In the Deal or No Deal game, the odds would be 50/50.
In LMD, you learn nothing when Monty opens a door so the odds are still 1/3 that your original choice is the car.
In the Deal or No Deal game, every case is potentially the million dollar case. Therefore each opened case gives you new information about the remaining cases and the odds on each remaining case changes.
In the Deal or No Deal scenario, I’m much less prone to guess at (Howie Mandel? The mysterious guy in the booth?)'s motive.
In the classic Let’s Make a Deal version, it’s presented like Monty is compelled to offer the switch (he’s not, but the textbook answer, and the way it’s presented, treat it as such).
In Deal or No Deal, the player might be justified in guessing the show is offering the switch at the last minute to save themselves money, because they’ve never done it before. It’d be hard to quantify, but odds would probably be better keeping your original guess.
If** Deal or No Deal** *always *offered a switch with the last unopened suitcase, I’d agree with the above posters it’s a 50/50 proposition.
I didn’t really watch Deal or No Deal, so correct me if I’m wrong.
All choices in Deal or No Deal are the contestant’s. The host never reveals the contents of any cases or eliminates any cases on his own, he merely shows the results of the cases chosen or not chosen. Correct?
In that case, then each reveal eliminates one of the options, and changes the odds on the remaining cases accordingly. (If at 20 cases, and you reveal one not the million dollars, then you now have 1 in 19 chances for the next pick).
This is distinct from Let’s Make a Deal, where the Host’s selection is based upon inside knowledge and constrained behavior to not reveal the prize.
The wikipedia pagesays it is assumed the Bank does not know the prize in the cases. They are only using a proprietary formula to determine how much to offer based upon the expected value of the remaining cases, discounted by some factor.
As far as the host goes, yes. In fact, it’s probable that he doesn’t even know what amounts are in which cases. (Mainly because memorizing those 30 values would be a pain, and there’s no value in doing so.)
However, there is the Bank to consider, which you address later in your post.
Powers &8^]
I suppose if the Bank knows which prize is where, then their offerings might be interpretable for clues. However, the wikipedia page says it is assumed the bank does not know and is using a formula based on the remaining prize values and number of prizes.
Getting back to this, this paragraph is incorrect. If Monty doesn’t know what’s behind the doors, then you don’t get any information about the remaining door when he reveals the goat. If he doesn’t know, and just happens to reveal the goat, then the odds of each door is 1/2.
The “2/3” answer depends on his knowing and being constrained to show a goat-door.
Think of it like this - if he doesn’t know, it’s the same basic problem as the Deal or No Deal setup, except with three unknowns instead of 30.
Actually, Chronos is right for the specific example he set, which allows one to swap to the car after it has been exposed.
You’re still picking the other two doors instead of your original door. In some cases the car is revealed so you know you’re getting the car. In other cases the car is not revealed. You’re still getting the 2/3 chance of car over your initial 1/3 chance.
If the host revealing the car meant you lost immediately, then you would have a point. That eliminates 1/3 of the original options.
The Monty Hall Problem (Again)
Let us sgart with a slightly different, albeit similar game.
Monty shows you the three doors.
A You pick a door.
B Month does nothing!
C Monty offers you a choice:
1 Keep whatever is behind the door you picked
2 Switch, and get everything behind the other two doors.
Clearly you chose the door with the car 1 in 3 tries. You are wrong 2 in 3 tries.
You have one chance in three your door has the car.
You have two chances in three the other two doors has the car.
What do you do? Unless you are a dyed-in-the-wool hunch player, you switch and take what is behind the other two doors.
Now let us try the original game
Monty shows you the three doors.
A You pick a door.
B Now Month shows you an empty door.
C Monty offers you a choice:
1 Keep whatever is behind the door you picked
2 Switch, and get everything behind the one unopened door.
In the first game you switched because 1/3 of the time you picked wrong.
You picked wrong 1/3 of the time in -this- game.
So switch!
That logic does not matter if your option is to swap to a door that is right only 1/3 of the time. The trick here is that Monty’s reveal is not random, so the switch option gives you a door that is right 2/3 of the time.