Choose 2 from N, since order is unimportant.
On my calculator, that's the "nCr" button
For N=27, that's 351 games to be played round-robin.
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27 players in games of three, where each player must play every other player once and only once. Each player only has to play 13 games total.
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No; Player 1 goes up against all 26 other players. Similarily for the others, so that's 26 games total for each player. 
26games*27people = 702 plays
That makes for 351 two-player games.
[ August 06, 2003, 22:11: Message edited by: Suicide Junkie ]