The Casino owner is closest to being correct. He must be concerned that he has adequate security, and that his staff (dealers, croupiers, etc.) are running the games properly, but he will win most of the time. His answer allows for that rare occasion when someone wins a Hollywood-style run at the tables.
The pollster is completely wrong. The most famous botched poll was the Literary Digest poll in the Presidential race of 1936. That was a case of sample bias, because a telephone survey, no matter how large, was unable to account for the large number of voters who had no telephone. It overrepresented those wealthy enough to own telephones. If you are asking the wrong people, it doesn't matter how many you ask, numbers won't help. There are other obvious sources of bias: instrument bias means the survey itself is written in a manner that gives an inaccurate result. Interview bias occurs when interviewers respond to the answers in such a way that affects the results; even if they are reading a script if they are happy when the mention candidate x and sour when they mention candidate y, candidate x will benefit. The Law of Large Numbers only helps the pollster if he has a randomly selected sample of the correct target population and avoids other forms of error.
The manufacturer in this example is completely wrong. If his process is flawed, or his materials unsatisfactory to begin with, large production means great waste. The Law of Large Numbers cannot be interpreted to mean that the probability of a result must improve, it means that the observed results will get closer to the true results, whether that means the observed success rate goes up or down. The second flaw here is that the Law of Large Numbers applies to sampling, and observational, error. The manufacturer is not describing a sample of anything, he is discussing the whole of his production. Similarly, he is not talking about the accuracy of observed results, he is saying his product is actually better.
