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.
Random search can be an effective strategy due to bounded rationality. As pointed elsewhere on this thread, the expected utility of a mixed strategy is not greater than the maximum utility of the pure strategies in its support. But determining the utility of the pure strategies may not be possible. For example, an ant cannot carry the neural machinery necessary to remember everything it has seen, or to use such information to determine with accuracy the most likely direction to food—but it can carry sufficient neural machinery to perform a random walk.
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.
Random search can be an effective strategy due to bounded rationality. As pointed elsewhere on this thread, the expected utility of a mixed strategy is not greater than the maximum utility of the pure strategies in its support. But determining the utility of the pure strategies may not be possible. For example, an ant cannot carry the neural machinery necessary to remember everything it has seen, or to use such information to determine with accuracy the most likely direction to food—but it can carry sufficient neural machinery to perform a random walk.