The Monty Hall Problem (Generalized)

[markredito]

In the three-door monty hall problem, the explanations make sense to me.

But in the generalized version where the sample size is bigger (n) and the number of new information (ie doors opened, k) can be any arbitrary number, it seems like the success rate changes.

I know that in general, switching doors is better (as explained in the three door problem), but it seems like the outcomes becomes different when number of doors (n) is larger and number of doors (k) is arbitrary.

My understanding is that the outcomes seem to depend on n and k. The more that k value is closer to n, the higher the probability of winning a car. In other words, in a big sample space like (n) a favorable outcome emerges the more new information (k) we have .

Am I understanding things correctly from an intuition standpoint?

[rmwkwok]

@markredito

the outcomes becomes different when number of doors (n) is larger and number of doors (k) is arbitrary.

Yes, and supposing that n means the TOTAL number of doors and k means that number of doors OPENED.

@markredito

Am I understanding things correctly from an intuition standpoint?

I think yes. The only thing that I am not certain is whether it is ok with the wording of k as the “amount of information” (under the information theory).

I support the following way of summarizing it:

@markredito

My understanding is that the outcomes seem to depend on nnn and kkk. The more that k value is closer to n, the higher the probability of winning a car .

Cheers,
Raymond

[markredito]

Thanks for your response. I appreciate it!