19. A person holds four ropes tightly in their hand, with only the ends of the ropes showing, then randomly connects two of the four heads at one end, and the other two, and does the same for the four tails at the other end. What is the probability that the four ropes will form a single loop when the hand is opened? $\qquad$
19. $\frac{2}{3}$.

There are 9 ways that meet the requirements, and 6 of these ways can form a loop as shown in Figure 10.
Figure 10

Therefore, the probability that four ropes will exactly form a loop is
$$
6 \div 9=\frac{2}{3} \text {. }
$$