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Subject: Rethinking guessing stones and the "Mondo" action. rss

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Nick Knack
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Howdy!
Allow me to begin by saying I'm a relatively new Zendo player, and I apologize in advance if the following wall of text comes from a lack of understanding.

I've recently pulled together a very nice home-brew Zendo set thanks to the advice of those who frequent this forum, and after a few plays with varying player counts, my group and I have greatly enjoyed the core induction puzzle of Zendo.
The problem we routinely run into at all player counts is in the way the guessing stone system works; both in acquisition and in use.

Now, I like the spirit of the Mondo action in that it keeps the game competitive by forcing you to potentially help others by helping yourself unless you get really clever with your Koan... And I love that if you get your stone and botch the guess, the next player down the line will have even more information to work with.
However, the implementation seems messy. At the beginning of the game, there's never a reason to let anyone else get guessing stones, so players only take the Master action until there's enough information present to deduce the rule, make a Mondo action that's guaranteed to be correct, then immediately use the stone to win.
To combat this, I made a house rule in which you cannot spend your guessing stone the same turn in which it is received, but this made it so that calling a Mondo guaranteed everyone else at the table who received a stone was guaranteed to guess before you. Again we fell into the "never call Mondo" fail state as players would routinely stall out the game with Master requests until someone buckled and gave everyone else guessing stones.

Even when played with friends less concerned about optimal strategy, another issue we had with the stones is in how they behaved at various player counts. With three people (1 master, 2 students) there was never any reason for anyone to call anything but Mondo. Every turn the player would get the same information as if they called Master anyway, while also getting a chance to either win or learn more than they would have anyway.
Master = 1 point of information
Mondo = 1 point of information + 1 more/victory.
It was simply more efficient.

In larger player counts (4+) a massive guessing economy disparity would be formed, starting on the outcomes of a couple very early very random votes, and snowballing all game from there. Every instance of a broke player attempting to remain relevant to the game by using Mondo would only add to the coffers of other players.

If players were allowed to spend stones the turn they earned them, guessing stones became a meaningless currency as any player could just build a guaranteed to succeed/fail Mondo, pick a stone up for free, and use it right away.
If, players by house-rule were not allowed to spend stones they just received, they were doomed to loose unless they got a lucky early vote, and had a stone to sit on by the time more information became available and it came to their turn again.




I'm looking for ideas on house-rules, redesigns, or corrections to my understanding of this system.

I want to somehow preserve the player interaction, and tension of having to help others by helping yourself, while creating a system robust enough to handle gamers trying to break the system to their advantage.



One solution I'm tempted to try is to remove the Mondo action all together, instead granting each player 2 guessing stones at the beginning of the game that they may use at their leisure. This creates a pressure dynamic, waiting for enough information to be present to safely use their valuable guesses, but not wanting to wait long enough that someone else figures it out it first.

The big draw back of this of course is that it introduces player elimination and time pressure to what is otherwise a peaceful, thoughtful semi-cooperative game. A big turn off to some.


And hey! Thanks for taking the time out to read and respond to this post!
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Russ Williams
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I've never had problems with the Mondo action like you're describing. It seems like you're exaggerating a problem, or your group has some kind of groupthink thing going on.

E.g.

Quote:
In larger player counts (4+) a massive guessing economy disparity would be formed, starting on the outcomes of a couple very early very random votes, and snowballing all game from there. Every instance of a broke player attempting to remain relevant to the game by using Mondo would only add to the coffers of other players.

What "snowballing"? Having more guessing stones doesn't make you get more guessing stones faster.

Quote:
If players were allowed to spend stones the turn they earned them, guessing stones became a meaningless currency as any player could just build a guaranteed to succeed/fail Mondo, pick a stone up for free, and use it right away.

A "guaranteed to succeed/fail" koan is not always guaranteed.

Quote:
If, players by house-rule were not allowed to spend stones they just received, they were doomed to loose unless they got a lucky early vote, and had a stone to sit on by the time more information became available and it came to their turn again.

I'm completely confused how you think someone would be "doomed" to lose.


To win the game does not depend very strongly on how many guessing stones you have. It depends on you getting the aha-insight and realizing what the rule is. People who happen to have more guessing stones are in no way guaranteed to beat someone with fewer guessing stones.


I wonder if I'm somehow misunderstanding your point, or if you're somehow misunderstanding some fundamental aspect of the rules...?
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Bwian, just
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I guess I have never seen a group come close to a guaranteed answer with no one mondoing. Even in the theoretical limit: once you are down to small enough number of possible rules, wouldn't a strategic player put down a useless koan rather than let the next player get the koan that separates two possible choices?

