Final move selection

To select the best move after play-out analysis is done, it is possible to simply pick the move $m_0$ with the highest heuristic value:

$$\arg \max_{m_0} h_h(m_0\mid \{\}).$$ (4)

This is the only option with first-order heuristics, but higher order heuristics allow for more. One can make a min-max tree search in the tree formed by known patterns. For instance, using the second-order heuristics, one selects the move $m_1$, for which the best answer $m_0$ by the opponent is the worst:

$$\arg \min_{m_1} \max_{m_0} h_h(m_0\mid \{m_1\}).$$ (5)