In motion transparency, one surface is very often seen on top of the other in spite of no proper depth cue in the display. We investigated the dynamics of depth assignment in motion transparency stimuli composed of random dots moving in opposite directions. Similarly to other bistable percepts, which surface is seen in front is arbitrary and changes over time. In addition, we found that helping the segregation of the two surfaces by giving the same color to all dots of one surface significantly slowed down the initial rate of depth reversals. We also measured preferences to see one particular motion direction in front. Unexpectedly, we found that all of our 34 observers had a strong bias to see a particular motion direction in front, and this preferred direction was usually either downward or rightward. In contrast, there was no consistency in seeing the fastest or slowest surface in front. Finally, the preferred motion direction seen in front for one observer was very stable across several days, suggesting that a trace of this arbitrary motion preference is kept in memory.