Well, considering my 3D Go idea "went", what about this? The catch is that it seems so obvious someone must have done it before.

Consider a three-dimensional grid. In a two-player game, each player has a bunch of stones in one of two colors (four colors total). The goal is simple: place stones in the grid so that no adjacent pair of stones (all 6 neighbors) have the same color.

I saw somewhere online that the three-dimensional version of the Four Color Theorem has no limit on the number of colors necessary. So it should be possible to force someone to place two stones of the same color next to each other in a 3D grid with a finite number of colors.

Maybe in the 2 player game each person gets 3 colors, 3 player each person gets 2, stuff like that.

Alternatively, you can have a 2D version where each player gets two colors but the same number of each color (so the Four Color Theorem isn't necessarily going to work with restrictions on the number of stones of each color -- hopefully, the restriction should interfere enough to prevent a successful tiling with four colors).

This must have been done before...has it?

Thanks in advance,

ACG

The idea of 3D Go with multiple players is actually quite interesting. Or even 2D Go.

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If Black and White combine their stones to make a wall/surface surrounding a bunch of Red stones, the Red stones are removed from the board. The territory goes to the player who contributed the most stones to the wall (it can't be split evenly: otherwise Black will wait until White's got virtually a complete ring and throw in the last piece to get half the territory -- great gain for little effort). Ideally Black would get (B/(W+B)) of the territory, but that would throw math into it and make things too compliated.

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You can also do this: two players, but each controls two sets of colors (say Black/White and Red/Green). A Red stone can block the liberties of all other colors, INCLUDING GREEN. A stone completely surrounded by the three other colors gets removed. I wonder what an effect this would have. Each player has an equal number of his two colors to make the choice of color to be played important.

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What do you think of a Set/Go combination? Take a set (er...) of four Set decks and put the pictures on 324 Go stones. Each player gets two decks. Two adjacent stones form a "wall" if they share N attributes. Note that the opponent can contribute his tile to the wall if he isn't careful. Mixed territories go to the person who contributed the most tiles.

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Incidentally, I told a game store about my Five Crowns poker odds. The owner of the store told the game's manufacturer, and they were ecstatic. They want me to give them a PDF of the odds (especially the math of determining the combinatorics) so they can post it on their website (both for poker purposes and teaching purposes).

ACG