There's a monthly meeting I attend with other gamblers in town where we discuss certain opportunities in casinos as well as discuss our own experiences gambling and even theoretical problems which may not be so useful in casinos but they're exercise for the brain.

One person at the meeting mentioned he's reading a book called The Black Swan by Nassim Nicholas Taleb. I haven't started reading it yet, but it sounds like a good book for people interested in probability, of which gamblers would be included.

One question posed at our meeting was inspired by the book. I'll give you the question now, and then in a couple days give you what the book's suggested answer would be.

The question:

There's an actuary and a lifetime professional expert gambler who are presented with a coin by a third person.

The third person says, "This is a fair coin with an equal chance of either heads or tails being face up after I flip it. The last 29 times I flipped this coin it landed on heads."

After that, the third person then asks each person what he says the probability of the next flip is going to be another heads.

What do you think is the answer, and do you think both the actuary and the gambler would agree with you? Why or why not?