interesting coin flip problem

[KenProspero]

[ QUOTE ]
There's a lot of work done with regard to the Monte-Hall problen, and I suggest you read some of it. The version of Monte-Hall problem you are thinking about (the one where the solution is 2/3) is not the interesting one, as that one is very easy to understand and solve.

[/ QUOTE ]

Of course it's easy to solve -- yet many people don't believe the answer. Other versions (which I believe were spawned to some extent by an interview with Monte, in which he said no one knows what he was thinking or something like this) which rely on psychology and game theory. Also they need to take into account the fact that Monte (and his producers) really want to give away the big prize as much as necessary to maximize ratings).

To my knowledge, when the problem started out, it was meant as the easily calculable exercise, but because it was phrased colloqually, people were able to turn it into a different kind of problem.

[ QUOTE ]
This is not "semantics", in the sense that understanding the nature of the information you have is crucial to solving the problem. In certain types of probability problems, the exact wording is very important, as opposed to most other kinds of problems. There are many examples for this.

[/ QUOTE ]

Not having been in the class, I can't say for sure what the Prof was getting at. However, I have a strong suspicion that he was trying for the easily calculable mathmatical solution, but phrased the problem colloqually. In cases like these, you can absolutely bust the Prof's chops and explain the ambiguity, or you can recognize what he was trying to do. Either approach is 'correct'. With many professors, only one has a +ev.

[ QUOTE ]
Would you (or anyone who thinks the answer to the first problem is definitely "2/3") take it, yes or no? And if not, why?

[/ QUOTE ]

Of course not -- in order to take the bet, you have to assume that the game isn't rigged (i.e., a 'random series of two coin flips was chosen). In a problem that is phrased colloqually, Like Monte, this condition is assumed.

Now, now if you were to come to me before the coins were flipped, and guarantee that you'd offer me 5-1 if at least one of the coins comes up heads -- well that would be a good bet. But we all knew that, right?

[PrayingMantis]

[ QUOTE ]
In cases like these, you can absolutely bust the Prof's chops and explain the ambiguity, or you can recognize what he was trying to do. Either approach is 'correct'. With many professors, only one has a +ev.

[/ QUOTE ]

I think that overall we are agreeing. There's ambiguity in the problem, and it can be answered differetnly according to different assumptions. I'm really not interested in that prof and what should the OP tell him. For all I care, always agreeing with your prof, no matter how smart or stupid he is, is the best play in most circumstances, and obviously that has pretty much nothing to do with solving or thinking serioulsy about a problem.

And about the bet I've offered you, I can't see why you think it's rigged. Let's change it a bit: I will FILM myself flipping 2 unbiased coins, and give the film to a witness you trust. There will be no editing done on the film. I'm telling you that the outcome for one of the coins on the film was heads. Now, I offer you the same bet on the second flip filmed, 5:1 if it's tails, for $1000. What's rigged about it? If you are able to put a number on the probability for the 2nd coin, why not take such a bet? You know what, I'll offer you 10:1. Even 100:1 if you insist.

I can't see why anyone who really thinks that the answer for the original problem is definitely 2/3 (and no room for different interpretations) will not take such a bet, as a rational gambler. This is essentially the same problem with exactly the same details, as I'm giving you the same information about something that had _already happened_.