My intuition agrees that Mondo should be called less often than it is. But it hardly seems possible to eliminate all possible rules without directing things with guesses. Unless you are only playing from the cards, and everyone has memorized them?
 
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Jeff Wolfe
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realityfoible wrote:
I've recently pulled together a very nice home-brew Zendo set

This may also be part of your problem. If you're finding it easy to come up with a guaranteed solution, your "Zendo" may not be Zendo enough.

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Nick Knack
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Thanks for taking the time out to respond!

russ wrote:
I wonder if I'm somehow misunderstanding your point, or if you're somehow misunderstanding some fundamental aspect of the rules...?

I think that I must be misunderstanding the rules a bit. I'll try to provide some more clarity in what I mean:

russ wrote:
Quote:
In larger player counts (4+) a massive guessing economy disparity would be formed, starting on the outcomes of a couple very early very random votes, and snowballing all game from there. Every instance of a broke player attempting to remain relevant to the game by using Mondo would only add to the coffers of other players.

What "snowballing"? Having more guessing stones doesn't make you get more guessing stones faster.

In a game with a few players, let's say a Mondo is called during a phase in the game where not much information is available. There will be some players who don't succeed in the vote, and maybe a couple that do succeed by educated guesswork.
At that point moving forward, players who already have a guessing stone have no motivation to call another Mondo as they would want to sit back, wait for new information, and suppress other people's ability to shoot for a win as much as possible. This puts the burden of distributing more guessing stones on the shoulders of the stoneless.
For a player without a stone to have a shot at winning, they must call Mondo using an obvious Koan that will likely provide them a stone, providing other players who already have stones a good chance to collect more.

russ wrote:
Quote:
If players were allowed to spend stones the turn they earned them, guessing stones become a meaningless currency as any player could just build a guaranteed to succeed/fail Mondo, pick a stone up for free, and use it right away.

A "guaranteed to succeed/fail" koan is not always guaranteed.

Well... yeah, technically. But it is very easy to build a one-off iteration of an existing Koan who's only significant change has already been proven not to matter.
Incentivizing players to build Koans that provide the table no new information to gain free guesses doesn't quite feel right.

russ wrote:
Quote:
If, players by house-rule were not allowed to spend stones they just received, they were doomed to loose unless they got a lucky early vote, and had a stone to sit on by the time more information became available and it came to their turn again.

I'm completely confused how you think someone would be "doomed" to lose.

If playing by the rule that you cannot spend your stone the same turn you get it, taking a Mondo action to gain a guess means granting every player a potential guess before it comes back to you, making it highly unlikely you'll be able to win, and less likely per each other player in the game given that it means more guessing opportunities and more information will be made available before you get a turn again.

russ wrote:
To win the game does not depend very strongly on how many guessing stones you have. It depends on you getting the aha-insight and realizing what the rule is. People who happen to have more guessing stones are in no way guaranteed to beat someone with fewer guessing stones.

It was my understanding of the rules that you could spend as many guessing stones as you like on your turn, granting undue weight to those who by the actions of others manage to accrue a fortune.
If this isn't true, that's great!
Except that it would seem that the amount of stones you have beyond 2 seem almost irrelevant. At that point, the only function of the guessing stone system is to create a situation where a player can have their "aha!" moment, but end up powerless to act upon it, which is frustrating.

Hence, my earlier proposal that all player start the game with a limited and set number of guesses, so that there's no feeling of power dichotomy encircling the ability to execute on inspiration - only risk capital.
Though, I haven't play tested this idea just yet, as it seems a bit vicious.


I try not to be negative for negativity sake, I seek to be disproven by stating my case.
Hopefully, by expounding upon my earlier claims I've exposed some flaw in my reasoning that I haven't quite caught yet... or given rise to some ideas about what may work to tailor the game our play style.

Thanks for bearing with me here.
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Nick Knack
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jeffwolfe wrote:
realityfoible wrote:
I've recently pulled together a very nice home-brew Zendo set

This may also be part of your problem. If you're finding it easy to come up with a guaranteed solution, your "Zendo" may not be Zendo enough.


This may well be!
Currently I'm using 36each of blue, red, and yellow see-thrugh 6-sided dice as my Koan "building blocks".

Examples of some of the rules we've seen are:

"The model must have have more Blue than yellow dice, and more yellow than red dice."

