From Barry Greenstein’s insightful poker book, Ace on the River:
Someone shows you a coin with a head and a tail on it. You watch him flip it ten times and all ten times it comes up heads. What is the probability that it will come up heads on the eleventh flip?
A novice gambler would tell you, “Tails is more likely than heads, since things have to even out and tails is due to come up.”
A math student would tell you, “We can’t predict the future from the past. The odds are still even.”
A professional gambler would say, “There must be something wrong with the coin or the way it is being flipped. I wouldn’t bet with the guy flipping it, but I’d bet someone else that heads will come up again.”
Yes I know the math student would really say “individual trials are uncorrelated,” not “we can’t predict the future from the past.” The lesson still holds.
Happy Labor Day, everyone.