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Let $u$ be a solution to the normalized p-harmonic obstacle problem with$p>2$. That is, $u\in W^{1,p}(B_1(0))$, $2<p<\infty$, $u\ge 0$ and $$ \d\left(|\nabla u|^{p-2}\nabla u\right)=\chi_{\{u>0\}}\textrm{ in }B_1(0) $$ where$u(x)\ge 0$ and $\chi_A$ is the characteristic function of the set $A$. Ourmain result is that for almost every free boundary point, with respect to the$(n-1)-$Hausdorff measure, there is a neighborhood where the free boundary is a$C^{1,\beta}-$graph. That is, for $\H^{n-1}-$a.e. point $x^0\in \partial\{u>0\}\cap B_1(0)$ there is an $r>0$ such that $B_r(x^0)\cap \partial\{u>0\}\in C^{1,\beta}$.

Almost Everywhere Regularity for the Free Boundary of the Normalized p-harmonic Obstacle problem $p>2$