Friday, February 12, 2010

Adding more players

I love to play games with more than just one other player. Getting a bunch of people around a board or table to do something interactive is excellent.

I really enjoy playing Magic: The Gathering, and when the rules were generalized to encompass more than two players, I was thrilled. Unfortunately, standard rules for just playing a big multi-player game can be a bit strange. Luckily, I've become familiar with fitting formats for 3, 4, 5 and 6 players.

Some combinatorial games generalize very well in terms of how to make a turn. All impartial games just act the same as they do normally. The rule for winning/losing might be a bit different: does only the first player who can't move lose and everyone else win? Or does the player that made the last move win and everyone else loses? Or do some of those other players get a "draw"?

In any of these cases, the value of the games change as players are added. One can no longer check whether the nimber of an impartial game equals 0, as the parity has been altered! I don't know anything about the difficulty of these games, except that it seems immediately daunting. I can only assume that adding players normally makes things more difficult!

Thus I'm curious: are there any games that suddenly become easy (or trivial!) with more than two players?

An additional note: thanks to those who prompted me to add rows to the game table. I will continue to add entries/info as I think of it or as I am harassed :) We had a snow day here at Wittenberg, and that helped me catch up with work a bit.

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