The stochastic multi-armed bandit problem is a popular model of the exploration/exploitation trade-off in sequential decision problems. We introduce a novel algorithm that is based on sub-sampling. Despite its simplicity, we show that the algorithm demonstrates excellent empirical performances against state-of-the-art algorithms, including Thompson sampling and KL-UCB. The algorithm is very flexible, it does need to know a set of reward distributions in advance nor the range of the rewards. It is not restricted to Bernoulli distributions and is also invariant under rescaling of the rewards. We provide a detailed experimental study comparing the algorithm to the state of the art, the main intuition that explains the striking results, and conclude with a finite-time regret analysis for this algorithm in the simplified two-arm bandit setting.