"Dice on the base level of a Koan must be odd. Dice on the second level of a Koan (stacked) must be even."

"Every segment of the Koan must have pips totaling 6."

"There must only be two colors, which must alternate."

"There must be a connected line of three dice, and the difference between die 1 & 2 must be 3, and the difference between die 2 & 3 must be 2."

"No blue dice may share the same showing numbers."


Let me know if the possibility space here is too limiting compared to the original Icehouse pyramid set.

We've also experimented a bit (jury's still out on if we like it) with using quantum tokens (yes&no) for Koans that match one part of a longer "and" or "or" rule, but contradict another part of it. Though, we haven't used those for the rules listed above.
 
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Greg Darcy
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You might want to read the designer's essay on the development of the game. It is quite long, but he goes into a lot of detail on the development of the Mondo system.

http://www.koryheath.com/zendo/design-history/
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Brian McCue
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Thank your for starting an interesting discussion!

Quote:
...players only take the Master action until there's enough information present to deduce the rule, make a Mondo action that's guaranteed to be correct, then immediately use the stone to win.


I find nearly every part of this statement to be surprising.

--"players only take the Master action until there's enough information present to deduce the rule"

In my experience (with quite a variety of players), there is rarely a sharply visible moment at which it becomes the case that there's enough information present to deduce the rule. In fact, I have experienced the following enough times that I consider it standard:

Newbie: I know the Buddha Nature and I have a guessing stone. Do I have to set up a koan or can I just guess.
Master: You have to set up a koan.
Newbie: Oh, okay. [sets up koan, maybe goes Mondo]
Master: [marks the koan with the opposite marker from what the Newbie was expecting]
Newbie: Uh...pass.

--make a Mondo action that's guaranteed to be correct

I guess if they really know the BN they can do that, but--again--I find it surprising that people could be in this position. Note that one is not allow to repeat an existing koan exactly.

--immediately use the stone to win.

Again, this is a level of certainty that I would say is rare.

To avoid the situation in which stating a wrong BN (and seeing the counterexample) aids the other players, I hold back any BN guesses until I have at least three stones, and then use them in a barrage of ever-improving guesses. When following this strategy, I am starting my guesses without being sure of the BN, in the belief that I am close enough that my supply of guessing stones will get me to the finish line.

Quote:
With three people (1 master, 2 students) there was never any reason for anyone to call anything but Mondo. Every turn the player would get the same information as if they called Master anyway, while also getting a chance to either win or learn more than they would have anyway.
Master = 1 point of information
Mondo = 1 point of information + 1 more/victory.


In this mode, are people always using guessing stones as soon as they get them? Again, I've found that it's better not to do so.

Quote:
In larger player counts (4+) a massive guessing economy disparity would be formed, starting on the outcomes of a couple very early very random votes, and snowballing all game from there. Every instance of a broke player attempting to remain relevant to the game by using Mondo would only add to the coffers of other players.


Unless s/he has a better idea of the BN than they, in which case s/he can get stones when they do not.

FWIW I consider the optimal number of players to be five or six.

Quote:
If players were allowed to spend stones the turn they earned them, guessing stones became a meaningless currency as any player could just build a guaranteed to succeed/fail Mondo, pick a stone up for free, and use it right away.


Again, this is a far higher level of certainty than I'm used to seeing people attain.

Quote:
I'm looking for ideas on house-rules, redesigns, or corrections to my understanding of this system.


Your experience is so different from mine (and others') that I wonder if the home-brewedness of your homebrew set might be a factor. From the description of the set some of your BNs (which seem to me to be quite challenging), I'm wondering how long your games last and if people flail until the very end and then think, e.g., "Aha, if the dice are read in spectral ROYGB order, the pips form segments of the Fibonacci Sequence!" and then just wait their turn, go Mondo to get one stone, state the BN, and win. FWIW my experience with the normal set is that it's just about the right size for a game (barring BNs or player belief-systems that cause shortages of some one pyramid in particular, like when everybody decides that the BN includes a small yellow); a an average of 3-4 pyramids/koan, that's 15-20 koans on the table as of the end of the game.

In terms of Shannon information of the BNs, I think that the 15-20 koans point to something slightly more than a 15-20 bit koan-space, because I think that when a candidate BN is rejected, the rejection conveys some amount of information (probably less than one bit) over and above the one bit carried by the ensuing counter-example.


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Nick Knack
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brianmccue wrote:
I guess if they really know the BN they can do that, but--again--I find it surprising that people could be in this position. Note that one is not allow to repeat an existing koan exactly.

