Klopp
Klopp
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March 10th, 2020 at 6:50:17 AM permalink
In the final segment of a game show for couples, the last remaining couple is presented with three closed doors, behind which, in random order, they will find a car, the key to the car, and a goat. One of the two players is given the task of finding the car, the other must find the car key. If both are successful, they get to keep the car. Each of the two players may open two doors; the second player may not see what is behind the doors chosen by the first player. The couple may discuss a strategy before the game starts. What strategy will afford the best odds of winning the car, and what are the winning odds?
EdCollins
EdCollins
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March 10th, 2020 at 7:18:40 AM permalink
Just to be clear, if the first person is given the task of finding the car, and the second person is given the task of finding the keys, but the first person finds the keys and the second person finds the car, that's a miss, correct, since neither was successful on their own, despite being successful together.

If so, I offer this simple solution, which I would hope can easily be improved upon.
The couple agree beforehand to each pick Door #1 and Door #2.

That's it.

If the goat is behind Door #3, they lose. Otherwise, they will win. There's a 1/3 chance the goat is behind Door #3. Thus, they have a 2/3 chance of finding the car and the keys.
Wizard
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Wizard
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March 10th, 2020 at 7:33:45 AM permalink
Question -- Can each contestant choose the second door after seeing what is behind the first door?
Last edited by: Wizard on Mar 10, 2020
It's not whether you win or lose; it's whether or not you had a good bet.
unJon
unJon
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March 10th, 2020 at 7:41:50 AM permalink
Seems like a variant of the secret Santa problem.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
CrystalMath
CrystalMath
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March 10th, 2020 at 7:42:38 AM permalink
Even if the players cannot see anything, they can have player 1 choose doors 1&2 and player 2 choose doors 2&3 for a 50% success rate.


Can the second player see which doors player 1 opened?
I heart Crystal Math.
DJTeddyBear
DJTeddyBear
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March 10th, 2020 at 7:44:40 AM permalink
I was going to agree with Ed, but then as I was typing it, it all fell apart in my head. ☹️
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
DJTeddyBear
DJTeddyBear
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March 10th, 2020 at 7:58:44 AM permalink
After further noodling the problem, and gasp taking out a pen and paper, I agree with CrystalMath.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
unJon
unJon
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Thanks for this post from:
CrystalMath
March 10th, 2020 at 7:59:03 AM permalink
Secret Santa logic:

I assume that a person picks his second door after opening the first.

Label the car #1, keys #2 and goat #3.

Player #1 must find car (#1). He begins by opening door #1. If it痴 the car behind the door, he痴 done. If it痴 the keys (#2) he opens door 2 next. If it痴 the goat (#3), he opens door 3 next.

Player #2 does the same algorithm but opens door #2 first, looking for keys.

Of the 6 ways to sort the three objects behind three doors, this method produces a winner in the following:

123
132
213
321

Or 2/3 of the time.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Wizard
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Wizard
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March 10th, 2020 at 7:59:28 AM permalink
While we wait for clarification on the rules from Klopp, allow me to ask the following Wizard Variant:

In the final segment of a game show for couples, the last remaining couple is presented with three closed doors, behind which, in random order, they will find a car, the key to the car, and a goat. One of the two players is given the task of finding the car, the other must find the car key. If both are successful, they get to keep the car. Each of the two players may open two doors; the second player may not see what is behind the doors chosen by the first player. Both players may choose their second door after seeing what is behind their first door. Neither player shall know any results from the other player. The couple may discuss a strategy before the game starts. What strategy will afford the best odds of winning the car, and what are the winning odds?
It's not whether you win or lose; it's whether or not you had a good bet.
CrystalMath
CrystalMath
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March 10th, 2020 at 8:00:37 AM permalink
Assuming player 2 can see which doors player 1 opened, but not their contents, then player 1 will choose door 1. If it contains player 2痴 item, then open door 3, otherwise door 2. Player 2 will open door 1if player 1 opened door 3, otherwise player 2 will open doors 2&3.

This gives a 2/3 success rate.
I heart Crystal Math.

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