"The possible guarantees for a randomized algorithm A computing some function F. In the tables above, the columns correspond to different inputs and the rows to different choices of the random tape. A cell at position r,x is colored green if A(x;r)=F(x) (i.e., the algorithm outputs the correct answer) and red otherwise. The standard \mathbf{BPP} guarantee corresponds to the middle figure, where for every input x, at least two thirds of the choices r for a random tape will result in A computing the correct value. That is, every column is colored green in at least two thirds of its coordinates. In the left figure we have an ""average case"" guarantee where the algorithm is only guaranteed to output the correct answer with probabilty two thirds over a random input (i.e., at most one third of the total entries of the table are colored red, but there could be an all red column). The right figure corresponds to the ""offline \mathbf{BPP}"" case, with probability at least two thirds over the random choice r, r will be good for every input. That is, at least two thirds of the rows are all green.  (\mathbf{BPP} \subseteq \mathbf{P_{/poly}}) is proven by amplifying the success of a \mathbf{BPP} algorithm until we have the ""offline \mathbf{BPP}"" guarantee, and then hardwiring the choice of the randomness r to obtain a nonuniform deterministic algorithm."