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\documentclass[tikz, margin=10pt]{standalone}
\usepackage{mathtools}% lädt amsmath

\usetikzlibrary{trees}

\begin{document}
\begin{tikzpicture}[
  grow=right,
  sloped,
  level distance=3cm,
  level 1/.style={sibling distance=6cm},
  level 2/.style={sibling distance=4cm},
  level 3/.style={sibling distance=2cm},
  level 4/.style={sibling distance=2cm, font=\footnotesize},
  edge from parent/.style={draw, font=\footnotesize},
  auto
]
  %1. Haupt Knoten 2.Child Knoten 3. Child Knoten 
\node[circle]{B}
  child {node {S}% Oben
    child {node {$\binom{v-p_0(k)-k}{p_0(k)+k-c}$}
      edge from parent node [auto=right]{$d=1$}
    }
    child {node {B} 
      child{node {S}
        child{node {$\binom{-p_0(k)}{p_0(k)}$}
          edge from parent node [auto=right] {$d=1$}% <- d=1
        }
        child{node {$\binom{v-p_0(k)-c}{p_0(k)}$}
          edge from parent node {$d=0$}% <- d=0
        }
        edge from parent node {$(p_0(k),c)$}
      }
      edge from parent node {$d=0$ }
    }
    edge from parent node [auto=right] {$(p_0(k),k)$; $k<c$}
  }
  child {node {S}
    child {node {$\binom{v-p_0(c)-c}{p_0(c)}$}
      edge from parent node [auto=right]  {$d=1$}
    }
    child {node {$\binom{-p_o(c)}{p_0(c)}$}
      edge from parent node {$d=0$}
    }
    edge from parent node {$(p_0(c),c)$; $k=c$}
  };
\end{tikzpicture}
\end{document}

\documentclass[tikz,margin=10pt]{standalone}
\usetikzlibrary{mindmap,trees}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[
  grow=right,sloped,
  level distance=3cm,
  level 1/.style={sibling distance=6cm},
  level 2/.style={sibling distance=4cm},
  level 3/.style={sibling distance=2cm},
  bag/.style={}
   level 4/.style={sibling distance=2cm},
  bag/.style={}
  ]
  %1. Haupt Knoten 2.Child Knoten 3. Child Knoten 
  4. 
\node[bag][circle]{B}
  child {node[bag] {S}%Oben
    child {node[bag]{$\binom{v-p_0(k)-k}{p_0(k)+k-c}$} {}
      edge from parent node[below]{\footnotesize $d=1$}
    }
    child {node[bag]{B} 
      child{node[bag]{S}
       child{node[bag]{\footnotesize $\binom{-p_0(k)}{p_0(k)}$}}
      child{node[bag]{\footnotesize $\binom{v-p_0(k)-c}{p_0(k)}$}}
        edge from parent node [above]{\footnotesize $(p_0(k),c)$}
      }
      edge from parent node[above] {\footnotesize $d=0$ }
    }
    edge from parent node[below] {\footnotesize $(p_0(k),k)$; $k<c$}
  }
  child {node[bag] {S}
    child {node[bag]{$\binom{v-p_0(c)-c}{p_0(c)}$} {}
      edge from parent node[below]  {\footnotesize $d=1$}
    }
    child {node[bag]{$\binom{-p_o(c)}{p_0(c)}$} {}
      edge from parent node[above] {\footnotesize $d=0$}
    }
    edge from parent node[above] {\footnotesize $(p_0(c),c)$; $k=c$}
    };
\end{tikzpicture}
\end{document}