Deal or No Deal

[Slinky Bender]

I made a cool $161,000.

(unfortunately my case was worth $200,000 though!)

Isn't 161,000 risk free against $200,000 high risk a pretty good deal?

 

[Slinky Bender]

There's obviously a cross between the classic Monte Hall Dilemma problem and this which I have not seen explored yet.

 

[JackT]

In the Monty Hall problem, the host opens a case (door, whatever) that does not contain the big prize (i.e., zero chance of big prize being eliminated before player is given the option to switch). This is quite different from DOND, where the contestant may eliminate the big prize before being given the Banker's Offer vs. Your Own Case option....

 

[JackT]

Said differently, the "switching" is advantageous in the Monty Hall problem because you are given a different choice based on later-gained knowledge... i.e., the choice between sticking with your 1/3 chance vs. choosing a case that has a higher chance of being the good one. You should use this later-gained knowledge to increase your chances.
This seems to me inapplicable to DOND under its set of rules.

 

[JackT]

Isn't 161,000 risk free against $200,000 high risk a pretty good deal?

Yes, but the key there is "high risk"....
quantifying the degree of risk is necessary to answer the question about whether any such deal is "pretty good"

 

[Slinky Bender]

What was in the other case? What was the expected value?

 

[SubmissiveAngel]

you two are long overdue for your heads up no limit texas hold'em rematch.
jackt, your cheese platter awaits.