In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities". In an encounter between player "X" and player "Y", "X" 's strategy is specified by a set of probabilities "P" of cooperating with "Y". "P" is a function of the outcomes of their previous encounters or some subset thereof. If "P" is a function of only their most recent "n" encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: formula_1, where formula_2 is the probability that "X" will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which "X" cooperated and "Y" defected, then formula_3 is the probability that "X" will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as "P"={1,0,1,0}, in which "X" responds as "Y" did in the previous encounter. Another is the win–stay, lose–switch strategy written as "P"={1,0,0,1}, in which "X" responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.