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In recent years, transformer-based language representation models (LRMs) have achieved state-of-the-art results on difficult natural language understanding problems, such as question answering and text summarization. As these models are integrated into real-world applications, evaluating their ability to make rational decisions is an important research agenda, with practical ramifications. This article investigates LRMs' rational decision-making ability through a carefully designed set of decision-making benchmarks and experiments. Inspired by classic work in cognitive science, we model the decision-making problem as a bet. We then investigate an LRM's ability to choose outcomes that have optimal, or at minimum, positive expected gain. Through a robust body of experiments on four established LRMs, we show that a model is only able to `think in bets' if it is first fine-tuned on bet questions with an identical structure. Modifying the bet question's structure, while still retaining its fundamental characteristics, decreases an LRM's performance by more than 25\%, on average, although absolute performance remains well above random. LRMs are also found to be more rational when selecting outcomes with non-negative expected gain, rather than optimal or strictly positive expected gain. Our results suggest that LRMs could potentially be applied to tasks that rely on cognitive decision-making skills, but that more research is necessary before they can robustly make rational decisions.