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Abstract When two bi-stable structure-from-motion (SFM) spheres are presented simultaneously, they tend to rotate in the same direction. This effect reflects a common state bias that is present for various multistable displays. However, it was also reported that when two spheres are positioned so that they touch each other, they tend to counterrotate instead. The latter effect is interpreted as a frictional interaction, indicating the influence of the embedded physics on our visual perception. Here, we examined the interplay between these two biases in two experiments using a wide range of conditions. Those included two SFM shapes, two types of disambiguation cues, the presence or absence of the disambiguation cues, different layout options, and two samples of observers from two different universities (in sum 26 participants). Contrary to the prior report, we observed a robust common state bias for all conditions, including those that were optimized for frictional and “gear meshing” interactions. We found that stronger coupling of perceptual states is accompanied by more frequent synchronous perceptual reversals of the two objects. However, we found that the simultaneity of the individual switches does not predict the duration of the following dominance phase. Finally, we report that stronger perceptual coupling speeds up perceptual alternations.