Pleasure and pain play an important role in human decision making by providing a common currency for resolving motivational conflicts. While Large Language Models (LLMs) can generate detailed descriptions of pleasure and pain experiences, it is an open question whether LLMs can recreate the motivational force of pleasure and pain in choice scenarios - a question which may bear on debates about LLM sentience, understood as the capacity for valenced experiential states. We probed this question using a simple game in which the stated goal is to maximise points, but where either the points-maximising option is said to incur a pain penalty or a non-points-maximising option is said to incur a pleasure reward, providing incentives to deviate from points-maximising behaviour. Varying the intensity of the pain penalties and pleasure rewards, we found that Claude 3.5 Sonnet, Command R+, GPT-4o, and GPT-4o mini each demonstrated at least one trade-off in which the majority of responses switched from points-maximisation to pain-minimisation or pleasure-maximisation after a critical threshold of stipulated pain or pleasure intensity is reached. LLaMa 3.1-405b demonstrated some graded sensitivity to stipulated pleasure rewards and pain penalties. Gemini 1.5 Pro and PaLM 2 prioritised pain-avoidance over points-maximisation regardless of intensity, while tending to prioritise points over pleasure regardless of intensity. We discuss the implications of these findings for debates about the possibility of LLM sentience.