Monty Hall problem

Quote: gordonm888

Quote: Wizard

I was screaming at the television last night, watching the latest episode of Survivor.

At tribal counsel, Deshawn had to play a game where he would either me immediately eliminated or granted immunity at Tribal Counsel. The game turned out to be the Monty Hall problem. Imagine my reaction when after Jeff revealed a "goat" and Deshawn was given the option to switch, he said "no." I was beside myself, screaming at TV. I prayed the gods of math would punish him by getting the other "goat" and being eliminated. Alas, it was not to be. As they say, sometimes it is better to be lucky than right.

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Yes, and one of the contestants (I believe it was Xander) called out "its the Monty Hall problem" before Deshawn made his decision. So, this was not lost on the at least one of the contestants.
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I had never heard of this before seeing Xander make that comment.

Made me wonder if a more likeable player than Deshawn had been in the situation if the producers would have chosen something with better odds to stay.

BTW - Xander has gotta be one of the best Survivor players in ages. I am so impressed with him.

Okay - let me preface this by saying I’m not a math guy at all, so I’m not sure if this applies here.

The 007 Die Another Day slot machines have an option where you can spend something like $20, $40, or $100 to “buy” a 3/7 chance of getting a bonus.

You pick one suitcase out of seven. Three have bonuses. Four have nothing. After you pick one, one will get eliminated (not necessarily one of the “no bonus” cases) and it will show you what was in that case. Then it will allow you to keep the one you chose or switch to a different case.

If the one that gets eliminated was a “no bonus” case - would it be best to switch to a different case than the one you originally picked?

Quote: ams288

The 007 Die Another Day slot machines have an option where you can spend something like $20, $40, or $100 to “buy” a 3/7 chance of getting a bonus.

You pick one suitcase out of seven. Three have bonuses. Four have nothing. After you pick one, one will get eliminated (not necessarily one of the “no bonus” cases) and it will show you what was in that case. Then it will allow you to keep the one you chose or switch to a different case.

If the one that gets eliminated was a “no bonus” case - would it be best to switch to a different case than the one you originally picked?
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Let's assume, for the sake of argument, the case that is eliminated was chosen randomly from the other six. Then it wouldn't make any difference whether you switched or not.

This should not be compared to the Monty Hall case, because you said the eliminated case can have a bonus or nothing. If it always showed nothing, then, yes, you should switch, assuming the end outcome wasn't predestined, as is often the case.

Thanks, Wiz! The chart you put in the article helped me understand this perfectly.

I guess my hang up was there only being 3 doors/cases. It makes much more sense with more!

Only having 3 is the mathematical equivalent of a 4 or 10 being the point in craps, so switching or not switching is not as big of a difference as more doors/cases would be!

Quote: mwalz9

Thanks, Wiz! The chart you put in the article helped me understand this perfectly.
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You're welcome.

They did this again on last night’s episode of Survivor.