3. There is a dice-throwing game that can randomly display one of the numbers from 1 to 6. A chess piece is placed at the vertex of a square $ABCD$ with a side length of 1. Each time the dice is thrown, the chess piece moves once. The movement rule is to start from the current position and move a distance equal to the number rolled in a counterclockwise direction along the perimeter of the square to reach another vertex. Assuming the chess piece is initially at $A$, what is the probability that the distance between the points reached after two moves is greater than 1? 
(A) $\frac{1}{2}$
(B) $\frac{1}{3}$
(C) $\frac{1}{4}$
(D) $\frac{1}{6}$
3. B.

For $X \in\{A, B, C, D\}$, let $P(X)$ denote the probability of moving from $A$ to point $X$ in one move. Therefore,
$$
P(A)+P(B)+P(C)+P(D)=1 .
$$

The distance between the points reached after two moves being greater than 1 is equivalent to the points being opposite vertices of the square. Thus, the required probability is
$$
\begin{aligned}
P= & P(A) P(C)+P(B) P(C)+ \\
& P(C) P(C)+P(D) P(C) \\
= & {[P(A)+P(B)+P(C)+P(D)] P(C) } \\
= & P(C)=\frac{1}{3} .
\end{aligned}
$$