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We consider a scalar field with a bottom-less potential, such as g3ϕ, finding that cosmologies unavoidably end up with a crunch, late enough to be compatible with observations if g≲1.2H02/3MPl1/3. If rebounces avoid singularities, the multiverse acquires new features; in particular probabilities avoid some of the usual ambiguities. If rebounces change the vacuum energy by a small enough amount, this dynamics selects a small vacuum energy and becomes the most likely source of universes with anthropically small cosmological constant. Its probability distribution could avoid the gap by 2 orders of magnitude that seems left by standard anthropic selection. Keywords: Cosmological constant, Relaxation, Multiverse