Just to clarify the utility of randomness issue, I think what some respondents are talking about is the benefit of unpredictablility, which is instrumental when playing a game against a live opponent. This is totally different from randomizing. I also don't think that saying that ants "randomly" search for food is the most accurate way to describe their process. So randomness, in its strict interpretation, is never optimal game strategy. Another thought I had is that there are some circumstances in which it would make sense to change one's prediction to red. If you had a good idea how many total cards were left and had the knowledge that blue cards had significantly over-represented themselves (50 total cards, 30 already flipped, all blue), it would lead to the conclusion that over half of the remaining cards would be red. Such a circumstance could lead to a higher than 70% success rate.