Probabilities in the Game of Set -- Ben Weiss, April 26, 2005

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I will describe the game and explain how it can be seen as completely
equivalent to statements about sets in vector spaces over Z_3 which do not
contain lines (these sets are known as caps). But as opposed to Prof.
Ellenberg's talk which focused on the maximal size of such caps, I will
discuss the probability of their existance.
To do so I will provide a brief lesson in probability theory and analytical
techniques, and then apply them to answer the question about the probability
a cap exists.