Deal or No Deal Normal Distribution?

[moonman239]

If the banker's offers were equal to the expected value of the remaining cases, would the offers be normally distributed?

I'd say the answer is yes. Take a roll of a die, for instance. Die rolls are normally distributed, with a mean of 3.5 and a standard deviation of 2 11/12.

 

[chiro]

If the banker's offers were equal to the expected value of the remaining cases, would the offers be normally distributed?

I'd say the answer is yes. Take a roll of a die, for instance. Die rolls are normally distributed, with a mean of 3.5 and a standard deviation of 2 11/12.

Die rolls are uniformly distributed (the discrete version).

You can have results like the central limit theorem, but that's another story.

For your die example, think about what the probability of each roll is. Also think about if each roll depends on the history of every previous roll.

 

[SW VandeCarr]

Also think about if each roll depends on the history of every previous roll.

What?

 

[chiro]

What?

Die rolls are considered random so history is of course irrelevant but I'm just asking the OP to think about the experiment so that he/she can formulate it precisely.

 

[Calrid]

Die rolls are considered random so history is of course irrelevant but I'm just asking the OP to think about the experiment so that he/she can formulate it precisely.

In deal or no deal as much as I despise that program though future events are determined by past events, there are only so many boxes. This is not indeed like a dice roll this is more like poker odds when faced with a series of sets of cards and an unknown distribution in the deck.

Texas hold 'em of course.

The chance of picking anyone box is 1/n the chance of picking any box after that is 1/n-1 so this is an iterative sum with a decreasing n not the usual random sum where n=a to put it in maths jargon.

OP I think you can therefore visualise the sequence and the distribution by using an iterative equation here.

A useful analogy here might be the Monty Hall problem, which of course is not really a problem.

At least if the banker always knows what's in every box. Then it becomes more complex than just probability, now a conscious game theory style equation is in play. Not sure how the program explicitly works but I suspect there is some element of a game (not some completely random nonsense) otherwise its even less worth watching than I thought.

 

[moonman239]

So if I played the game hundreds of thousands of times, then the number of times a certain offer came up would be approximately normally distributed. How do I figure out the chances that the next deal will be better than the current one? EDIT: I just figured it out -- to calculate those chances, all I have to do is figure out the chances of eliminating the lower-value cases. (dope-slap)

 

[chiro]

In deal or no deal as much as I despise that program though future events are determined by past events, there are only so many boxes. This is not indeed like a dice roll this is more like poker odds when faced with a series of sets of cards and an unknown distribution in the deck.

When I was talking about dice, I was only talking about dice and not the process involved in deal or no deal.

 

[Calrid]

So if I played the game hundreds of thousands of times, then the number of times a certain offer came up would be approximately normally distributed. How do I figure out the chances that the next deal will be better than the current one? EDIT: I just figured it out -- to calculate those chances, all I have to do is figure out the chances of eliminating the lower-value cases. (dope-slap)

Precisely there are 15 boxes and each box contains a value higher than $n_1$ which is the first box selected. Once you have selected a box you then know how many boxes are better than it or worse and hence the dealer if he uses some standard equation will always offer the same amount. Of course if he knows in certain situations that you are likely to keep the box that contains say 200,000 and not swap to a lower value he might offer you more to swap or play other mind games. But if its just the boring bit where people just chose random boxes then the offer is probably pretty standard and just uses fairly standard probabilities such as the one you mention in the OP. If 100,000 is out this doesn't change the probability of any remaining box is what you have to bear in mind, it only becomes contingent when the value of the boxes is important, and then you can just "eliminate" boxes and work out an equation according to how you value them.

 

[BWV]

the bankers offers should be lognormally distributed otherwise there would be a non-zero probability of a negative offer

 

[moonman239]

Question: I'm the process of building a DoND calculator (which is why I started this thread in the first place). Should I use the normal distribution or the lognormal distribution?