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Puzzle Games (Games)

tomhudson's Journal: Monty Hall vs Deal Or No Deal 8

Journal by tomhudson

Gee ... nobody took the bait :-)

A while back, I posted that the choice is 50-50 to either keep the original prize door, or swap with the unopened door, and *nobody* bothered to jump in.

The correct choice is to always switch. The real problem is that when people try to explain their solution, they make it overly complex (or they used it as an intro to push their particular brand of "enlighenment"). A simple "truth table" suffices.

You vs The Other Doors
===================
0 -- 0 -- 1
0 -- 1 -- 0
1 -- 0 -- 0

The same setup after removing one of the other doors that doesn't have the prize:

You vs The Remaining Door
===================
0 -- 1
0 -- 1
1 -- 0

So, what does this have to do with Deal or No Deal?

Here's the scenario - you're down to 2 suitcases - the one you picked in the beginning, and one left on-stage. One of them has $1,000,000.00, and one has $0.01.

Do you swap?

Your friends and family are giving you the following advice:

  1. The Monty Hall scenario applies - swap.
  2. The Monty Hall scenario doesn't apply - It's 50-50. Do whatever you want.
  3. The odds of you picking the $1,000,000.00 were 1/26. Swap.
  4. The odds of you avoiding picking the $1,000,000.00 up until now were 1/25 - so its 95% sure you're holdng the million - don't swap.
  5. The odds of you picking the $1,000,000.00 at any point were 1/26+1/25+1/24+ ... +1/2. You almost definitely have already picked the $1,000,000.00, and since it wasn't on-stage, you're almost certainly already holding it. Don't swap.
  6. The ods that you'll make the right decision are 50-50. Do whatever you want.
  7. The odds that you've made the right pick 25 times in a row are astronomical. Swap.

Do you swap, and why or why not?

Follow-up: Just prior, you've been offered a "deal" of $300,000.00 for your suitcase. This is well below the average expected payout of a half-million. Do you take the "deal?"

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Monty Hall vs Deal Or No Deal

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  • In the Monty Hall example, the chances are altered in your favour (well, against your choice, but in your favour in that you know that swapping will help) in that whatever door the host opens will NOT be the one with the prize money. eg,

    If the situation is:

    1 2 3 L L W X

    The host will open door 2. If the situation is:

    1 2 3 L W L X

    the host will always open door 3. The only other combination is:

    1 2 3 W L L X

    which is the one scenario in which you'd lose by switching, hence the odds are 2:1 in favou

    • ...ok, here's the comment cleaned up...

      In the Monty Hall example, the chances are altered in your favour (well, against your choice, but in your favour in that you know that swapping will help) in that whatever door the host opens will NOT be the one with the prize money. eg,

      If the situation is:

      1 2 3
      L L W
      X

      The host will open door 2. If the situation is:

      1 2 3
      L W L
      X

      the host will always open door 3. The only other combination is:

      1 2 3
      W L L
      X

      which is the one scenario in which you'd lo

  • If it came down to two cases and the million was still live, it is a 50/50 proposition. You are the one responsible for removing the other cases and your choices are random - unlike the Monty Hall Problem, you do no have any knowledge of where to big prize(s) is(are) so your choices do not skew the probabilities the same way.

    If I was offered $300,000, I'd prolly take it - $300k is a heck of a lot more then $0.01! I'm not likely to be in the same situation ever again, so the expected value of $500k is not a
    • by nizo (81281) *
      Yeah I would take the 300K too, since I would feel totally retarded if I didn't get the million, and I'm not greedy :-) Besides fewer people would come out of the wordwork if I won 300K on national TV, but if I won a million dollars......
      • What's that old saying, "300k in the hand beats a mil in the suitcase?"

        For my life, 300k, afte taxes, would be enough to wipe out debt and help get a nice house with land. The mil makes yout empted to think that you have more money than you actually do. In the long run, I think I'd be better of with the 300K.

        But that's me. That plus after too many discussions with my mathematician of a brother over the Monty Hall problem: I see it as proof that mathematics is an invalid system. Now if you excuse me,

  • by RM6f9 (825298) *
    Deal! I can easily triple it plus in a year and a half to 2 years...
  • This is so stupid, why doesn't someone spend the 10 seconds needed to write a simulation?

    My feeling is:

    You are shown two doors, told that behind one of them there is a million dollars.

    Before you pick, the announcer also tells you "Oh, by the way, there is a fire door over there, see that fire door? No money behind it"

    There is NO difference between this and picking a door first, THEN being told "Oh yah this door here is empty".

    In essence, you are given two doors to choose from, and told that one of them has
  • 1. The Monty Hall scenario applies - swap.
    Monty Hall doesn't really apply; Squiggle hit that one right on the head.

    2. The Monty Hall scenario doesn't apply - It's 50-50. Do whatever you want.
    Any choice between two unknowns is always 50-50, so this is completely correct.

    3. The odds of you picking the $1,000,000.00 were 1/26. Swap.
    Irrelevant in terms of probability at this point.

    4. The odds of you avoiding picking the $1,000,000.00 up until now were 1/25 - so its 95% sure you're holding the millio

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