Biases in perceptual decision-making tasks serve as indicators of both short-term serial effects and long-term inferential strategies. While recent studies have provided mixed results on how adding a secondary confidence measurement task affects decision accuracy, there is little information on how such confidence measurements influence the reasoning behavior that underlies perceptual biases. Recently, we reported a new long-term bias in a sequential decision-making paradigm that reflected the contextual model participants used to interpret events during the experiment, leading to radically different, sometimes counterintuitive, behavior. In the current study, we investigate the effect of pairing different confidence measurements with this decision-making task on the reported long-term biases. We used a 2AFC decision-making task with four conditions, based on two factors: the timing of confidence measurement—either introduced only during the test phase or present throughout both training and test phases—and the method of confidence measurement: instantaneous joint reports of decision and confidence versus 2-step reports. To maximize contrast, we chose two very distinct implementations of confidence-reporting paradigms. In the first, confidence was inferred from movement dynamics in a mouse-tracking task, where participants indicated their decision by drawing a leftward or rightward stroke, with stroke length encoding confidence. In the second, participants provided explicit confidence ratings via a post-decision continuous slider. We found that introducing confidence assessments did not significantly alter the reasoning behavior observed in sequential decision-making, as overall long-term biases remained the same. This suggests that these biases stem from stable internal models. The method of confidence measurement may or may not alter these results, indicating an independent effect of measurement method on the reasoning strategy. In summary, the selection of internal decision-making models determining observable decisions and biases remains intact with the addition of the confidence-reporting task, but these models are not independent of the method used to measure confidence.