This is perhaps not surprising, as the decision making environment becomes more complex and a randomized strategy becomes the optimal solution.
* To counter the difficulty many students face in choosing a truly randomized strategy, students could be provided a die, where strategy actions have been assigned to each side and the roll of the die determines their move for the round.
If students are resistant to the conversation or the instructor is not sure that the experiment proceeded as intended (i.e., they are concerned that students did not observe the importance of playing a randomized strategy) one could pursue an alternative path of discussion.
Several students noted that their training in other courses emphasized logic and that before the experiment they were struggling to see the logic of a randomized strategy. As a professor, this lack of intuition was apparent from classroom conversation and written homework where students struggled to articulate the importance of a randomized strategy.