 A second series of simulations with a wider class of strategies, however, forced them to revise their opinion. The strategies considered in the second series allowed each player to base its probability of cooperation on its own previous move as well as its opponent's. A strategy can now be represented as \(\bS(p_1, p_2. p_3, p_4)\) where \(p_1, p_2, p_3, p_4\) are the probabilities of cooperating after outcomes \((\bC, \bC)\), \((\bC, \bD)\), \((\bD, \bC)\), and \((\bD, \bD)\), respectively i.e., after receiving the reward, sucker, temptation and punishment payoffs. (Again, we can ignore the probability of defecting on the first move as long as the \(p_i\) s are not zero or one.) The initial population in these tournaments all play the random strategy \(\bS(.5, .5, .5, .5)\) and after every 100 generations a small amount of a randomly chosen (non-deterministic) mutant is introduced, and the population evolves by proportional fitness. The results are quite different than before. After \(10^7\) generations, a state of steady mutual cooperation was reached in \(90\%\) of the simulation trials. But less than \(8.3\%\) of these states were populated by players using TFT or GTFT. The remaining \(91.7\%\) were dominated by strategies close to \(\bS(1,0,0,1)\). This is the just the Pavlovian strategy \(\bP_1\) of Kraines and Kraines, which replays its last move after receiving \(R\) or \(T\) and changes to the other move after receiving \(P\) or \(S\). Kraines and Kraines had been somewhat dismissive of \(\bP_1\). They recall that Rapoport and Chammah, who identified it early in the history of game theory had labeled it “simpleton” and remark that “the appellation is well deserved”. Indeed, \(\bP_1\) has the unfortunate characteristic of trying to cooperate with \(\bDu\) on every other turn, and against TFT it can get locked into the inferior repeating series of payoffs \(T, P, S, T, P, S, \ldots\). But Nowak and Sigmund rename the strategy “win-stay lose-shift” and trumpet its advantages. Their simulations suggest that the defects mentioned here do not matter very much in evolutionary contexts. One reason may be that \(\bP_1\) helps to make its environment unsuitable for its enemies. \(\bDu\) does well in an environment with generous strategies, like \(\bCu\) or GTFT. TFT, as we have seen, allows these strategies to flourish, which could pave the way for \(\bDu\). Thus, although TFT fares less badly against \(\bDu\) than \(\bP_1\) does, \(\bP_1\) is better at keeping its environment free of \(\bDu\).