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In the ultimatum game, the challenge is to explain why responders reject non-zero offers thereby defying classical rationality. Fairness and related concepts have been among the main explanations so far. Here, the ultimatum game is reformulated based on probabilistic lotteries, enabling other decision-making tools to be applied to this problem. We explain the rejection behavior via the following principle: if the responder regrets less about losing the offer than the proposer regrets not offering a better option, the offer is rejected. We show that several experimental results normally prescribed to fairness can be given an alternative explanation. We also propose experiments that can distinguish these two scenarios. (With Armen Allahverdyan and Lida Aleksanyan).