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05the posterior of the chosen button

because the task's bayesian posterior is known at every round, each choice can be scored by how probable the chosen button was. an optimal agent always picks the most probable button, so this readout rises across rounds. without extended reasoning, gpt 5 samples almost independently of the evidence (the sampled button stays near the 25% chance level) and its final choice reaches only 52% after 15 rounds. with extended reasoning both rise, to 61% for sampling and 80% for the final choice.

fig. 5 posterior of the chosen button, data vs fitted model
left right
data model game length:

x axis: rounds before the final choice. final-choice curves show how probable the eventually chosen button was after each round; sampling curves show the posterior of the button sampled at each round.