I'd like to toss in my 1.7 cents.   1. I got the impression that the expression something like "even if 300 3rd cousins" was meant to indicate a large number. I would like to point out what a SMALL number this really is. Assume all your ancestors, and everyone in your family had exactly 2 children. Further assume that all of your generation, and all of the generation above you are still alive. In that case you would have living:   A. Sibling: 1 B. Aunt/Uncle: 2 C. First Cousins: 4 D. 1c1r: 8 E. 2nd Cousins: 16 F. 2c1r: 32 G. 3rd cousins: 64   So that's a total of 127 people that you could match - with just 2 kids per couple. If you move that number to 3, you get 378. With just 3 kids per couple, you have very nearly 300 potential matches just with 3rd cousins and 2c1r alone.   Now imagine how many you might have with large families. With 7 kids per, you'd have 300+ SECOND cousins alone, and that's from just ONE set of your sets of great grandparents.   Geometric progressions get big fast. I think people would be astonished to learn how many 3rd cousins they really had, particularly if they are of the generation born prior to the 2nd World War. In my generation, maybe not so much. I have a whopping 3 first cousins. And if you add together all the children of all my siblings and all my first cousins, there are 7 total in that next generation. Do that same calculation with any of my grandparents, and you get a big number.   2. I think the probability of match is like the birthday paradox Ann suggested. And it can be imagined this way...take the 127 matches I outlined in point 1 above, and consider the matching not from your point-of-view, but from the point-of-view of your 3rd cousin #64. By counting the number of cousins you have and comparing it to the number in the database, you are essentially asking what is the chance that ANY ONE (or pair) of your ancestors is the same as the (let's say pair of 2-greats-grandparents) PARTICULAR ONE (or pair) that you have outlined in the common descent tree. But that isn't the only way you could match. You could match any one of your ancestors to ANY ONE of his ancestors. Look at your 3rd cousin's pedigree. You'll see your common ancestor in there, it is true, but what you'll see mostly is just blank space. And the matching could also come from anywhere in that great unknown.   So then it comes back to the point of populations. In a sufficiently isolated and immobile population, the probability of match tends toward certainty.   Gregg Bonner