The standard operational framework of quantum theory is time-asymmetric. This asymmetry reflects the capabilities of ordinary agents, who are able to deterministically pre-select the states of quantum systems, but not to deterministically post-select the outcomes of quantum measurements. However, the fundamental dynamics of quantum particles is time-symmetric, and is compatible with a broader class of operations where pre-selections and post-selections are combined in general ways that do not presuppose a definite direction of time. In this talk I introduce a framework for quantum operations with indefinite time direction, providing an example, called the quantum time flip, where an unknown, time-symmetric process is accessed in a coherent superposition of two alternative time directions. To highlight the potential of quantum operations with indefinite time direction, I will show a game where a hypothetical agent with access to the quantum flip can in principle outperform all agents who operate in a definite time direction.