  We obtain confidence intervals for the location of the percolation phase
transition in H\"aggstr\"om's divide and color model on the square lattice
$\mathbb{Z}^2$ and the hexagonal lattice $\mathbb{H}$. The resulting
probabilistic bounds are much tighter than the best deterministic bounds up to
date; they give a clear picture of the behavior of the DaC models on
$\mathbb{Z}^2$ and $\mathbb{H}$ and enable a comparison with the triangular
lattice $\mathbb{T}$. In particular, our numerical results suggest similarities
between DaC model on these three lattices that are in line with universality
considerations, but with a remarkable difference: while the critical value
function $r_c(p)$ is known to be constant in the parameter $p$ for $p<p_c$ on
$\mathbb{T}$ and appears to be linear on $\mathbb{Z}^2$, it is almost certainly
non-linear on $\mathbb{H}$.
