Comment author:jimrandomh
02 April 2009 05:10:47PM
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10 points
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I like the concept of the Paranoid Debating game, but would propose one modification. Rather than always having a player assigned to deceive, have one with 50% probability, but don't reveal to anyone (except the deceiver) whether there is a deceiver in the group. To implement this with a group of n players, first choose a spokesman and give him a spade, then deal each other player one card from a deck containing 2n-3 black cards and one red card.
As another possible variant, introduce a small (say, 1/52) chance that everyone except the spokesman is red, and everyone except the spokesman knows it. To implement this, first choose a spokesman at random, then choose a dealer from the remaining players. The dealer looks at one card at random. If it's the ace of diamonds, he prepares a deck containing only diamonds; otherwise, he prepares a deck containing 2n-3 black cards and one heart, shuffles it and then deals from it. Getting a diamond means that everyone else has a diamond; getting a heart means that everyone else has black cards.
Comment author:MattFisher
03 April 2009 05:26:17AM
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0 points
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A simple variant with interesting results would be to deal everyone one card from a full deck. Anyone who is dealt a diamond is a deceiver.
The dealer can be the spokesman, so it will rotate each turn.
This way there is a 1/4 chance that any given person is a deceiver, and a small (1/(4^n))-ish chance that all n players (including the dealer) are trying to deceive each other.
Trying to reach the best outcome for everyone with an unknown number of deceivers in the mix? Sounds like life.
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I like the concept of the Paranoid Debating game, but would propose one modification. Rather than always having a player assigned to deceive, have one with 50% probability, but don't reveal to anyone (except the deceiver) whether there is a deceiver in the group. To implement this with a group of n players, first choose a spokesman and give him a spade, then deal each other player one card from a deck containing 2n-3 black cards and one red card.
As another possible variant, introduce a small (say, 1/52) chance that everyone except the spokesman is red, and everyone except the spokesman knows it. To implement this, first choose a spokesman at random, then choose a dealer from the remaining players. The dealer looks at one card at random. If it's the ace of diamonds, he prepares a deck containing only diamonds; otherwise, he prepares a deck containing 2n-3 black cards and one heart, shuffles it and then deals from it. Getting a diamond means that everyone else has a diamond; getting a heart means that everyone else has black cards.
A simple variant with interesting results would be to deal everyone one card from a full deck. Anyone who is dealt a diamond is a deceiver. The dealer can be the spokesman, so it will rotate each turn. This way there is a 1/4 chance that any given person is a deceiver, and a small (1/(4^n))-ish chance that all n players (including the dealer) are trying to deceive each other.
Trying to reach the best outcome for everyone with an unknown number of deceivers in the mix? Sounds like life.