\usepackage{tikz}
\begin{document}
\begin{tabular}[b]{@{}ccc@{}}
\begin{tikzpicture}[grow=right,sloped]
\tikzstyle{level 1}=[level distance=2cm, sibling distance=2cm]
\tikzstyle{level 2}=[level distance=2cm, sibling distance=1.5cm]
\node[rectangle,draw]{}
child{node[circle,draw]{}
child{node{$P_{T|s}$}} edge from parent node[below]{$t\neq s$}
}
child{node[circle,draw]{}
child{node{$z$} edge from parent node[below]{$1-p$}}
child{node{$x$}edge from parent node[above]{$p$}}
edge from parent node[above]{$t=s$}
};
\end{tikzpicture}
&
$\sim$
&
\begin{tikzpicture}[grow=right,sloped]
\tikzstyle{level 1}=[level distance=2cm, sibling distance=2cm]
\tikzstyle{level 2}=[level distance=2cm, sibling distance=1.5cm]
\node[rectangle,draw]{}
child{node[circle,draw]{}
child{node{$P_{T|s}$}} edge from parent node[below]{$t\neq s$}
}
child{node[circle,draw]{}
child{node{$z$} edge from parent node[below]{$1-p$}}
child{node{$x$}edge from parent node[above]{$p$}}
edge from parent node[above]{$t=s$}
};
\end{tikzpicture} \\
\end{tabular}
\end{document}

I'm really sorry but I searched a lot but really couldn't find a solution. I want to include two pictures and one math symbol here in the tabular. I thought the default vertical position is centered! but I cannot position the \sim symbol in the middle! Thank you in advance for any help! I apologise for being such a noob!


This gets everything aligned on the square but eliminates any need for guessing how far to raise one or the other of the pictures or