There is a blind test that asks participants to distinguish Coke and Pepsi. A participant will test 6 cups of drink and tell whether it was Coke or Pepsi. Assuming that the participant can tell the difference between them, though not perfect, if he judged that the first three were all Coke, then he would think it is much more likely that the remaining three would be Pepsi rather than Coke. Then the last three experiments cannot give precise information about the participant's ability to distinguish.
Such a problem can happen when the participant knows a priori that there would be equal numbers of Coke and Pepsi. Then the experimenter might think of flipping a coin six times to decide which cola is given to the participant. Then it is possible that all or most of 6 cups are Cokes. It may be problematic when the participant is good at telling Coke a Coke but not as good at telling Pepsi a Pepsi.
Is there any methods to solve this problem?