A number of people sent me their answers by email. No one appears to have used the comments to reply which is what I had hoped for. Ah well... anyway, I wanted to follow up and not leave all of you hanging. I'll repeat the question and then give the answer.

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?

.....

Here's the answer as we discussed it in our gambler's meeting.

The actuary would say that the past trials have no bearing at all on future results and say that the chance of a heads on the next flip is still 50/50.

The gambler would say that the chance of a perfectly fair coin landing heads 29 out of 29 times is so astronomically low, that he would conclude that the coin isn't fair and that heads is more likely than tails. In other words, he would question the premise of the coin being fair in the first place.

Many of you had close to the right answer, but I wouldn't say that anyone had it exactly right. Many of you thought the gambler would think that the heads was some kind of streak which meant it would be more likely to be heads again or that tails would be "due."

A professional gambler doesn't see a streak as affecting the mathematical odds of a particular result going forward. A streak might lead a gambler to question what he sees, however.

Is either answer correct? I'd say no, but I'd go with the gambler in this one. That's just my gut feel.