In an influential paper, James Lenman argues that consequentialism can provide no basis for ethical guidance, because we are irredeemably ignorant of most of the consequences of our actions. If our ignorance of distant consequences is great, he says, we can have little reason to recommend one action over another on consequentialist grounds. In this article, I show that for reasons to do with statistical theory, the cluelessness objection is too pessimistic. We have good reason to believe that certain patterns of action will tend to have better consequences, and we have good reason to recommend acting in accordance with strategies based on those advantageous patterns. I close by saying something about the strategies that this argument should lead us to favour.