We present an approach to accelerate multi-view stereo (MVS) by prioritizing computation on image patches that are likely to produce accurate 3D surface reconstructions. Our key insight is that the accuracy of the surface reconstruction from a given image patch can be predicted significantly faster than performing the actual stereo matching. The intuition is that non-specular, fronto-parallel, in-focus patches are more likely to produce accurate surface reconstructions than highly specular, slanted, blurry patches — and that these properties can be reliably predicted from the image itself. By prioritizing stereo matching on a subset of patches that are highly reconstructable and also cover the 3D surface, we are able to accelerate MVS with minimal reduction in accuracy and completeness. To predict the reconstructability score of an image patch from a single view, we train an image-to-reconstructability neural network: the I2RNet. This reconstructability score enables us to efficiently identify image patches that are likely to provide the most accurate surface estimates before performing stereo matching. We demonstrate that the I2RNet, when trained on the ScanNet dataset, generalizes to the DTU and Tanks & Temples MVS datasets. By using our I2RNet with an existing MVS implementation, we show that our method can achieve more than a 30× speed-up over the baseline with only an minimal loss in completeness.