[LolWolf]

There is not, actually! You can show this strategy does as well as the case where prisoners have full information of each other's moves.[0] So any other strategy where each prisoner is blind to others' actions can always be executed in the full-information case above; so this bound is tight and this strategy is optimal: if there was a strategy that did better in the blind case, you could execute it in the full-information case to get a better outcome, but this is impossible.

For a nice exposition of this, see Curtin and Warshauer's article "The Locker Puzzle."

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[0] More specifically, a game where all lockers are left open, so every strategy has the same probability of winning.

[nemetroid]

To be precise, the strategy is shown to be optimal as well in a modified game where all lockers are left open and you cannot open any more lockers if you find your own number.