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 I have to calculate a threshold value for a probability, lambda*. My code for the simplified version is working but it breaks down for the more complex version. Here are defined probabilities and the working calculation for one alternative  r = \[Epsilon]*\[Lambda] + (1 - \[Eta])*(1 - \[Lambda]); s = \[Eta]*(1 - \[Lambda]) + (1 - \[Epsilon])*\[Lambda]; \[Lambda][r] = (\[Epsilon]*\[Lambda])/(\[Epsilon]*\[Lambda] + (1 - \[Eta])*(1 -\[Lambda])); \[Lambda][s] = (\[Eta]*(1 - \[Lambda]))/(\[Eta]*(1 - \[Lambda]) + (1 - \[Epsilon])*\[Lambda]); Simplify[r*(y - m - c + \[Alpha]*\[Lambda][r]) + s*(y - m + \[Alpha]*(1 - \[Lambda][s])) == y + \[Alpha]*(1 - \[Lambda])]; Solve[r*(y - m - c + \[Alpha]*\[Lambda][r]) + s*(y - m + Subscript[\[Alpha], i]*(1 - \[Lambda][s])) == y + \[Alpha]*(1 - \[Lambda]), {\[Lambda]}]  It does not work for two alternatives (1,2):  \[Mu] = 1 - c1 - c2; \[Xi] = c1 - y; \[Beta] = 1 - c1; \[Gamma] = c1 - y; (*Further probabilities *) r1 = \[Epsilon]1*\[Lambda]1 + (1 - \[Eta]1)*(1 - \[Lambda]1); r2 = \[Epsilon]2*\[Lambda]2 + (1 - \[Eta]2)*(1 - \[Lambda]2); n1 = \[Eta]1*(1 - \[Lambda]1) + (1 - \[Epsilon]1)*\[Lambda]1; n2 = \[Eta]2*(1 - \[Lambda]2) + (1 - \[Epsilon]2)*\[Lambda]2; \[Lambda][r1] = (\[Epsilon]1*\[Lambda]1)/(\[Epsilon]1*\[Lambda]1 + (1 - \ \[Eta]1)*(1 - \[Lambda]1)); \[Lambda][r2] = (\[Epsilon]2*\[Lambda]2)/(\[Epsilon]2*\[Lambda]2 + (1 - \ \[Eta]2)*(1 - \[Lambda]2)); \[Lambda][s1] = (\[Eta]1*(1 - \[Lambda]1))/(\[Eta]1*(1 - \[Lambda]1) + (1 - \ \[Epsilon]1)*\[Lambda]1); \[Lambda][s2] = (\[Eta]2*(1 - \[Lambda]2))/(\[Eta]2*(1 - \[Lambda]2) + (1 - \ \[Epsilon]2)*\[Lambda]2); (* Expected Payoff *) EMS1 = \[Mu]*\[Xi]*(\[Lambda]2*\[Alpha]2 + (1 - \[Lambda]1) \[Alpha]1 \ - c2 + y) + \[Mu]*(1 - \[Xi])*(\[Lambda]1*\[Alpha]1 + \[Lambda]2*\ \[Alpha]2) + (1 - \[Mu])*\[Xi]*(\[Lambda]1*\[Alpha]1 + (1 - \ \[Lambda]2)*\[Alpha]2) + (1 - \[Mu])*(1 - \ \[Xi])*(\[Lambda]1*\[Alpha]1 + \[Lambda]2*\[Alpha]2 + 2*c1 + c2 - y); (* Solving *) Simplify[r1*r2*EMS1 + r1*n2*(\[Alpha]1*\[Lambda][r1] - c1 + \[Alpha]2*(1 - \[Lambda]2[n2])) + n1*r2*(\[Alpha]2*\[Lambda][r2] - c2 + \[Alpha]1*(1 - \[Lambda]1[n1])) + n1*n2*( \[Alpha]1*(1 - \[Lambda]1[n1]) + \[Alpha]2*(1 - \[Lambda]2[ n2])) - s1 - s2 == r1*(y^p - s1 - c1 + \[Alpha]1*\[Lambda][r1]) + n1*(y - s1 + \[Alpha]1*(1 - \[Lambda][ n1])) + \[Alpha]2*(1 - \[Lambda]2)] Solve[ r1*r2*EMS1 + r1*n2*(\[Alpha]1*\[Lambda][r1] - c1 + \[Alpha]2*(1 - \[Lambda]2[n2])) + n1*r2*(\[Alpha]2*\[Lambda][r2] - c2 + \[Alpha]1*(1 - \[Lambda]1[n1])) + n1*n2*( \[Alpha]1*(1 - \[Lambda]1[n1]) + \[Alpha]2*(1 - \[Lambda]2[n2])) - s1 - s2 == r1*(y^p - s1 - c1 + \[Alpha]1*\[Lambda][r1]) + n1*(y - s1 + \[Alpha]1*(1 - \[Lambda][ n1])) + \[Alpha]2*(1 - \[Lambda]2), {\[Lambda]2}]