Add EXPECTIMINIMAX

norvig · web-flow · commit 209599eaf30b · 2018-04-05T16:34:22.000-07:00
diff --git a/md/Minimax-Decision.md b/md/Minimax-Decision.md
@@ -1,4 +1,4 @@
-# MINIMAX-DECISION
+# MINIMAX-DECISION and EXPECTIMINIMAX
 
 ## AIMA3e
 __function__ MINIMAX-DECISION(_state_) __returns__ _an action_  
@@ -22,3 +22,10 @@ __function__ MIN\-VALUE(_state_) __returns__ _a utility value_
 
 ---
 __Figure__ ?? An algorithm for calculating minimax decisions. It returns the action corresponding to the best possible move, that is, the move that leads to the outcome with the best utility, under the assumption that the opponent plays to minimize utility. The functions MAX\-VALUE and MIN\-VALUE go through the whole game tree, all the way to the leaves, to determine the backed\-up value of a state. The notation argmax <sub>_a_ &Element; _S_</sub> _f_(_a_) computes the element _a_ of set _S_ that has maximum value of _f_(_a_).
+
+---
+__function__ EXPECTIMINIMAX(_s_) =     
+&emsp;UTILITY(_s_) __if__ TERMINAL\-TEST(_s_)  
+&emsp;max<sub>_a_</sub> EXPECTIMINIMAX(RESULT(_s, a_)) __if__ PLAYER(_s_)= MAX  
+&emsp;min<sub>_a_</sub> EXPECTIMINIMAX(RESULT(_s, a_)) __if__ PLAYER(_s_)= MIN  
+&emsp;∑<sub>_r_</sub> P(_r_) EXPECTIMINIMAX(RESULT(_s, r_)) __if__ PLAYER(_s_)= CHANCE  
