I thought that I had a pretty good understanding of DNA and genetics, but the things you have said on this subject have contradicted some basic ideas I have held.
First, you have said that 12 out of 13 is enough for you. While it might be an extremely unlikely thing to happen(depends on which alleles are chosen), to use your lottery example, 12 out of 13 still doesn't win the lottery. If there is a marker in the DNA that doesn't match the control sample, or a marker in the control that is not in the other sample, doesn't that prove that the two samples of DNA are not from the same person? If not, I wish you would be as lengthy and detailed as is necessary to convince a reasonable person.
Now, I understand that you needn't test every single marker to be fairly confident that you have a match, but when people say that they matched 12 markers or 25 markers to obtain a match, I always understoood that to mean that the markers were selected for rarity and unrelatedness in the first place, and that none of the markers failed to match. Specifically, 12 markers is a match, but only if it is 12 out of 12 rare and fairly orthogonal(for lack of field-specific term) markers.
Please tell me how a person's DNA can not match any individual marker from his or her own DNA. Irrespective of how many matches are found, how can you have a marker on some of your DNA that is not on some of your other DNA?
I know that if you undertake to match any random bits of DNA, you will get lots of matches -- humans share 98% of their genetic information with chimpanzees, and even more with eachother.
Now, what happens if they take that DNA and compare it to someone NOT AT RANDOM, but someone from the VD family? What are the CHANCES then? ANd doesn't it depend on what MARKERS you pick ?