 To present this last condition, one more definition is required, alongside a piece of notation: For any two lotteries \(P_f\) and \(P_g\) and \(\lambda\in[0,1]\), one can define a third simple lottery \(\lambda P_f + (1-\lambda)P_g\) in \(\mathcal{P}\), the \(\lambda\)-mixture of \(P_f\) and \(P_g\), by setting \((\lambda P_f + (1-\lambda)P_g)(x)\), the probability assigned to outcome \(x\) by the mixture lottery, equal to \(\lambda P_f(x) + (1-\lambda)P_g(x)\). It is heuristically useful to think of \(\lambda P_f + (1-\lambda)P_g\) as a higher-order lottery that yields a probability of \(\lambda\) of playing lottery \(P_f\) and a complementary probability of playing \(P_g\). The condition then reads: