Multiply by $\left(\frac{2(7)}{3+7}\right)^{1/3} = 1.1187$
More generally, suppose that player $A$ rolls $n$ times and player $B$ rolls $m$ times. As others have already noted, the (unscaled) score of player $A$ is $$X \sim Beta(n, 1)$$ and the score of player $B$ is $$Y \sim Beta(m, 1)$$ with $X$ and $Y$ independent. Thus, the joint distribution of $X$ and $Y$ is $$f_{XY}(x, y) = nmx^{n-1}y^{m-1}, \ 0 < x, y < 1.$$
The goal is to find a constant $c$ such that
$$P(Y \leq cX) = \frac{1}{2}$$.
This probability can be found in terms of $c$, $n$ and $m$ as follows.
\begin{align*} P(Y \leq cX) &= \int_0^{1/c}\int_{cx}^1 nmx^{n-1}y^{m-1}dydx \\[1.5ex] &= \cdots \\[1.5ex] &= c^{-n}\left\{\frac{m}{n+m} \right\} \end{align*}
Setting this equal to $1/2$ and solving for $c$ yields
$$c = \left(\frac{2m}{n+m}\right)^{1/n}.$$