\begin{frame}
  \frametitle{piecewise linear and convex}
  \framesubtitle{policy and V function}
   V function:\\
   \begin{align}
    V_1(b)&=max_ur(b,u)\\
    &max=\left\{
\begin{aligned}
-100p_1+100(1-p_1) \\
100p_1-50(1-p_1)\\
-1
\end{aligned}
\right\}.
   \end{align}

 \end{frame}

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