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Deal or No Deal

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BuckeyeTillIDie said:
Am I the only one who thinks that everyone on Deal or No Deal are actors? It seems so fake and over-the-top dramatic to me.

Howie Mandel sucks, the concept of the show sucks... but the girls are hot.
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I would agree with you but my buddy stayed in line 4 hours here in Cleveland for the casting call. It is just that to even get a seat at that show you have to show them how crazy you are. It is all casting, they pick the characters that are willing to do stupid things and if you are as smart as a pile of rocks all the better.
 
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MolGenBuckeye said:
What do you mean by this part? The probability of getting a remaining amount on the board does increase as you remove other amounts, right?

Maybe I'm misinterpreting?
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I believe that Dryden supplied a decent explanation.

What I do to communicate what Dryden laid out, is bring in a deck of cards, without the jokers. Most know that probability of randomly selecting the ace of clubs on a single draw is 1/52. Now if I have you randomly select a card and say that I will give you $1,000,000 if you have selected the ace of clubs, do not let you look at your selected cards, and then I proceed to look at the cards and discard 50 of them, leaving your selected card and one other card, and tell you that one of the remaining two cards (the one you selected or the one I left out) is the ace of clubs and then give you the option of changing cards, would you change? You should since the probability that you selected the ace of clubs is still 1/52; many look at the scenario I laid out as there are only 2 cards left so your probability is 1/2. They forget that the probability of the event of selecting the ace of clubs from the full deck has a sample space of 52 hence the probability doesn't change.
 
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buckiprof said:
I believe that Dryden supplied a decent explanation.

What I do to communicate what Dryden laid out, is bring in a deck of cards, without the jokers. Most know that probability of randomly selecting the ace of clubs on a single draw is 1/52. Now if I have you randomly select a card and say that I will give you $1,000,000 if you have selected the ace of clubs, do not let you look at your selected cards, and then I proceed to look at the cards and discard 50 of them, leaving your selected card and one other card, and tell you that one of the remaining two cards (the one you selected or the one I left out) is the ace of clubs and then give you the option of changing cards, would you change? You should since the probability that you selected the ace of clubs is still 1/52; many look at the scenario I laid out as there are only 2 cards left so your probability is 1/2. They forget that the probability of the event of selecting the ace of clubs from the full deck has a sample space of 52 hence the probability doesn't change.
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Good explanation.

This is similar to the Monty Hall paradox where someone picks from three doors with prizes behind them, is shown what is behind one of the doors, and asked if they want to change to the third door or stay with their choice. If they stay, the odds of winning the big prize are 1/3; if they change, the odds are 1/2.
 
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Deety said:
Good explanation.

This is similar to the Monty Hall paradox where someone picks from three doors with prizes behind them, is shown what is behind one of the doors, and asked if they want to change to the third door or stay with their choice. If they stay, the odds of winning the big prize are 1/3; if they change, the odds are 1/2.
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Exactly like the Monty Hall paradox!

A prof in grad school presented this paradox to the class and expected an answer the next day. The next day he did it with $10 as the prize but if you lost you owed him $10. Most in the class didn't get it, but I told prof I would take the challenge. He kept asking if I was sure, etc., etc., then didn't play the game with me. I had to explain my reasoning to the class and the card scenario I laid out above was my explanation. IMO it is easier to see with the card scenario, yet there were still a few folks who didn't "get it".
 
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Funny when I went to the Wikipedia site they had the link to Deal or No Deal and an explanation that it is similar but not like the Monty Hall paradox...

Comparison with the Monty Hall Problem

When only two cases remain, Deal or No Deal might appear to be a version of the Monty Hall problem. Consider a game with three cases (similar to the three doors in the Monty Hall problem). The player chooses one case. Then, the player chooses a case to expose. Finally, the player is given the option to trade his case for the one remaining. The Monty Hall problem gives the player a 2/3 chance of winning with a switch and a 1/3 chance of winning by keeping his case. However, statistical testing has shown that there is no advantage in switching in the Deal or No Deal situation. The player has a 50/50 chance of increasing his winnings by either switching or keeping his case.

