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Totally symmetric non-random games?

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Blake's picture
Joined: 01/05/2009

Hi everyone, I was just wondering if any of you know of any totally symmetric non-random games? By "totally symmetric" I basically mean games that not only have a symmetric setup (like in Checkers), but also have no asymmetry in turn order, (like Diplomacy, which uses a form of simultaneous action selection along with simultaneous action execution). By "non-random" I mean no dice or card shuffling or anything like that.

If anyone knows of any I'd love to hear about them, and any thoughts on how they play would be much appreciated as well if you've actually tried them out.


Joined: 05/25/2010
I would be surprised if this

I would be surprised if this existed. I have a personal project that is totally symmetric, including turn order. But uses shuffled decks, so not non-random. I can't imagine any game evolving out of a non random game with symmetric turns, I'm currious as to see if anyone tried what your asking.

I suspect this thread will be full of games that have 90+% of the requirements, but not all.

Markus Hagenauer
Joined: 12/04/2009
symmertic randomness

I´m not sure if there are symmetric games with no randomness. But there are some with "symmertic randomness", where the random choices effect both, for example Ricochet Robots.

Pastor_Mora's picture
Joined: 01/05/2010
Real time abstracts: RPS / Auction

Rock-Paper-Scisors fits your description. It plays pretty dumb.

As I see it. No-randomness doesn't imply no-luck. If your description implies there is no luck involved. Then you have a scripted game by definition (i.e. no choice). For example, in an auction where all people have the same money and all items yield the same amount of points. No choice, no game.

Keep thinking!

Joined: 12/31/2010
I remember a WW1 dogfighting

I remember a WW1 dogfighting game I used to play with my dad when I was younger where you each had a book with an image of your opponents relative position and a choice of aerial manoeuvres. Both players chose their move at the same time and told each other the corresponding page number where they then had to check the result of both moves combined.

Sorry for the hideous description but it's the only game I can think of that comes close.

Blake's picture
Joined: 01/05/2009

Thanks for the comments everyone! Ricochet Robots, Rock-Paper-Scissors, and quite possibly the WWI dogfighting game all (at least in my mind) qualify as symmetric non-random games. Because the randomness occurs before the game really begins in Ricochet Robots (if I understand it correctly) and it affects everyone equally, it does seem like a symmetric non-random game to me. And that WWI game sounds interesting too (and strangely familiar, like I've heard about it before somewhere).

Rock-Paper-Scissors is really an excellent example of what I was thinking about, and I don't know why I didn't think of it myself. And yes Pastor_Mora, luck probably will play a large role in any such game, though not necessarily randomness.

I'm not really sure why I find the idea of symmetric non-random games so interesting, but thank you all for the comments/insights.


Joined: 12/15/2009
Game Theory & Pure Symmetry

I'm not really a games theorist (in the sense of the branch of maths called 'game theory') but the following observations seem applicable here:

Note: mathematical game theorists mean very precise things by their terms, which are sometimes different from how board gamers use those words. In particular, a "strategy" in game theory is a complete plan for every eventuality in a game - something which tells you what decision to make whenever you get to make a move.

When there is no luck or hidden information in a game (i.e. when you know the results of your moves in advance), then, for perfect players, the result of the entire game is already decided before you start. Chess is a game like this - either there's a single winning "strategy" (in the game-theoretic sense) for White, or for Black, or both players have a non-losing strategy leading to a draw. What makes chess interesting as a game is that we haven't figured out what the perfectly optimal strategy/ies are (in game theoretic terms, chess is not "solved").

But in the abstract, chess has an optimal "pure" strategy. Suppose chess is solved, and it turns out that White is the winner. Then there is (at least one) correct move White can make at every possible turn which will result in eventually checkmating Black.

However, in games like scissors-paper-stone, players don't know in advance what the result of their move will be (because it depends on what the other players choose). It's known in game theory that you can guarantee (on average) minimal loss in these games by using a "mixed strategy": one in which you take random decisions. In scissors-paper-stone, if you play completely at random, nobody can get an advantage over you by strategic play. In other games, the randomness of the "unbeatable" (in game theory, this means "unbeatable except by pure luck") mixed strategy might be much more complicated, but the principle is the same.

Of course, a game could have both types of complexity: chess-like (where it's effectively impossible to determine the best pure strategies), and mixed-strategy (where the unbeatable strategy requires random choices), without even having any randomness in the game rules. Imagine playing Race For The Galaxy with the deck of cards shuffled and turned face-up at the start of the game (and every player's hand face up). You'd know exactly which cards were coming up, but because of the simultaneous role selection, you still wouldn't know who would get them.

You could also have a totally symmetric game in which players took turns: imagine a game which involved playing two games of chess at once, one as White and one as Black. The turn sequence would run as follows: Player A takes a move as White (on the first board), then Player B takes a move as White (on the second board), then Player B takes a move as Black (on the first board), then Player A takes a move as Black (on the second board).
This is effectively what happens when you play a 2-game match of chess. (My girlfriend tells me that in some chess tournaments, they play simultaneously.)

larienna's picture
Joined: 07/28/2008
Games must not be perfect to be well designed

For non-random game, puerto rico is the leader in that matter.

Anyways, What I want to point out is that I read in a book a quote of another author which explain what are the properties of something "well designed". I wrote a summary on my website, that I will copy-paste here, as as you can see, for games to be well designed, it needs to be symmetric and assymetric at the same time. It's an interesting theory that I find very useful and effective.


