Back in 2007 I was watching one of the "new" Star Trek TOS remastered episodes, and there was a scene
with Kirk and Spock playing Tri-Dimensional Chess. I recalled when I was younger my uncle brought over
a collectible set to play with my other uncle when he was visiting. I was fascinated by the game, but
was not allowed to play it because the equipment was fragile. So after the episode ended, I went on
eBay and wound up buying a used set a few days later. I had only played regular Chess occasionally
before that. I was so interested in the game that I looked up info on the rules even before the set
arrived. I found http://chessvariants.org, a fascinating site.

There I not only read about the "standard" rules and variations of rules to Tri-Dimentional Chess, but more authentic three dimensional chess variants, like Raumschach. Eventually I became interested in some of the other games like Shogi and the Shogi variants, especially Chu Shogi and Dai Shogi. Slowly, and unconsciously at first, I began to compare the different games' structure, noticing rules that seemed to improve games compared to others, as well as those that harmed games compared to others. The three-dimensional variants, which I was most interested in, I soon recognized all had significant structural problems.

I wanted to develop an improved version. One of the first things I noticed about the quality of Chess games was that the ones that worked better were generally the ones that had pieces with opposite, but corresponding, patterns of movement (like the Rook and Bishop). So I determined to develop a game where all pieces corresponded exactly to an oppositely powered piece. Then came the first problem. If you include a Knight, then according to this principle you should have a piece that jumps two spaces orthogonally, as well as one that jumps two spaces diagonally. But those pieces themselves are very weak, compared to the other pieces. The best, albeit imperfect, solution is to have some sort of combined piece with those powers, but then the piece tends to be excessively powerful. The other option is to eliminate Knights and jumping pieces entirely, but that would make a dull game. Of course, the examples I just gave you were in 2D, and I also tried implementing these principles in 3D, which is exponentially more difficult because many more types of piece need to exist in 3D than in 2D. So my ultimate solution was: Simplify. Why do you have more than one type of piece in the first place, it is unnecessary, and creates unsolvable problems. But again, a Chess-type game with only one type of piece or move is again overly dull. Furthermore I had concluded by this point that first move advantage was a major flaw. (About 30% of top professional Chess games end in draw.) So, one possible solution would be to have a movement based game with only one type of piece in which captures are worth a set number of points and the player to move second is given a certain statistically determined komi. However, as I mentioned before, the game would probably be dull, and it would also be inelegant because the second player would have to capture less pieces than the first to win. Furthermore, it is uncertain if the komi could be refined enough, seeing as it would be unlikely that its value would be exactly equivalent to the capture of a certain number of pieces.

So I concluded that what was needed was a game where movement was not involved but point scoring was, so the second player could be compensated. Also, with my experiments with 3D and other games, I had concluded that simplicity was the key. Three dimensional games create technical problems (without even thinking about problems caused by there physical requirements) that are unnecessary to deal with. The game should have the smallest number of dimensions necessary for meaningful interaction to occur. That excludes 0D and 1D. So the board must be two dimensional. Is this starting to sound familiar?

So the game needs to have:
1. One type of unit, of two opposite "charges".
2. Two dimensions.
3. No movement.
4. Komi.
5. All rules must be simple as possible to avoid unnecessary complication.
6. Enough variation to challenge humans.

"This is Go!" That was the conclusion I came to. I had learned the game while I was studying the flaws of Chess, and unwittingly I discovered the basic principles behind Go as the solution!

Just a couple of closing notes. The "units" or stones, should only have influence in the directly
orthogonally adjacent positions. Connection and removal are required to allow proper scoring. Adding diagonals are an unnecessary complication. The basic concept of claiming area, and the lack of stone movement, is necessary to satisfy conditions 3 and 4. The design of the stones and the lack of additional arbitrary rules (Like prohibiting suicide!), as well as the board geometry and ko rules are required by conditions 1, 2, and 5.

So anyway, once I had determined this, I was so impressed by the game that I had to start playing it, to satisfy the one last question: It works logically and functionally, but does it really make the best game? And the conclusion I came to: overwhelmingly yes!

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War

Massive wall of text is massive...could you add some line breaks in the first paragraph for easier reading?

Fascinating

Suggestion: more paragraph breaks.

_________________
That which can be destroyed by the truth should be.
--
My (sadly neglected, but not forgotten) project: http://dailyjoseki.com

Is it better or worse now?

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War

You will have a hard time demonstrating that the movement of rooks and bishops is "opposite but corresponding" in any but the most superficial sense.


