  Our aim in this paper is to attain a sharp asymptotic estimate for the greedy
constant $C_g[\mathcal{H}^{(p)},L_p]$ of the (normalized) Haar system
$\mathcal{H}^{(p)}$ in $L_{p}[0,1]$ for $1<p<\infty$. We will show that the
superdemocracy constant of $\mathcal{H}^{(p)}$ in $L_{p}[0,1]$ grows as
$p^{\ast}=\max\{p,p/(p-1)\}$ as $p^*$ goes to $\infty$. Thus, since the
unconditionality constant of $\mathcal{H}^{(p)}$ in $L_{p}[0,1]$ is $p^*-1$,
the well-known general estimates for the greedy constant of a greedy basis
obtained from the intrinsic features of greediness (namely, democracy and
unconditionality) yield that $p^{\ast}\lesssim
C_g[\mathcal{H}^{(p)},L_p]\lesssim (p^{\ast})^{2}$. Going further, we develop
techniques that allow us to close the gap between those two bounds,
establishing that, in fact, $C_g[\mathcal{H}^{(p)},L_p]\approx p^{\ast}$.
