Roulette inflation with Kähler moduli and their axions

We study 2-field inflation models based on the ``large-volume'' flux compactification of type IIB string theory. The role of the inflaton is played by a K\"ahler modulus corresponding to a 4-cycle volume and its axionic partner. The freedom associated with the choice of Calabi-Yau manifold and the nonperturbative effects defining the potential V (, ) and kinetic parameters of the moduli brings an unavoidable statistical element to theory prior probabilities within the low-energy landscape. The further randomness of (, ) initial conditions allows for a large ensemble of trajectories. Features in the ensemble of histories include ``roulette trajectories, '' with long-lasting inflations in the direction of the rolling axion, enhanced in the number of e-foldings over those restricted to lie in the -trough. Asymptotic flatness of the potential makes possible an eternal stochastic self-reproducing inflation. A wide variety of potentials and inflaton trajectories agree with the cosmic microwave background and large scale structure data. In particular, the observed scalar tilt with weak or no running can be achieved in spite of a nearly critical de Sitter deceleration parameter and consequently a low gravity wave power relative to the scalar curvature power.