The reason that the Monty Hall problem gives the player an advantage is because the host purposely exposes a losing door. In other words, there is no randomness to the door exposed. It is purely based on the player's first choice. In the Deal or No Deal situation, the player chooses one case and then exposes another. The one exposed may very well be the winning case, leaving two lesser cases still in play. Therefore, there is no relation between the player's first choice and the case that is exposed. That breaks the Monty Hall advantage in switching.
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Deety said:
Good explanation.

This is similar to the Monty Hall paradox where someone picks from three doors with prizes behind them, is shown what is behind one of the doors, and asked if they want to change to the third door or stay with their choice. If they stay, the odds of winning the big prize are 1/3; if they change, the odds are 1/2.
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If they change, the odds are 2/3, rather than 1/2. :wink2: See Piney's link.

On bukiprof's deck of cards scenario, if he allowed a switch at the end, the odds would be 51/52 if you switched, and 1/52 if you didn't.

With the deck of cards, it's 1/52 at the end because the 50 cards being eliminated were not done so randomly. If the 50 cards were picked randomly, and none was the Ace of clubs, the odds of each card being the Ace of clubs at the end is 50%. Because at the start, the probability that the last remaining card will be the Ace of clubs was also 1 in 52.

But this situation will only occur once in 26 attempts, because the odds are 50 out of 52 that the Ace of Clubs will be one of the 50 cards randomly chosen to be eliminated.

So in the TV show, since the person is randomly choosing cases (as opposed to he Monty Hall situation where the show is knowingly eliminating losing choices), any remaining dollar amount has an equal chance of being in any of the remaining cases. If there are 5 cases left, and the $1 million case hasn't been revealed, the person then has a 1 in 5 chance of having the $1 million case.

What I'm wondering about in Deal or No Deal, is if the banker knows what dollar amounts are in which cases as he's making the offers. I've hardly watched the show, do they say whether or not the banker is aware of where the amounts are?
 
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What I'm wondering about in Deal or No Deal, is if the banker knows what dollar amounts are in which cases as he's making the offers. I've hardly watched the show, do they say whether or not the banker is aware of where the amounts are?
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They've said before that nobody knows what's in the cases except for an independent firm... not the bank, Howie or the producers.
 
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Comparison with the Monty Hall Problem

When only two cases remain, Deal or No Deal might appear to be a version of the Monty Hall problem. Consider a game with three cases (similar to the three doors in the Monty Hall problem). The player chooses one case. Then, the player chooses a case to expose. Finally, the player is given the option to trade his case for the one remaining. The Monty Hall problem gives the player a 2/3 chance of winning with a switch and a 1/3 chance of winning by keeping his case. However, statistical testing has shown that there is no advantage in switching in the Deal or No Deal situation. The player has a 50/50 chance of increasing his winnings by either switching or keeping his case.

The reason that the Monty Hall problem gives the player an advantage is because the host purposely exposes a losing door. In other words, there is no randomness to the door exposed. It is purely based on the player's first choice. In the Deal or No Deal situation, the player chooses one case and then exposes another. The one exposed may very well be the winning case, leaving two lesser cases still in play. Therefore, there is no relation between the player's first choice and the case that is exposed. That breaks the Monty Hall advantage in switching.
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They've said before that nobody knows what's in the cases except for an independent firm... not the bank, Howie or the producers.
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And that is where expected values comes into the equation; similar to the Monty Hall paradox, in that people's lack of basic probability is exploited along with a carrot dangled. Knowing a little about expected values can help the contestants quite a bit.

All of this reminds me too much of grad school when I had to have an area of application. When told that my first choice, climatology, wouldn't cut it, I picked statistics even though I hated stats, as most math folks do.

On bukiprof's deck of cards scenario, if he allowed a switch at the end, the odds would be 51/52 if you switched, and 1/52 if you didn't.
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It is so simple to see with a larger sample space (52) and I was ready to take the prof's money. I was a little bummed that, once he knew that I knew, he wouldn't play. What was more of a bummer was that some in the class still didn't get it.

Regardless, the sample space from which the initial pick was made determines the probability if the $1 million dollar case has been selected throughout. People should realize this and attack the game from an expected value point of view. BTW, I rarely watch the game since it reminds me too much of how little basic math type knowledge people really have. And watching it this month, Mathematics Awareness Month, would not be good for me since awareness is all too lacking for many :wink2:
 
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