Christopher Alexander's theory

This is an architect which tries to define how something can have the quality of being "well designed". He explains that through various attempt, you can refine your design until it get the quality he cannot name. Alexander defines 15 properties that design should have because they are in common with some qualities that living things have.

* Levels of Scale: For example, a player can achieve short term goals to reach mid-term goals which will eventually allow to fulfill long term goals.
* Strong Centers: There should be a strong center element in the game.
* Boundaries: Game should have boundaries which could be expressed by space or rules.
* Alternating Repetition: You should alternate between elements that are repetitive instead of only repeating the same element.
* Positive space: A bit hard to explain, it the concept where there should be complementary elements which are both beautiful. The Yin and the Yang is an example.
* Good Shape: Again hard to explain, I think a snail spiral shell will fit here: It's shape makes it beautiful.
* Local Symmetries: Some elements inside the game should be symmetrical but not necessarily the whole game.
* Deep interlock and Ambiguity: This is the concept where an element is meaningless if it is not placed in relation with another element. Go is an example where the piece placement is meaningless if you don't know where are the opponent's pieces.
* Contrast: There should be strong contrast between certain elements to make the game feel more meaningful and powerful.
* Gradients: This refer to elements and values that changes gradually.
* Roughness: A game must not be completely perfect in order to have some character.
* Echoes: Repetitive elements which are related to each other. For example: A level full of spiders with the mother spider as a boss at the end of the level.
* The void: Ok, this one, I cannot understand it. Here is Alexander's citation "In the most profound centers which have perfect wholeness, there is at the heart a void which is like water, infinite in depth, surrounded by and contrasted with the clutter of the stuff and fabric all around it."
* Simplicity and inner calm: A simple design is more likely to achieve the inner calm.
* Not-Separateness: Each element of the game should be a part of the whole game. Each element should be connected with the rest of the elements in order for the game to feel alive.

Hope these thoughts can help.

richdurham's picture
Joined: 12/26/2009
A lot of bidding games are non-random

Games like "Revolution!" has zero-randomness determined by cards or dice. It is solely trying to outguess your opponents bids on influential people. This makes it more like Rock-paper-scissors in essence.

For games where all the randomness starts before the game, try "Endeavor." This one does not have simultaneous turn resolution, but the "starting player" rotates around amongst the players, so it is something you plan for. You're better off getting a description of play from board-game-geek than me, though.

Blake's picture
Joined: 01/05/2009

DogBoy, what you've written is very interesting. I've actually just returned to college to study math and am very interested in learning some game theory.

larienna, though I must confess to not understanding all of that, it was all very interesting. Very nicely put.

richdurham, I'd heard about Revolution!, but didn't really know anything about it. After watching a video review of it, it sounds very interesting. Think I may have to give it a try.

Thanks everyone!

Blake's picture
Joined: 01/05/2009
Freud/Montaigne (my own designs)

I just posted the rules to two games (Freud and Montaigne) over on BGG if anyone wants to take a look. They are both totally symmetric and non-random. My hope is to design one more of a similar nature (both are also three player games playable with a standard deck of cards in under fifteen minutes) and then move on.


Joined: 08/11/2010
Symmetric & nonrandom

I quite like Freud! Montaigne is actually already a game; I can't remember now what it was called, but I used to play it with friends when I was a kid (we often shuffled the bank, which makes it random but still symmetric).

I think it's provable that any symmetric, nonrandom game will always end in a draw, unless A) players make mistakes (because, for example, it's Chess, and we don't know what the perfect winning strategy is), or B) players are forced to make decisions without knowing everything about the game (for example, your making people select cards without knowing what the other players picked).

I also think B) can only happen if you have players make decisions simultaneously and secretly - if it's nonrandom, then you can't have any secret knowledge *except* for the decisions of the players.

Blake's picture
Joined: 01/05/2009

Thanks dpledpage, I quite like Freud too. It also doesn't totally surprise me that Montaigne has already been around for a while (though presumably under a different name), at least in some form or another. When I came up with the idea, it just seemed too obvious somehow. That being said, it is growing on me a little, even if Freud is still the one I am far more interested in.

As far as Freud goes, my worry is that people won't perceive that there is any strategy in it (this appeared to be the case during the first and only playtest I've run of it so far), so my hope is to post a bit over on BGG over the next week about some basic strategies and tactics and how well they hold up when played off of one another.

Joined: 04/25/2009
Thoughts on Freud and Montaigne

Both games sound interesting, and I'd like to try them out. As for monetizing the idea, and adding flexibility in regards to number of players, I would suggest working on a unique deck of cards specific to the game play, that could allow for more than three players to play at the same time. I don't know how you would sell a game that uses a standard deck of playing cards. It would be much easier to sell a game if it used a unique deck of cards.

I believe the games are definitely worth pursuing!!

Blake's picture
Joined: 01/05/2009
Thanks Baroombah!

Thanks for the encouragement Baroombah! I've yet to playtest Montaigne, but have been putting some effort into Freud. Seven people other than myself have tried it at this point, and I just passed the rules on to a friend so she can try it with her husband and son (I'm very interested to see if children find it at all interesting).

As far as allowing for more players, the basic setup I've been considering is:
(1) If everyone chooses the same title, everyone other than the person with that title looses two power.
(2) If an odd number of people (less than the full number of players) choose a title, the person with that tile looses one power.
(3) If neither (1) nor (2) is the case, then everyone whose title was not chosen looses one power.

As far as cards specific to the game go, I've also been working on that, but I'll need a little more time before I'm ready to share what ideas I've come up with (they still need a lot of polishing).

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