Perhaps the root of the issue we've been having comes from our headspace during play, and the tactical meta that it creates.
The last three times I brought this out (the same group of friends each time), we would exclusively take the Master action for around 8-13 Koans (depending on how tricky the BN was) - which was generally (with some outliers) as much as was needed to really hone in and remove variables from the BN.

The reason we would only use the master action, is because no-one wanted to afford anyone else the opportunity to make a guess, until you absolutely know dead to rights what the BN has to be and can swing for a hit the same turn you get your stone.
Especially because we all knew that if we got a single detail wrong we'd be conceding the game to the next player up to bat, who we just gave free ammunition to.
It created a really odd "count down timer" of remaining variables to control for. One's inner monologue could be: "Ok. At this point we all know the BN is a straight line with the colors red and yellow alternating. But does the third die have to show 5 pips? If I control for that, and then Bob controls for the pips for the second die, then we have it nailed by Sam's turn, who'll then Mondo and win unless one of us builds a pointless Koan to stall, or takes a game ending risk."

brianmccue wrote:

To avoid the situation in which stating a wrong BN (and seeing the counterexample) aids the other players, I hold back any BN guesses until I have at least three stones, and then use them in a barrage of ever-improving guesses. When following this strategy, I am starting my guesses without being sure of the BN, in the belief that I am close enough that my supply of guessing stones will get me to the finish line.


I'll have to try that! Maybe by just taking more Mondo options earlier in the game, even when it might help others more than myself, it'll shake things up and change the dynamic of our group behavior.

 
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If you know what the rule is and have no stones, you can still make a mondo, get the stone, and then guess right after. And for your own sake, the mondo better be as specific as possible. The oposite of easy and predictable, because you do not want everyone to hear your guess. It might give them the a-ha moment.

Anyone who does mondo in any other situation is wasting time and giving out information.

Having 60 stones is meaningless, unless the rule is so hard you simply have to do a machine gun approach.
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Malachi Brown
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This is an interesting discussion and I have to agree with many of the respondents that there is something odd going on. It could be group think, but it could also be something like the master not properly disproving guesses in all scenarios (i.e. being able to build something that has the BN but does not follow the guess, or something that follows the guess but does not have the BN).

Either that, or the rules you group is playing with are not difficult enough. In my experience, it is rare for players to be absolutely certain and finish the game on the first guess and it is also unusual to be correct and so confident that a player builds a structure that is obviously correct/incorrect in order to get the guessing stone to win. It is always still worth building something that tests an area of uncertainty while also trying to get the guessing stone.

realityfoible wrote:
The reason we would only use the master action, is because no-one wanted to afford anyone else the opportunity to make a guess, until you absolutely know dead to rights what the BN has to be and can swing for a hit the same turn you get your stone.
Especially because we all knew that if we got a single detail wrong we'd be conceding the game to the next player up to bat, who we just gave free ammunition to.
It created a really odd "count down timer" of remaining variables to control for. One's inner monologue could be: "Ok. At this point we all know the BN is a straight line with the colors red and yellow alternating. But does the third die have to show 5 pips? If I control for that, and then Bob controls for the pips for the second die, then we have it nailed by Sam's turn, who'll then Mondo and win unless one of us builds a pointless Koan to stall, or takes a game ending risk."

This seems like an important clue to the problem you seem to be having. Because the problem space so large, it should be very, very difficult (or impossible) to get to the point that the answer has been narrowed down with no possible ambiguity.

For every rule you listed above, it should be possible to create a similar rule that would cover all of the same right and wrong koans built so far, while also not being an accurate guess.

Quote:
"Every segment of the Koan must have pips totaling 6."

"Every segment(?) of the Koan must have pips totaling a multiple of 6."

Quote:
"There must be a connected line of three dice, and the difference between die 1 & 2 must be 3, and the difference between die 2 & 3 must be 2."

"There must be a connected line of at least three dice, and the difference between any sequential pair of dice must alternate between 3 and 2"

Of course, those are just possible overlapping rules that may not have actually worked with the koans that had been built, but you get the idea. In my mind, a good rule is difficult to exhaustively test in a reasonable period of time and every possible rule has some larger overlapping rule that is equally correct given the current koans but would be evaluated different for a yet-to-be-constructed koan.

