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