Zendo: The Game of Inductive Logic
looneylabs.com
looneylabs.com
I was actually a little disappointed in the loss of the Buddhist terminology. Master, koan, mondo, etc. They've been replaced with "Moderator", "exam" etc.
While I understand the reasoning (unfamiliar words will turn people off, also there's a smattering of cultural appropriation), moderator and exam seem so... sterile.
I tried bringing it to a company game night recently, and it was not super well received. A colleague of mine described it as, "less a game and more a way to slowly melt your mind".
Trying the game with my local gaming group was… not successful. If we were into harder games, maybe it would have gone over better.
You can tell the difference between developers who play this game, as opposed to more "ordinary" people in that they approach the game differently. Developers come up with rules like "The sum of the pips pointing at other pieces is even." A new player in the latter group came up with one of my favorite Koans of all time: "One piece is highest."
One of my favorite rules was "an even number of colors". Easy to state but hard to pattern match.
After that my friends wouldn’t play Zendo with me.
[1] https://www.lesswrong.com/posts/n3MMA2cA9Rapi6TBt/zendo-like...
It's very elegant and I think it leaves a mark on them, you get to watch all our little cognitive biases bubble up realtime
Would love to play a computerized version.
Would also love to see someone try and program a zendo ai.
Would it interest someone who also likes mastermind (the board game, don't know if that's available in the US)
Both felt a little confused but after a round or two they were coming up with their own crazy secrets like "has a green piece pointing at the door". Going to look for Pyramid Arcade in the UK.
Proof by induction is actually a little more general than that.
The idea of induction is that if:
(1) you start with an object that has some property;
(2) you modify it by a series of steps; and
(3) all modification steps preserve this property
then whatever object you end up with will also exhibit the property in question. The style of induction you're talking about modifies small numbers into larger numbers by the process of adding 1; in order to prove that your property holds for all integers larger than whatever your base case is, you also need a theorem that tells you all larger integers can be reached from smaller integers by a process of repeatedly adding 1.[1] (This is true, but it tends to get left out of ordinary induction proofs.)
It is very common to use induction in this more general form when you have a set that is defined as (a) some elements that are in the set by definition, plus (b) some elements that are in the set by virtue of a membership rule [which usually takes the form "if x is in the set, then f(x) is also in the set"]. If you can prove that all of the base elements [from step (a)] have a property, and you can show that every membership rule produces an element that shares that property, then you have shown that every member of the set has the property. As an example, we can define the Fibonacci sequence this way:
1. The ordered triple (0, 0, 1) is in the set.
2. If (a, b, c) is in the set, then so is (a+1, c, b+c)
Now every Fibonacci number F_n is the second element of the triple in the set whose first element is n. [Theorem: for any n >= 0, there is exactly one such element.] You can do induction on the Fibonacci numbers by proving things about the three dimensional map f(a, b, c) = (a+1, c, b+c).
(You could also do induction on the more fundamental Fibonacci map f(a,b) = (b, a+b), but then you'd lose the ability to refer to the index of the Fibonacci number.)
[1] Note: it's not necessary that there be no other way to reach your target element. As long as you can get from base case to target by using only steps that preserve the property, the target will have the property. If there's another path, using other steps, that doesn't necessarily preserve the property at every intermediate step, that doesn't matter.
>> The style of induction you're talking about modifies small numbers into larger numbers by the process of adding 1; in order to prove that your property holds for all integers larger than whatever your base case is, you also need a theorem that tells you all larger integers can be reached from smaller integers by a process of repeatedly adding 1.
But you get to define what the domain of the problem is; induction is just about functions preserving properties of their input. If your induction proof fails to cover a particular space, it's still a valid induction proof for some subset of the space.
Most first time masters choose rules that are too hard. "There are more red than blue pieces but the pieces are valued by size with 1 for smallest and 3 for largest" is too hard for non-expert players to ever figure it out. It feels easier to guess a rule you know than it really will be.
Well, if you used different values for the pieces it might be, but those specific values are literally marked on the pieces. The rule "there are more red points than blue points" isn't especially challenging.
When I've brought out the set the last few times we all take turns being the moderator and the Rules cards help ease everyone into it, including people that don't think they can do it.