In general, it is good strategy to wait and only call mondo when you think you have some idea of what to guess, but the formulaic approach you outlined where multiple players have already figured out what aspects of the rule to test as well as what aspects the subsequent players would/should test and how many steps away the final answer is seems really weird to me.
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Brian McCue
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I was thinking about this some more. Most respondents (including me) think that the situations you describe are unusual. To me, they seem unusual specifically in that they involve a sharp transition from ignorance to certainty, such that people suddenly know the BN and can trivially go Mondo for the first and only time, and get the BN on one try with.

Fenway Park has long shaped Red Sox baseball and I was wondering if your non-standard set is somehow giving rise to the effects you are seeing. It seems number-heavy and configuration-light: six numbers instead of three, no flat/upright distinction, and probably little or no pointing. One could construct an argument that these considerations lead to the sharp transitions to certainty, but I think the only way to know is to try it.

The plastic pyramids are expensive but instructions and a template for making paper ones can be found at

http://www.instructables.com/id/Papercraft-Looney-pyramids/

Or, at more expense but faster, you could buy a three sizes of wire nuts in the Electric Stuff aisle of the hardware store, and four colors of spray paint. The wire nuts being basically bullet-shaped, they would support most of the configurations of the pyramids--flat, upright, weird, pointing, and stacking. Nesting might not work.

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Nick Knack
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Malachi wrote:

For every rule you listed above, it should be possible to create a similar rule that would cover all of the same right and wrong koans built so far, while also not being an accurate guess.


brianmccue wrote:

One could construct an argument that these considerations lead to the sharp transitions to certainty, but I think the only way to know is to try it.


I think you both bring up good points.
It may be that number/pattern heavy possibility spaces lead faster to hard conclusions once variables start getting locked down, and that my group and I may be just too much into each-other's heads around aggressive guess denial and expectations of formulaic problem solving.

I think ultimately I'm just going to go ahead and buy into the proper Icehouse pieces, invite new players at a FLGS to join our group and let them design their own BN's.
This should throw off any homogeneity in our play patterns, and rule out play piece oddities.

Just goes to show that with tight game design, tweaking any little piece of it can have massive unexpected results.



That all said, and assuming that it really is the dice that are having this effect, I kind of like the idea of having different "types" of Zendo. Where the problem solving becomes more or less pattered depending on the type play set used.
If I can figure out a set of house rules to make my home-brew set work in it's own way, I'm thinking I might be able to evolve it into it's own beast all together.
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Russ Williams
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FWIW I don't think the mere use of dice instead of pyramids is a major factor, since I've often played with simple sets of colored cubes as koans (with spatial arrangement not even being relevant: only numbers of each color was relevant), and the basic flow of the game was the same as when playing with pyramids (with the additional attributes like size and spatial stacking). (Similarly for the play-by-forum games with strings of emoticons as koans.) But I don't know.
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brianmccue wrote:
The plastic pyramids are expensive but instructions and a template for making paper ones can be found at

http://www.instructables.com/id/Papercraft-Looney-pyramids/

That papercraft template is very plain. Fancier ones with various decorations are available here on BGG:
+ Printable Pyramids - Elements
+ DIY Printable Pyramids
+ Make Your Own paper/cardboard Icehouse Pyramids -- big and sturdy tokens, colourblind- and b&w-printer-friendly! Bring some markers!
and another plain design one here:
+ Make Your Own IceHouse Pieces

(I remember there being more pyramid designs than just those listed above. Either some files got taken down from BGG or they were associated with different games.)

And now I offer a few words of advice about papercraft pyramids...

Use heavy paper. Plain office paper is too flimsy. The cheap, lightweight (65 pound) cardstock typically sold in the office supply section of U.S. department stores is still too flimsy. Get the heavy cardstock (110+ pound or 250+ gsm) instead. Better yet, print on colored office paper and glue it to lightweight cardboard such as the side of a cereal box. Use a "bone folder" (which is a tool that looks a bit like a knife but with a blunt, non-cutting edge) and a straight edge to score the fold lines before folding the pyramids into shape.

Be aware that papercraft pyramids have the same amount of surface area but weigh much less than the molded plastic commercial ones. The slightest breeze or table bump could send them flying or tumbling. Stacking works a little differently too. Unlike molded plastic, papercraft pyramids have almost no wall thickness, so if two pyramids of the same size are stacked they could appear to be just one pyramid.
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Nick Reymann
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I feel the "game" works best if turns and mondos are just eliminated altogether, and it is viewed as a cooperative puzzle that the Master sets up and the Students try to solve. Also, this way it is completely playable with just two players.
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