Q.Using the payoff table of Worked Example 6, with $P(S_1)=0.3$, $P(S_2)=0.5$, $P(S_3)=0.2$, compute the Expected Monetary Value (EMV) of each course of action and state which should be chosen. Also compute the Expected Opportunity Loss (EOL) of each action and verify that it points to the same choice.

With the probabilities of the states of nature now known, the EMV criterion weights each action's payoffs by these probabilities, and the equivalent EOL criterion (built from the regret table) should always point to the same recommended action. …

EMV calculation, using the payoff table $A_1=(200,200,200)$, $A_2=(100,300,300)$, $A_3=(50,200,400)$ and probabilities $P(S_1)=0.3,P(S_2)=0.5,P(S_3)=0.2$:

Highest EMV is $A_2$ (240) → choose $A_2$.

EOL calculation, using the regret table from Worked Example 6 — $A_1=(0,100,200)$, $A_2=(100,0,100)$, $A_3=(150,100,0)$ — with the same probabilities:

Lowest EOL is $A_2$ (50) — the same action EMV recommended. …

Recompute each criterion's recommended action by re-scanning the payoff/regret table a second time: independently verify $EMV(A_i)+EOL(A_i)$ equals the same constant (290, the expected payoff under perfect information) for ever …

Using the wrong probability against the wrong state of nature column (the probabilities must line up with $S_1, S_2, S_3$ in that same order for every action); and treating EMV and EOL as two independent, possibly conflicting criteria rather than recognising that maximising EMV is mathematically equi …