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Sudden death in the fourth dimension

Back in 1987, I and my best friend in school, Barbara, would meet about once a week, drink sake, and play backgammon.

When we grew bored of the sake we switched to ginger ale with Aspirin + C in it, and when we grew bored with backgammon we'd either copy games we'd seen in stores, or invent our own.

Ginger Ale with Aspirin + C

1 glass of Ginger Ale, from a bottle, not from a can.
1 ``Aspirin + C'' or your national equivalent.

Pour Ginger Ale in glass.  Drop Aspirin + C in Ginger Ale.  Wait until tablet has dissolved.  Try to drink without suffocating.

(Aspirin has been linked to ulcers lately, so it's probably not a good idea to get used to a drink involving it.)

Sudden death in the fourth dimension

2 players
1 hypercube (16 corners in 4 dimensions)
8 tokens, 4 in each color

Each player picks a color and finds 4 coins, stones, or pieces of paper of that color. 

The game starts with tokens of alternating colors at the (graphically) "outer" corners of the hypercube.

Then, players take turns moving one of their tokens along the edges of the cube to unoccupied other corners.
The objective of the game is to move the tokens of your color into a connected group; the first player to form a chain or star wins.
What are the combinatorics of this game? Does the first player always win? (Yes, says one correspondent; no, the players get into endless loops, is what I think.)

Clues and suggestions welcome; send email to jutta@cs.tu-berlin.de.