Seizing the Deck: A History of Blackjack Choose Ohio First Scholarship Program: Success in Mathematics Bethany Baranyk, Juliana Puskorius, and Jessica.

Seizing the Deck:A History of Blackjack

Choose Ohio First Scholarship Program: Success in Mathematics

Bethany Baranyk, Juliana Puskorius, and Jessica Capestrain

History of Blackjack

• Started in France in 1700s

• Called “vingt-et-un”, which means twenty-one in English

• One of the only games where the player can have an advantage over the dealer

• In 1956 Roger Baldwin was the first to apply mathematics to blackjack in his paper, “The Optimum Strategy in Blackjack”.

• In 1962, Edward O. Thorp developed the first card counting techniques.

“Blackjack”

The name blackjack came from the special pay out that occurred when a black Jack was used to make 21. The name stuck as the name gained popularity and the higher payout was dropped.

Roger Baldwin• “The Optimum Strategy in Blackjack” was published in the Journal of

the American Statistical Association.

• