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#1
07-24-2005, 08:25 PM
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A zero-sum game
A game is played between two players. They choose numbers one at time from {-4, -3, -2, -1, 0, 1, 2, 3, 4} and no number can be chosen twice. The first player to obtain three numbers (out of three, four or five) that sums to zero wins.
Which player, if any, has a winning strategy? 
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#2
07-24-2005, 08:59 PM
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Re: A zero-sum game
Now, I've only been thinking about this for about 3 minutes, but it feels like this is a Tic-Tac-Toe kind of game. The first player will always set the pace of the game, but the second player should be able to counteract any moves made.
The only way to get to zero, are: 0,-x,+x 1,2,3 1,3,4 As long as player 2 recognizes this, it should be pretty easy to end every game in a tie. But, I'm still thinking.
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#3
07-24-2005, 11:36 PM
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Re: A zero-sum game
[ QUOTE ]
it feels like this is a Tic-Tac-Toe kind of game. [/ QUOTE ] It is tic-tac-toe. Arrange the numbers into a magic square, where all rows add to zero, and that's your mapping. This would make a good money hustling game against people who won't realize they are playing tic-tac-toe. You can let them go first or second, and you can never lose, but they will have trouble seeing the double threats coming and you should win some games. Edit: Also you don't have to use negative numbers. Just use 1-9 and the goal is to get 15.
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#4
07-24-2005, 11:40 PM
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Re: A zero-sum game
[ QUOTE ]
[ QUOTE ] it feels like this is a Tic-Tac-Toe kind of game. [/ QUOTE ] It is tic-tac-toe. Arrange the numbers into a magic square, where all rows add to zero, and that's your mapping. This would make a good money hustling game against people who won't realize they are playing tic-tac-toe. You can let them go first or second, and you can never lose, but they will have trouble seeing the double threats coming and you should win some games. [/ QUOTE ] This solution is correct. Very nice work. I did hustle a friend with it until she realized what was going on. [img]/images/graemlins/laugh.gif[/img]
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#5
07-25-2005, 01:14 AM
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Re: A zero-sum game
[ QUOTE ]
[ QUOTE ] [ QUOTE ] it feels like this is a Tic-Tac-Toe kind of game. [/ QUOTE ] It is tic-tac-toe. Arrange the numbers into a magic square, where all rows add to zero, and that's your mapping. This would make a good money hustling game against people who won't realize they are playing tic-tac-toe. You can let them go first or second, and you can never lose, but they will have trouble seeing the double threats coming and you should win some games. [/ QUOTE ] This solution is correct. Very nice work. I did hustle a friend with it until she realized what was going on. [img]/images/graemlins/laugh.gif[/img] [/ QUOTE ] This is a brilliant hustling game. Very, very nicely done.
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#7
07-24-2005, 09:12 PM
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Re: A zero-sum game
I believe the first player will have the winning strategy if he does not pick 0 first. The second player will always be one move behind. Like playing tic tac toe.
Just tought I will give it a try.
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#10
07-24-2005, 10:09 PM
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Re: A zero-sum game
The only way for the second player not to lose would be to pick the numbers that the other player needs to get to 0. For example:
P1 P2 -4 4 3 1 2 -1 -3 -2 0 The game will end up with no one winning. If the second player does not follow that strategy and if the first player does not pick 0 first, then the first player will always win. I hope I am explaining myself correctly
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