Editing Expectiminimax (section)

==Pseudocode==

The expectiminimax algorithm is a variant of the [[minimax]] algorithm and was firstly proposed by [[Donald Michie]] in 1966.<ref>{{cite book |doi=10.1016/B978-0-08-011356-2.50011-2 |chapter=Game-Playing and Game-Learning Automata |title=Advances in Programming and Non-Numerical Computation |date=1966 |last1=Michie |first1=D. |pages=183–200 |isbn=978-0-08-011356-2 }}</ref>
Its [[pseudocode]] is given below. 

 '''function''' expectiminimax(node, depth)
     '''if''' node is a terminal node '''or''' depth = 0
         '''return''' the heuristic value of node
     '''if''' the adversary is to play at node
         // Return value of minimum-valued child node
         '''let''' α := +∞
         '''foreach''' child of node
             α := min(α, expectiminimax(child, depth-1))
     '''else if''' we are to play at node
         // Return value of maximum-valued child node
         '''let''' α := -∞
         '''foreach''' child of node
             α := max(α, expectiminimax(child, depth-1))
     '''else if''' random event at node
         // Return weighted average of all child nodes' values
         '''let''' α := 0
         '''foreach''' child of node
             α := α + (Probability[child] × expectiminimax(child, depth-1))
     '''return''' α

Note that for random nodes, there must be a known probability of reaching each child. (For most games of chance, child nodes will be equally-weighted, which means the return value can simply be the average of all child values.)