Real Mathematics – Algorithm #3

Card Games

I remember vividly; at least once a week I was dragged to family meetings. All I wanted was to stay home and play Duke Nukem. But I had to go to those meetings and keep score of a card game which dads play. There were rumors about my high mathematics grades, and I really wanted to fail mathematics just because I might have escaped this responsibility. And game had absurd scores too: “300 to us, 4250 to them, did you write 20 points to us?”

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Everyone who had experienced campus life knows that living in a dorm meant both misery and lots of fun. Personally my favorites were the times when I sat down with three other guys and played card games for hours. After four years I became addicted to the very thing I despised as a child.

I love playing competitive games but if a game has algorithms on the background then I get addicted to that game. In some card games players develop algorithms in their heads. And in a group of close friends, everyone is aware of his/her opponents’ algorithms. This is why making simultaneous adjustments on your algorithm might win you the game.

Pico

Pico is a German card game that shows how mathematics can be used in card games perfectly. Even though Pico is a simple game it has astonishing mathematics that lies behind it.

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  • In this multiplayer game there are eleven cards which have 2, 3, 4, 5, 6, 7, 8, 9, 10, 13 and 16 written on them.
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  • Cards are shuffled and dealt. Each player gets five cards.
  • The only card left gets turned over so that both players know which cards his/her opponent has.
  • In every hand players select a card simultaneously.
  • The card that has the highest number on it wins the hand unless it is more than twice of the other card.
  • The winning card is placed next to the player who won the hand. The number on that card is the score he/she gets.
  • Losing card goes back to its owner.
  • Game continues until either one of the players holds exactly one card.

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    In case there is a deck of cards in your home, you could assign K to 13 and J to 16 so that you can play Pico.

Seko

I thought about writing a new game which I called Seko:

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  • Seko is a multiplayer game just like Pico. There are numbers from 2 to 50. Each player selects six numbers at once. Players roll a dice in order to determine who starts selecting first.
  • Twelve selected numbers are written on a paper.
  • Out of these twelve numbers, each player selects six numbers but this time one by one. Again they roll a dice in order to determine who starts selecting first.
  • In the first hand players select a number simultaneously.
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  • If the difference of those numbers is odd, bigger number wins. If the difference is even and less than 20, smallest number wins.
  • The winning number is written in front of the winner. Loser gets his/her number back.
  • Game continues until a player has exactly one number left.

One wonders…

Instead of finding the difference in Seko, add the numbers. If the addition is odd, biggest number wins. If addition is even and less than 50, smallest number wins.

Can you find an algorithm to use in every game of Seko?

M. Serkan Kalaycıoğlu

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