A Game -- Rings

[jducoeur]

A possible board game that came to me this morning, and should be tried out:

The game is conceptually similar to Othello, in that you're placing white and black pieces on the grid, and flipping your opponent's pieces to your own color. But this one works with rings, instead of lines.

Consider a Go board. Each point can be considered to rest on eight different 3 x 3 "rings", like this:

   . . x 1 x . .
   . . x . x . .
   . . x x x . .

Point 1 is in the ring shown; it's also in seven other rings, in each of the possible positions within a ring. (Points on the edge of the board will, obviously, be contained in fewer rings.)

On your move, you place a piece of your color on the board. If that piece completes a ring, then all pieces in that ring are flipped to your color. When the board is filled, the player with the most pieces of his color wins.

That's the basics. There are some options to consider for tuning:

-- You might only flip the pieces that are adjacent to the finishing one that are of the other color. For example, in this setup:

   . . w 2 w . .
   . . b . w . .
   . . W W b . .

If black plays at point 2, then only the points marked "w" are flipped, but not the ones marked "W". This is closer to the Othello rule. My suspicion is that it complicates things for no good reason, though.

-- I suspect intuitively that this game would be best played on a triangle grid, with hex rings of 6 points each. But Go boards are easier to obtain.

-- I don't know what the optimal size for a game is. I'm sure that a full Go board is pointlessly large.

I don't know if the game is any good, but I'll have to try it out sometime and see. If anyone else experiments with it, tell me what you find.

Comments

[tangerinpenguin.livejournal.com]

Interesting!

The endgame will involve extensive flipping, given that in a densely-packed board, most moves are going to complete a loop (and probably complete several.) On a small to medium board, the pattern of actual captures through midgame may end up being unimportant, and the game may reduce to the optimum final series of two or three "money" moves for each player.

The player making the last move, for example, is guaranteed to complete at least one loop (if the last move is a corner) giving them at least 8 pieces of their color. A last move to an edge next to a corner is two overlapping loops, 12 pieces. To an edge more than one space from a corner, three overlapping loops, 15 pieces. The optimal case, a final move to the interior, could flip an entire 5x5 square.

Possible variants that come to mind to make the early decisions more interesting:

a) The inside of a completed loop is "dead" and cannot be played. (This still probably puts you on a larger board; in fact, it probably makes a full GO board a more playable size.)

b) You can only capture those loops that you complete that already contain another piece of your color. (Getting us back to some of the Othello dynamic.)

[jducoeur]

Your analysis sounds about right. On your specific ideas:

a) The inside of a completed loop is "dead" and cannot be played. (This still probably puts you on a larger board; in fact, it probably makes a full GO board a more playable size.)

I like it. This adds an interesting low-level strategic twist -- not the sort of deep strategy that I tend to dislike (because I'm weak at it), but it makes you at least consider the order of your decisions a lot more carefully.

b) You can only capture those loops that you complete that already contain another piece of your color. (Getting us back to some of the Othello dynamic.)

Possible. I agree that it makes the game more Othello-like, although it adds back in Othello's tendency towards runaway wins: once you've mostly captured an area, it's very difficult to lose any of it. I'm not sure if I like this one or not, but it's probably worth trying, to see how it affects the tuning of the game. It arguably makes the game fairer, by rewarding good early play...

Both good ideas, and worth experimenting with. Thanks...

[mindways]

The endgame will involve extensive flipping, given that in a densely-packed board, most moves are going to complete a loop (and probably complete several.) On a small to medium board, the pattern of actual captures through midgame may end up being unimportant, and the game may reduce to the optimum final series of two or three "money" moves for each player.

One way around this is to read the rules the way I originally did - that a "loop" is only a loop if the center square is empty.

This might lead to degenerate strategies (fully-filling-in an area from one corner outwards); I'm not sure off the top of my head if more aggressive/interesting strategies would be able to effectively counter such a thing...I'd need to try it out.

The inside of a completed loop is "dead" and cannot be played.

I like this notion.

(Justin - if you're ever around, I'd be happy to give this game a whirl with you. :-)

[cellio]

Interesting idea.

If you go with the rules variant about w and W pieces, you should consider what happens when a play completes multiple rings. Specifically, does the player choose the order in which to resolve them, or is it predetermined?