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Emprworm's Riddle #17: Mess of Tokens


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EMPRWORM'S RIDDLE #14

A FAIR BET?

One night, while at a party, you bump into a guy named Plisken, who has a reputation for being a charismatic con artist. With his slick appearance and flamoyant smile, he proposes to you a little bet over a friendly game of cards. Of course, you are very familiar with his antics- always making a quick buck at someone else's expense.

But this time, he assures you it'll be different,

"I promise you," he says, "This game is complete chance, there are no hidden tricks. Get me a deck of cards and watch."

You give him a deck of cards, checking it first to make sure it isn't tampered with. Plisken then proceeds to find nine cards: 10C, 9H, 8S, 7H, 6S, 5C, 4S, 3C, 2H. He hands the nine cards to you.

"Ok, now group them by suit," he says.

You do as he asks- and now you have three groups of three cards.

"Now flip each pile face down and shuffle them. Put the pile of hearts on the right, the pile of clubs in the middle, and the spades on the left."

When you've done this, he proposes the game.

"Okay, here's how the game is played. You will go first and pick a random card from any pile, but don't show me the card. Then I'll point to one of the other piles, and then you pick a random card from that pile. If your card is higher, I owe you 10 bucks. If my card is higher, you owe me 10 bucks. Can't be much fairer than that, can it?"

Knowing Plisken, it probably could be. But you must admit, it does sound fair- so what's the catch? Should you take this bet? Why or why not?

cards.jpg

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now would that happen to be Iriquois Plisken? lol. uhm...nm. i bet most people didn't get that. well...

[hide]well if you pick the clubs and get the three then he'll win and draw the 10 next. but then there's always a possibilty that you could draw that ten which means you'd win no matter what. so i think it is fair. it's might be a little one sided but it's all chance. or at least i think it's all chance. if someoen gets the 10 then win by default.[/hide]

it's not right and i know it. i read the question wrong.

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Don't tell me this is another probability riddle ... :P

[hide]Well if you pick from the Club, you have a third chance to get the 10, and so he can pick from any other deck and get a 2/3 chance of getting over you, providing you don't have the 10. So if you pick the club, the chances are in his favor. If you pick from the hearts, it goes the same way. He has the higher odds of getting a better hand. [/hide]

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[hide]

That doesn't work for hearts:

C S H

10 8 9

5 6 7

3 4 2

If you get 9 or 7 hearts (2/3 chance), he has only 1/3 of chance of getting more than you, so therefore if you go with hearts, the odds are in your favor. So you see, if you go with Clubs or Spades - he has more chances to win that you, but if you pick Hearts- you have a better chance to win[/hide]

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[hide]"10C, 9H, 8S, 7H, 6S, 5C, 4S, 3C, 2H"

If you get

10C, you win

9H, he goes clubs, and you win 2/3 of the time

8S, he goes H or C, and you win 2/3 of the time

7H, he goes H, and you win 1/2 of the time

6S, he goes H, and you win 1/3 of the time

5C, he goes H or S, and you win 1/3 of the time

4S, he goes S, and you lose

3C, he goes C, and you lose

2H, you lose

Naturally, you can pick the most favourable suit.

10C, you win

5C, he goes H or S, and you win 1/3 of the time

3C, he goes C, and you lose

1/3 + 1/9 + 0 = 8/18

9H, he goes clubs, and you win 2/3 of the time

7H, he goes H, and you win 1/2 of the time

2H, you lose

2/9 + 1/6 + 0 = 7/18

8S, he goes H or C, and you win 2/3 of the time

6S, he goes H, and you win 1/3 of the time

4S, he goes S, and you lose

2/9 + 1/9 + 0 = 6/18

So you will choose clubs each time, winning only 4 in 9 times. Therefore do not play the game.[/hide]

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[hide]

The first person to pick has only a 33% chance of winning regardless of what suit he chooses.

[PRE]

----Range-----

Type High, Mid, Low

Clubs: 10, 5, 3

Hearts: 9, 7, 2

Spades: 8, 6, 4

[/PRE]

If Person 1 chooses Clubs then Person 2 will choose Spades.

If Person 1 chooses Hearts then Person 2 will choose Clubs.

If Person 1 chooses Spades then Person 2 will choose Hearts.

(added text) Each suit has one card that is the leader of its class. Clubs has the best High card. Hearts has the best Mid-ranged card. Spades has the best low card.

Likewise, each suit has a particular weakness. Club's is mid-ranged cards, Hearts' is low-ranged cards, and Spades is high-ranged cards. Person 2's job is to choose the suit whose weakness is in the same range as Person 1's suit's strength. Each person has an equal chance of picking their Auto-Win card or the Auto-Lose card. Person 2's advantage is that he can choose the suit whose Chance card trumps Player 1's. (end added text)

Look at it like the boardgame Risk. Each player matches the highest cards, the second highest cards, and the lowest cards together. In every case Player 2 has two winning pairings as opposed to Player 1's single winning pairing.

