One of the most robust findings in experimental economics is that individuals in one-shot ultimatum games reject unfair offers. Puzzlingly, rejections have been found robust to substantial increases in stakes. By using a novel experimental design that elicits frequent low offers and uses much larger stakes than in the literature, we are able to examine stakes' effects over ranges of data that are heretofore unexplored. Our main result is that proportionally equivalent offers are less likely to be rejected with high stakes. In fact, our paper is the first to present evidence that as stakes increase, rejection rates approach zero.