Study the following positions of a dice and determine how many dots are there on the dice face opposite the one with three dots.

Let's systematically find the adjacent and opposite faces by studying the given four positions of the dice:
1. From the second position, the visible faces are $1,3,$ and $4$. This implies that the faces with $1$ dot and $4$ dots are adjacent to the face with $3$ dots.
2. From the fourth position, the visible faces are $1,2,$ and $3$. This implies that the faces with $1$ dot and $2$ dots are adjacent to the face with $3$ dots.

Combining these observations, the faces adjacent to $3$ are: $1,2,$ and $4$.

3. Now let's analyze the first position. The visible faces are $3,4,$ and $6$. This tells us that the face with $6$ dots is also adjacent to $3$.

Listing all adjacent faces to the face with $3$ dots:

$$\text{Adjacent faces}=\{1,2,4,6\}$$

Since a standard dice has faces numbered from $1$ to $6$, the only remaining face that is not adjacent to $3$ must be opposite to it. The number missing from our adjacent list is $5$.

Therefore, the face opposite to the one with $3$ dots contains $5$ dots.