Well, rule 4 leaves us with very few other choices among existing games, doesn't it? But it's interesting that the game you describe is the modern komi Go and not the game that has been played for thousands of years before the invention of komi. Is komi Go that much more perfect? But we don't even know what the correct value of komi is!

Anyway komi is not the only solution for "fairness". Pie rule is another, and then the whole families of connection (hex, twixt, gonnect) and m,n,k games (tic-tac-toe, connect 4, gomoku) also satisfy your conditions.

Paragraphs for every line don't really help...

_________________
That which can be destroyed by the truth should be.
--
My (sadly neglected, but not forgotten) project: http://dailyjoseki.com

Might want to undo the double spacing as well.

The orthogonal direction and diagonal direction are the moves that change one variable at a time and two variables at a time, respectively, when moving. This makes them "corresponding".



Yes, it is that much better, and a komi of 7 has a reasonable statistical basis. In terms of humans playing the game and margin for error, this is probably as close as you can get. However, if further studies indicate otherwise, it can always be modified to be more accurate.


Actually, I find it ironic that John Nash's invention of Hex was intended to develop a game superior to Go, but I think it actually illustrated why it is best. The pie rule is an interesting concept but the idea that it makes the game perfectly fair is not necessarily true. There have been strategies developed for Hex that could give one side or the other an edge in spite of the pie rule. I think any game not based on scoring runs into problems here. Let's try Hex for example. If played on a 3x3 board with the pie rule, the second player will always win. This may be true for all odd numbered boards with perfect play. If played on even numbered boards the game should be a draw with or without the pie rule, as long as the second player mirrors. So it may theoretically work on even numbered boards, but it cannot produce a workable game for humans.

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War

All right, I know it's not perfect, but that's my final edit.

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War

I do not buy it that only one type of playing pieces and their movement would lead to a dull game. It must be possible to design a game as interesting as go (for players preferring movement to no movement).

I don't disagree here. It may be possible, but it would not meet my standards set forth here. Understand, I in no way mean to imply that any of these other games are bad, just that they are not the best, by my standards. I like many games which I consider to be of somewhat flawed design. Certainly my requirements exclude most games that exist. I understand that many people like games such as poker, which by my definition are flawed from the outset. There's nothing wrong with that. It's fine to for many, if not most games to have arbitrary designs. My goal is the most logically consistent game. For me, that is also the best. People are free to play whatever games they like.

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War

Also, komi does not make the sides equal. The roles of Black and White are still fundamentally different. If you want true fairness, you need simultaneous play (cumbersome but feasible with a board; trivial with computers). Surely some game with simultaneous play is "more perfect" than Go?

Not equal in terms of role, but as close as possible in terms of equal chances. That's what I call fair.


That is a good point, and I have considered the concept. There are two issues I find with it: one functional and the other structural. The functional issue is I think such a game is probably too difficult for humans; the structural issue is that you then have a new type of ko: point fights, where both players try to play on the same critical point at the same time. I think it gets worse from there. But tell you what, if you manage to develop something workable based on the concept, I'll be the first to support it.

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War

Eh, I don't have motivation to try to develop the perfect game, I'm satisfied with our imperfect go

The biggest difference between go and various connection games like hex and havannah is not that go is somehow better (I don't think komi is a compelling argument), but that go is much more researched, there's a ton of books on it, there're many people who play it, etc. Imagine if go didn't exist and somebody had just invented it today. Even if they managed to get others to play, I doubt they'd ever reach SDK or figure out high-level concepts on their own. They would miss out on all the depth and beauty of go, despite having invented it.

Then how would you refute my argument? I don't think the Pie rule and simultaneous play work that well if you analyze them.

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War

Because I think the whole issue is not important. People play chess without any problems.

You could argue that go is broken, not chess, because go needs komi and chess doesn't.

Okay, so you don't really disagree with my argument, you just don't think it's important, right? Actually I think Chess needs something like komi, but its structure prevents it. This is one of the basic flaws cited in my original post.

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War

What if both players want to play on the same point (as they often do), how would that work with simultaneous play?

If you want a fair game you can play it twice, alternating colours. The final score being the number of games won. It'll result in more draws, but I don't see anything wrong with that.

If we're talking about games in general - you could design a game in such a way that this is legal.
If we're talking about Go, see http://www.win.tue.nl/~engels/go/variants.html#simul - not really very practical.

Well, I don't consider 30% draws at the top professional level to be "without any problems".

Why would you want more draws if you could avoid it? In a game like Go, draws occur when players play almost equally well, and thus it is rather rare. In Chess, on the other hand, draws often occur because e.g. the position gets blocked, etc. This is why draws are so common in Chess; it's not that all the players are so equal.

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War