game. Not necessarily for long, if somebody else takes a turn: see the section on strategy, below.

Endgame

If no more moves appear to be forthcoming, the latest player may ask the other players and bystanders for permission to claim victory. This gives everyone else one last chance to snatch away the prize.

Up until this point, each turn has ended with the implicit or explicit assertion that at least two rules remain. To ask permission to claim the victory, a player must reduce this assertion to a single rule. (The player isn't asserting that only one fair rule remains. He or she is simply not asserting that more than one remains.)

Asking permission to claim victory

Normally, only the latest player is allowed to ask to claim victory. But if nobody has taken a turn in at least 72 hours (a week, if there are very few players), any player who can see two still-viable rules is entitled to step up and make the claim. In other words, if the incumbent player hasn't taken the win in a reasonable time, another may take a turn in this way. Of course, the incumbent player could block this at any time by claiming the victory.

In order to claim victory, a player posts the more complex of the two remaining rules (if neither rule is clearly more complex, either may be revealed first) and disproves it by marking the last unmarked koan. Next, the player asks if anyone can still build an ambiguous koan.

This type of turn typically looks something like this:

"The rule is not AKHTBN if whatever, as the previous koan now shows. I still have a fair rule for all koans. May I now claim the victory, or can anyone offer a koan which could still be marked in more than one way?"

Blocking the claim

When a player asks permission to claim victory, he or she has posted two of the three parts of a normal turn (the rule, and the stone, but not the koan). Until a consensus of players and bystanders have agreed that nobody else is going to take a turn, any player (including the person asking to claim victory) may take ownership of the turn by posting the needed koan. As this once again implies that at least two rules are in play, the claim to victory is blocked and normal play resumes.

This means that, once someone has asked permission to claim victory, a player needs to discover only two viable secret rules in order to block the claim. The claim-blocking koan distinguishes between the two secret rules: one rule gives it a white stone, one doesn't.

Completing the claim

Barring a timely objection to the claim for victory, the claimant next reveals the remaining, simpler rule and claims victory. (The victory itself is final after a reasonable interval, to allow everyone time to confirm it. Until it is final, the claim to victory is vulnerable to a challenge; see below.)

In case the player's revealed rule is flawed (by being overly complex or in error with regard to already-posted koans, for example), that player's move is null and the game continues from the previous valid move. The best defense against a charge of an over-complex rule, of course, is revealing the more complex rule first.

The winning player is awarded the title of sensei and a score of one point for each marked koan posted before claiming victory. (Thus it pays not to claim victory too soon.) There are no points for anyone but the sensei.

Who is the master?

In this game, most of the duties of the post of Master in regular Zendo are given to each player in turn. The community of players and bystanders are charged with holding all players to a reasonable code of conduct. That is to say, just as with Albert and Bonita and their friends, we all know what's a fair secret rule, and what isn't. AKHTBN if it has more flat pyramids than there are blue pips not touching the table is a fair rule, but AKHTBN if it is one of these particular three ad-hoc seventeen-piece monsters is surely unfair.

Challenges and Judgments

Any player or bystander may challenge a move at any time before victory is final. If there is a problem with a move, a consensus of players and bystanders should cooperatively decide what to do about it. A player may withdraw an erroneous move with no penalty.

A move is defective if any of the three required parts is defective. The rule, for example, is defective if another koan already disproves the posted rule, or if a consensus decides that a rule is unfair. (Players and bystanders are encouraged to be flexible, but players are asked not to abuse this flexibility.)

Players are asked to pay special attention to ensuring that their posted rules are not ambiguous. In case of ambiguity, a consensus of players and bystanders should decide how to interpret any rule, aiming for the author's intended meaning as it was at the time the rule was posted.

It's normal in Zendo for a master to make silent judgment calls about such issues as whether pieces touch, or what a piece points at. If there is a need for a judgment call in order to make a rule work, a player may "make the judgment call" by posting a note at the appropriate koan. (For example: "The red pyramid is not touching the small yellow.") This may be done when the koan is first posted, or later. Please do not make judgment calls public until a posted rule compels you to post them. Note that judgment calls in one game are not binding in another, even if the identical image is posted to both.

A player should be able to clarify what is in an image with words, however. "There is a small yellow pyramid nested inside the medium green and large blue." Please do this, as needed, at the time an image is posted. Ideally, the image should speak for itself, of course. But if you don't want to see a consensus decide the wrong thing about your image, make sure it's clear, one way or the other.

In case of dispute over the rules, a consensus should decide what to do, including clarifying these rules for the benefit of future games. Bear in mind that we're not here to argue over minutiae but to have fun!

Team play

Build a bigger brain by teaming up. Your team may include as many people as you can recruit. With everyone searching for rules, somebody on your team will find the ones you don't. Agree upon what to go with and post your turn. If you want to take credit for it under a nickname ("The Seven Monks of East St. Louis"), that's fine. You don't even have to be logged in. But come back and take the win, if you've gotten it, please.

Strategy and tactics

Because having more than three rules can get a better score, it helps to keep a private list of rules that you've found are still in play. Each new marked koan will eliminate many of the remaining rules on your list.

When you want to take a turn, having a rich rule list means that there's a better chance that the unmarked koan doesn't deserve the same stone from each of your rules. Whichever way you mark it, you're losing some of your rule list. You may want to keep the longer list, and post one of the rules from the shorter one. But if you've got an especially sweet rule on the short list, you could opt to keep that rule around for a later turn, knowing that you're spoiling many rules on other players' lists at the same time.

33 rules and none to play

If your rules all agree about the unmarked koan, you can't take a turn. But you can keep looking for additional secret rules while you wait for someone else to play. Eventually, somebody will play a rule. At that point, if you're lucky, all of your 33 rules may still be viable. If you're not, none of them will be.

33 rules and waiting to play

Or maybe you have 33 rules and you're in no hurry to play. If you can discover 33 rules, you can afford to wait for a few more koans to be marked. Don't wait too long, though, because not all of your rules may survive the next few stones.

You can't lose

If you've kept the secret rules you claimed, you can't lose when you make a move. (You may fail to win, of course.) And moves are easy to make, at least at the beginning.