From Ancestry's white paper about their categories (sorry, the formatting is lost):
Ancestry’s NEW method for calculating matches (V2) as of November 2014:
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Confidence Details
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Extremely High Approximate amount of sharing: More than 30 centiMorgans. Likelihood you and your match share a single recent common ancestor (within 5 or 6 generations): Virtually 100%Description: You and your match share enough DNA to prove that you’re both descendants of a common ancestor (or couple) -- and the connection is recent enough to be conclusive.
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Very High Approximate amount of sharing: 20-30 centiMorgans. Likelihood you and your match share a single recent common ancestor (within 5 or 6 generations): 99%Description: You and your match share enough DNA that we are almost certain you’re both descendants of a recent common ancestor (or couple).
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High Approximate amount of sharing: 12-20 centiMorgans. Likelihood you and your match share a single recent common ancestor (within 5 or 6 generations): 95%.Description: You and your match share enough DNA that it is likely you’re both descendants of the same common ancestor or couple, but there’s a small chance the common ancestor(s) are quite distant and difficult to identify.
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Good Approximate amount of sharing: 6-12 centiMorgans. Likelihood you and your match share a single recent common ancestor (within 5 or 6 generations): More than 50%.Description: You and your match share some DNA, probably from a recent common ancestor or couple, but the DNA may be from distant ancestors that are difficult to identify.
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Moderate Approximate amount of sharing: 6 centiMorgans or less. Likelihood you and your match share a single recent common ancestor (within 5 or 6 generations): 20-50%.Description: You and your match might share DNA because of a recent common ancestor or couple, share DNA from very distant ancestors or you may not be related.
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Barbara