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Dumb Game math problem

#1 User is offline   gwnn 

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Posted 2009-March-24, 05:41

You deal everyone approximately the same number of (bridge) cards.

Everyone contributes to a trick with the top card of his stack of cards (you can't look at your cards) and the trick continues until someone plays a heart. The trick is taken by the player who played the heart and his LHO will start the next trick.

Unless you haven't won any tricks yet, the bottom card of your stack needs to be a heart. The key moments are when someone starts a trick with a heart, then he or she can lose a heart and hearts are obviously very important. If your RHO won the trick and you have only 1 card remaining, you play it and you're out of the game. The winner is the one who takes all 52 cards (variation: the one who finishes first).

Is it possible to get into an infinite loop? Obviously any game that doesn't end involves an infinite loop, since the states of the game are finite. How can this be calculated?
... and I can prove it with my usual, flawless logic.
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#2 User is offline   Trumpace 

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Posted 2009-March-24, 08:56

Where would the winner of the trick place the cards won? At the bottom of the his stack? If he can place at the top, then there could be an infinite loop, I believe.
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#3 User is offline   gwnn 

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Posted 2009-March-24, 09:08

At the bottom of his stack.
... and I can prove it with my usual, flawless logic.
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#4 User is offline   FrancesHinden 

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Posted 2009-March-24, 09:30

gwnn, on Mar 24 2009, 11:41 AM, said:

You deal everyone approximately the same number of (bridge) cards.

Everyone contributes to a trick with the top card of his stack of cards and the trick continues until someone plays a heart. The trick is taken by the player who played the heart and his LHO will start the next trick.

The key moments are when someone starts a trick with a heart, then he or she can lose a heart and hearts are obviously very important.

Um... the way you specified it, if I lead a heart the trick is over, and my LHO starts the next trick. This game never ends.

Do you mean that the trick continues until someone other than the first person to play to a trick plays a heart?
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#5 User is offline   TimG 

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Posted 2009-March-24, 11:24

gwnn, on Mar 24 2009, 06:41 AM, said:

The key moments are when someone starts a trick with a heart, then he or she can lose a heart and hearts are obviously very important.

I think this means "other than the first person to play to a trick".
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#6 User is offline   gwnn 

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Posted 2009-March-25, 01:01

Um.. I shouldn't attempt written English earlier than 3PM :o Yes, it does sound like that.

The first card doesn't count. Every time you take a trick you just flip the big stack of cards upside down and put your original stack on top of it.

The game can be played by trained monkeys because you have no legal choices in it, except maybe sometimes you can try to play a card from the bottom and try not to get caught. After a couple of beers it is OK though.
... and I can prove it with my usual, flawless logic.
      George Carlin
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