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The expected utility is the utility of winning times the probability that the opponent concedes at <math>X \;\forall X \le T_i\,</math>, plus the utility of losing times the probability that the opponent hasn't conceded by <math>T_i\,</math>. For notation, <math>H(T)\,</math> will be the distribution of the opponent's optimal time of concession and <math>h(T)\,</math> the associated density function. The expected utility is:
:<math>EU(T_i) =[1-H(T_i)] U^L(T_i) + \int_0^{T_i } U^W(x) h(x) dx\,</math>
This equation can be simplified as shown on equation (8) in the paper on page 1177.
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