Obviously, if there is a single move that wins you the game every time - being able to consult the oracle, in your example - then this pure strategy is dominant, and no mixed strategy is called for.

http://en.wikipedia.org/wiki/Pure_strategy#Pure_and_mixed_st... http://en.wikipedia.org/wiki/Strategic_dominance

It is obvious that if there is a dominant pure strategy, then that is the strategy to play, and there is no need for a mixed strategy.

Anyone with elementary game theory knows this, and, really, no 'good game theorist' is going to 'dogmatically' assert otherwise.