In Peter Norvig’s interesting post The Odds of Finding a Set in The Card Game SET, he concludes that the odds against there being no set in 12 cards, during a game, is 16:1. This is an average value, but it doesn’t tell the whole story.
A more detailed analysis shows that the odds when playing a game of SET start off at 30:1 for the first round. Then they quickly fall, and after about the 4:th round they are 14:1 and for the next 20 rounds they slowly fall towards 13:1. So for the majority of the rounds played, the odds are between 14:1 and 13:1.
Is there a set here?
Henrik Warne's blog 