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We investigate concurrent two-player win/lose stochastic games on finitegraphs with prefix-independent objectives. We characterize subgame optimalstrategies and use this characterization to show various memory transferresults: 1) For a given (prefix-independent) objective, if every game that hasa subgame almost-surely winning strategy also has a positional one, then everygame that has a subgame optimal strategy also has a positional one; 2) Assumethat the (prefix-independent) objective has a neutral color. If everyturn-based game that has a subgame almost-surely winning strategy also has apositional one, then every game that has a finite-choice (notion to be defined)subgame optimal strategy also has a positional one. We collect or designexamples to show that our results are tight in several ways. We also apply ourresults to B\"uchi, co-B\"uchi, parity, mean-payoff objectives, thus yieldingsimpler statements.

Sub-game optimal strategies in concurrent games with prefix-independent objectives