:::
There are six rounds of the tournament, and the sisters have to co-exist in a given round, to meet in it. They co-exist in the first round, where they have a 1/63 chance to meet, by the logic that wherever the first sister is placed in the 64 spots, the second has a 1/63rd chance of being in opposition to her spot. Thus if the sisters co-exist in a round, they have a 1/(n-1) chance of meeting in that round, where n is the number of competitors in that round. If they do not meet, then the chance of both advancing is .5 * .5. So the chance they both advance to the next round, and meet there, is (.5^2) * (1/31). The chance they do not meet there and advance to the third round and meet there is (.5^(2 * 2)) * 1/15. Next round you get (.5^(2 * 3)) * 1/7, and so on. Sum the probabilities for the total chance they ever meet.
:::