This is indeed a valuable lesson. But an interesting counterpoint I have heard is that if the event has occurred as just one of the outcomes the past ten times,

This is indeed a valuable lesson. But an interesting counterpoint I have heard is that if the event has occurred as just one of the outcomes the past ten times, you need to revisit your assumption that the two outcomes have equal probability. In many real-life scenarios, the probability that the assumption is incorrect may be greater than the probability of such a sequence of outcomes given the assumption. I think I read about this in Taleb's The Black Swan, though I'm sure it's an older idea than that.