2 boxes, you open one and find it has $100

[OverVolt]

There is a reason I decided not to pick that battle .

 

[Schfifty Five]

His point is that knowledge changes your probability. Suppose the door the host opened contained the prize and you were offered a chance to switch to another door, what is your chance of picking the prize now?

In that case, and in yours, you're not talking about the Monty Hall Problem anymore. You're doing some variation of it.

At this point, it seems this discussion is going in a circle. While I understand what you and Dr. Pizza are talking about it, it does seem irrelevant in that when we are talking about the MH problem, it's understood that he always offers you a choice, and he'll always open up one door that doesn't have the prize.

 

[Schfifty Five]

If you know that the host is always malevolent, then you can change your strategy and improve your odds.

But if the host knows that you know that the host is always malevolent you are back to the original problem.

Bit if you know that the host knows that you know that the host is always malevolent ...

Do you see where this is going? I have utmost respect for DrPizza but I think is unnecessarily complicating the essence of the puzzle.

I agree with this.

 

[Tweak155]

In that case, and in yours, you're not talking about the Monty Hall Problem anymore. You're doing some variation of it.

At this point, it seems this discussion is going in a circle. While I understand what you and Dr. Pizza are talking about it, it does seem irrelevant in that when we are talking about the MH problem, it's understood that he always offers you a choice, and he'll always open up one door that doesn't have the prize.

Yeah I only read the last post or 2, I always assume the host offers it. But knowledge about the host's reason for offering could change your probability, so still semi relevant.

I wouldn't get too worked up either way.

 

[Rakehellion]

On Monty Hall, as someone stated above, it's understood that the host always offers the chance to switch - it's part of the game. The wikipedia makes no mention of this part; people assume that it's understood. In the version I proposed, I followed the way Wikipedia proposed the problem. However, you odds if you switch are exactly zero, because the only time I offer to let you switch is if swirching results in you losing.

Two possibilities - you pick the correct door with your first pick, or you pick the wrong door. if you pick the correct door, I open another door and allow you to switch. if you switch, you will lose. If you pick the incorrect door, I show you what you won - oops, I'm sorry, you lost. There's no opportunity to switch doors if your choice was a losing door.

In other words, you need to know what motivates the host to offer the switch - is it *always* a part of the game? Or is the host more clever than you are and realizes the offer will make you lose.

Okay, but Wikipedia didn't invent that problem so you're making a dangerous assumption that they're any authority on it.

 

[sontakke]

Consider following:-

A fair coin is being tossed. You get to call head or tail. The only thing which is NOT stated that the person conducting the test will NOT discard some of the tests. What are your odds of being right on coin tosses?

Most of reasonable persons will automatically assume that test results are not discarded by the conductor. There is no reason to make that assumption explicit. Would DrPizza insist that none of the results would be discarded before venturing the guess on the odds?

 

[OverVolt]

How2Statistics

 

[Schfifty Five]

Consider following:-

A fair coin is being tossed. You get to call head or tail. The only thing which is NOT stated that the person conducting the test will NOT discard some of the tests. What are your odds of being right on coin tosses?

Most of reasonable persons will automatically assume that test results are not discarded by the conductor. There is no reason to make that assumption explicit. Would DrPizza insist that none of the results would be discarded before venturing the guess on the odds?

lol what?

 

[OverVolt]

lol what?

He sucks at poker is the point he was trying to demonstrate I think.

 

[sontakke]

The point was some assumptions don't need to be explicitly stated down. Normal person just assumes that the results will not be discarded. DrPizza could in theory discard the results because "hey, because I never told you that I will NOT to discard the results at my will"!

This side track started when DrPizza claimed that something which everybody just assumed was NOT explicitly stated.

This was my way of showing that sometimes it does not have to be.

 

[JulesMaximus]

Depends on how much of a gambler you are really. Would you trade the chance of losing half of what you already have for the chance at doubling your money?

 

[momeNt]

What if the other box either has double or nothing?

 

[cubby1223]

On Monty Hall, as someone stated above, it's understood that the host always offers the chance to switch - it's part of the game. The wikipedia makes no mention of this part; people assume that it's understood. In the version I proposed, I followed the way Wikipedia proposed the problem. However, you odds if you switch are exactly zero, because the only time I offer to let you switch is if swirching results in you losing.

Two possibilities - you pick the correct door with your first pick, or you pick the wrong door. if you pick the correct door, I open another door and allow you to switch. if you switch, you will lose. If you pick the incorrect door, I show you what you won - oops, I'm sorry, you lost. There's no opportunity to switch doors if your choice was a losing door.

In other words, you need to know what motivates the host to offer the switch - is it *always* a part of the game? Or is the host more clever than you are and realizes the offer will make you lose.

I forgot to come back to this thread earlier in the week to see what your explanation was...

I figured it was going to be some technical mind-game. It's a game show that people watch for entertainment. Contestants will know going in whether the host will offer a switch all the time or some of the time.

It is EXACTLY the reasoning I gave for why switching in the "2 boxes" situation earlier is the better option. Because it allows you to learn about the game to make educated choices going forward, choices based more on knowledge than on strict randomness.


If you want to categorize your puzzle, it's a psychology puzzle far more than it is a logic puzzle.

 

[tranceport]

I had a girlfriend who I was pretty serious about. She was pretty amazing. But one day I mentioned some task I wasn't crazy about doing and she with a straight face suggested I hire some kid to do it. I didn't say anything but it made me wonder about her.

It's called outsourcing and she was a keeper.

 

[DrPizza]

There IS no assumption.

The problem as stated on widipedia:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

How in the world you think anyone is "assuming" this is always the case is a baffling. Why you even brought it up is a mystery.

And, as someone so eloquently stated, wikipedia is not an authority. If you look at some math discussions of the problem, there's no way to know if it's to your advantage, unless you know that the host is acting in a neutral manner.

You need to know the reason that the host offered the chance to switch doors - is it a required part of the game? Or is the host doing so only when you've chosen the correct door, giving you the opportunity to no longer have the correct door. See the italicized part - that cannot be assumed - and you guys are making that assumption. Many years ago, the problem was stated correctly most of the time. But as the problem has been retold and retold and retold, people started leaving out required parts of the problem.