[/hide]

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SOLUTION TO A FAIR BET

Bashar solved this one - excellent work, though your odds were off a bit, I'll still give it to you since you adequately explained it in detail. GOod job!

ANSWER:

[hide] Plisken deliberately selected a collection of cards that allow him to exploit an aspect of probability sometimes referred to as the voting paradox or the Arrow Paradox. The voting paradox is based on the fact the probability is not always a transitive property. Consider this:

The clubs hand consists of 3, 5, and 10

The spades hand consists of 4, 6, and 8.

The hearts hand consists of 2, 7, and 9.

If the two piles picked from are clubs and spades, spades wins 5 times out of 9. If the two piles are spades and hearts, hearts wins 5 times out of 9. But even though spades will beat clubs, and hearts will beat spades, hearts isn't a safe bet. Because clubs beats hearts 5 times out of 9.

So no matter which pile you pick, there's another pile that will beat it. Therefore, Plisken will beat you more than you will beat him (5/9) just by pointing to the pile that he knows will beat yours.

[/hide]

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I'm afraid I can't really accept credit for solving the puzzle. I did come up with the correct outcome, however, my logic was at fault. I completely disregarded the fact that Mid or High value cards can still beat Low value cards, regardless of whether or not they are that particular hand's strength which is why my odds were in error of 9%.

My apologies to the others. I should not have rushed my calculations.

--Bashar

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EMPRWORM'S RIDDLE #15

THE ACCIDENT

Detective Shihalud arrived at the accident scene in a bit of a hurry. He was several miles away when the call first came to him from the police dispatch. The accident took place on a lonely stretch of Highway between two small towns in eastern washington early that morning. A small Ford Escort with a driver and passenger, had smashed into a tree along the side of the road at a high rate of speed. The passenger, a young woman, was killed, presumably instantly. Amazingly enough, the driver was virtually unharmed, except for a few nicks and scratches- in part because only the right front side of the car hit the tree- it was a straight-on collision.

An ambulance was there, carting off the dead body while several police were gathering details.

Shihalud approached the survivor, who was named Paul.

"Hello, Paul, my name is Detective ShiHalud. Can you tell me what happened here?"

"Yes sir," he said frantically. It was obvious he was shaken up. "Me and my girlfriend were driving early this morning about 5:30 am. We were going about 100 KPH (about 60 MPH) and suddenly hit a patch of ice. I lost control and slammed into the tree. I think I must have been knocked out for a while. All I remember after that is waking up hunched over the steering wheel with an awfully sore neck. I looked over at her and she was slumped over. She never even said a word, she was dead. O dear, this is horrible."

"Hmmmm..." Shihalud looked around. Starting in the far right lane, there was a pair of skid marks leading straight to the tree- probably about 30 feet. He had remembered traffic reports earlier that morning of patches of ice on the roads, it was very cold at 5:30 am. Inside the car, there was shattered glass scattered around the front seats.

"Paul, did you and your girlfriend get along well?" The detective asked.

"Yes sir. You know, we had our problems like any other couple, but overall, we had a very close relationship"

"What lane were you driving in?," asked the detective.

"The right lane. We were going at the speed limit," Paul said.

"Did anyone else see the accident?"

"I do not believe so. I had not seen any other cars on the road. It was quite dark, and there were no other headlights at all that I could see."

Officer Jerry walked up to Shihalud. "So, Detective, what do you think?"

"I'm not sure," the detective replied, "But one thing I do know, is that this man is lying to us. There is more to this 'accident' then he is leading us to believe."

What did Shihalud know?

highway.jpg

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I'll try...

[hide]

I think he knew that when the right front side of the car crashes into the tree, the shattered glass would not go inside, but it would go out. Therefore, the man probably killed his gf and then crashed the car slightly, breaking the front window himself with a blunt object. Then he got into the car and pretended to be unconsious.[/hide]

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[hide]Why would it fly out? All the head-on collisions I've seen had the victims cut up with glass all over the place, unless for some reason it being hit only on the right causes the glass to do some funky reverse pull?[/hide]

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Is this one of those 'What did he know' ones where we cannot deduce from the text the contradiction of which Detective ShiHalud (!) is thinking, and we just have to guess from the context what he might know that would lead him to believe that the man is lying.

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this riddle is quite solvable. ShiHalud has deduced from the mans statements and what he sees at the scene, that it is highly unlikely his story is true. perhaps there is a .1% chance it is true, but in his vast experience, and based upon the facts of the case and his statements, most likely he is lying.

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[hide]Is it to do with the fact that there are skid marks on the road (on the right side, the origin point of the loss of control), when it was apparently ice patches that caused the accident? You may not have skid marks on the road if there's ice in the way.

Or is it the fact that he shouldn't have been going at 60mph on an icy road?[/hide]

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