3. Three people, A, B, and C, are playing the game "Scissors, Rock, Paper." In each round, A, B, and C simultaneously show one of the gestures: scissors, rock, or paper, and they do so independently. Let the number of people who beat A in a round be $\xi$. Then the expected value $E \xi$ of the random variable $\xi$ is ( ).
(A) $\frac{1}{3}$
(B) $\frac{4}{9}$
(C) $\frac{2}{3}$
(D) 1
3. C.

Notice,
$$
\begin{array}{l}
P(\xi=0)=\frac{3 \times 4}{27}=\frac{4}{9}, \\
P(\xi=1)=\frac{3 \times 4}{27}=\frac{4}{9}, \\
P(\xi=2)=\frac{3 \times 1}{27}=\frac{1}{9} .
\end{array}
$$

Then $E \xi=\frac{4}{9} \times 0+\frac{4}{9} \times 1+\frac{1}{9} \times 2=\frac{2}{3}$.