  We analyze the number of tile types $t$, bins $b$, and stages necessary to
assemble $n \times n$ squares and scaled shapes in the staged tile assembly
model. For $n \times n$ squares, we prove $\mathcal{O}(\frac{\log{n} - tb -
t\log t}{b^2} + \frac{\log \log b}{\log t})$ stages suffice and
$\Omega(\frac{\log{n} - tb - t\log t}{b^2})$ are necessary for almost all $n$.
For shapes $S$ with Kolmogorov complexity $K(S)$, we prove
$\mathcal{O}(\frac{K(S) - tb - t\log t}{b^2} + \frac{\log \log b}{\log t})$
stages suffice and $\Omega(\frac{K(S) - tb - t\log t}{b^2})$ are necessary to
assemble a scaled version of $S$, for almost all $S$. We obtain similarly tight
bounds when the more powerful flexible glues are permitted.
