# Card Counting by n25pSd87

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```									CARD
COUNTING
By: Amanda Luedke, Matt Scalise, Becci Wynen
The Game
   The dealer starts with a deck of cards and flips over the
top card.
   Player guesses whether the next card is higher or lower
than that card.
   If the guess is correct, the player wins the round.
   If the guess is incorrect the dealer wins the round.
   If the cards are equal, it is a tie, no one wins.
Hypothesis
   What is the best strategy for winning?
 We  want the player to guess correctly more than 70% of the
time!
Guessing Correctly
Guessing Higher   Guessing Lower
   Ace~ 48/51       Ace~ 0/51
   2~ 44/51         2~ 4/51
   3~ 40/51         3~ 8/51
   4~ 36/51         4~ 12/51
   5~ 32/51         5~ 16/51
   6~ 28/51         6~ 20/51
   7~ 24/51         7~ 24/51
   8~ 20/51         8~ 28/51
   9~ 16/51         9~ 32/51
   10~ 12/51        10~ 36/51
   Jack~ 8/51       Jack~ 40/51
   Queen~ 4/51      Queen~ 44/51
   King~ 0/51       King~ 48/51
Guessing Correctly
Guessing Higher   Guessing Lower
   Ace~ 48/51       Ace~ 0/51
   2~ 44/51         2~ 4/51
   3~ 40/51         3~ 8/51
   4~ 36/51         4~ 12/51
   5~ 32/51         5~ 16/51
   6~ 28/51         6~ 20/51
   7~ 24/51         7~ 24/51
   8~ 20/51         8~ 28/51
   9~ 16/51         9~ 32/51
   10~ 12/51        10~ 36/51
   Jack~ 8/51       Jack~ 40/51
   Queen~ 4/51      Queen~ 44/51
   King~ 0/51       King~ 48/51
The Math
   In this game Aces are low and Kings are high.
   We need to calculate the probability of guessing correctly.
   Lets say we flipped a 3.
   The best guess would be higher, correct?
Probability
   We need to figure out all the possible outcomes.
   The deck has 52 cards.
   We flipped over 1, leaving us with 51 cards.
   There are 11 cards that are lower than or equal to a 3, (4
Aces, 4 2’s, and 3 3’s). Which means there are 40 (51-11)
cards that are higher than a 3.
   The probability of winning the round is 40/51 or 78%.
   Card Sharks
Guessing Correctly
Guessing Higher      Guessing Lower
  Ace~ 48/51          Ace~ 0/51
  2~ 44/51            2~ 4/51
  3~ 40/51            3~ 8/51
  4~ 36/51            4~ 12/51
  5~ 32/51            5~ 16/51
  6~ 28/51            6~ 20/51
  7~ 24/51            7~ 24/51
  8~ 20/51            8~ 28/51
  9~ 16/51            9~ 32/51
  10~ 12/51           10~ 36/51
  Jack~ 8/51          Jack~ 40/51
  Queen~ 4/51         Queen~ 44/51
  King~ 0/51          King~ 48/51
History of Card Counting
   Card counting is not just applied to the game of Hi-
Lo, but also in Blackjack.
   In 1962 the book Beat the Dealer was published.
 Edward   Thorpe
   21 {movie clip!!}
Is It Illegal?
   NO

   YES
   If using a computer device.
Bibliography
   "Card Counting." Card Counting. 1 Nov. 2008. Wikipedia. 2 Nov. 2008
<http://en.wikipedia.org/wiki/card_counting>

   "Law of Large Numbers." Law of Large Numbers. 29 Oct. 2008. Wikipedia.             2 Nov. 2008
<http://en.wikipedia.org/wiki/law_of_large_numbers>

   Olson, Andrew, ed. "The Effects of Card Counting on a Simple Card Game."           Free Science Fair
Project Ideas, Answers, and Tools for Serious     Students. 10 Oct. 2007. 2 Nov. 2008
<http://www.sciencebuddies.org/science-fair-
projects/project_ideas/math_p044.shtml?isb=cmlkojc1ntcxnyxzawq
6msxwojesawe6twf0aa&fave=no&from=tsw>

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