Background
One of the reasons these cross-product sample spaces and the probability of repeated or multiple events are so popular in games is that the results are not easy to predict, and do not agree with what it “looks like” is happening.

One example is the “streaky” roulette wheel. Casinos often hang large illuminated signs over every roulette wheel, showing the results of the most recent spins. The idea is that gamblers will notice when a sign is showing all red, all black, or some other pattern, and instantly rush over to place their bets and take advantage of the streak. Unfortunately for the gamblers, if the wheel is fair, then every spin is independent, and they have no greater chance of winning than they would making the same bet at any other wheel. But those signs are good marketing for the casino, nevertheless.

Question
Consider other examples of multiple or repeated events – choosing lottery numbers, winning streaks, losing streaks, hitting streaks, free-throw shooting, etc. Your example doesn’t have to be game related – red lights, coincidences, bad things coming in 3’s, etc., would all make good examples.

Choose one specific example that interests you, share your feelings about what would happen next, and compare that with the actual probability that governed what would happen next. Do you think the results are truly independent, or do you think there is a hidden dependence that is affecting the results?

In your response post, state whether you agree with the analysis in the post you are responding to, and why or why not. Then add your own thoughts to the analysis given.