18. (15 points) Two players, A and B, are playing a certain game with the following rules: In each round, the winner gets 1 point, and the loser gets 0 points; the game ends when one player's score is 2 points higher than the other's. Additionally, the game is limited to a maximum of 20 rounds; if after 20 rounds, the player with the higher score wins the game, and if the scores are equal, it is a draw. It is known that the probability of A winning each round is $p(0<p<1)$, and the probability of B winning is $q=1-p$. Assume that the results of each round are independent. Let the game end after $\xi$ rounds. Find the range of the expected value $E \xi$.

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The problem is translated as requested, maintaining the original format and line breaks.
18. Let the probability that the game ends after $k$ rounds be $p(\xi=k)$.

If $k$ is odd, then the difference in scores between A and B is also odd, and the game cannot end.
Consider when $k$ is even, the results of the first two rounds:
(1) A wins both or B wins both, referred to as a decisive two rounds, with a probability of $p^{2}+q^{2}$;
(2) A and B each win one, referred to as an indecisive two rounds, with two possible scenarios, hence a probability of $2 p q$.

Thus, the 1st and 2nd, 3rd and 4th, ..., $k-3$ and $k-2$ rounds are all indecisive.

If $k \neq 20$, then the $k-1$ and $k$ rounds are decisive. Therefore,
$$
p(\xi=k)=(2 p q)^{\frac{k}{2}-1}\left(p^{2}+q^{2}\right) .
$$

If $k=20$, then the game must end. Therefore,
$$
p(\xi=20)=(2 p q)^{9} \text {. }
$$

In summary,
$$
E \xi=\left(p^{2}+q^{2}\right) \sum_{i=1}^{9} 2 i(2 p q)^{i-1}+20(2 p q)^{9} \text {. }
$$

Let $u=2 p q \in\left(0, \frac{1}{2}\right]$. Then
$$
\begin{array}{l}
E \xi=(1-u) \sum_{i=1}^{9} 2 i u^{i-1}+20 u^{9} \\
=\sum_{i=1}^{9} 2 i u^{i-1}-\sum_{i=1}^{9} 2 i u^{i}+20 u^{9} \\
=2+\sum_{i=1}^{8}(2 i+2) u^{i}-\sum_{i=1}^{8} 2 i u^{i}+2 u^{9} \\
=2+2 \sum_{i=1}^{9} u^{i}=\frac{2\left(1-u^{10}\right)}{1-u} .
\end{array}
$$

Since $0<u \leqslant \frac{1}{2}$, we have
$$
2<E \xi \leqslant 4-\left(\frac{1}{2}\right)^{8} \text {. }
$$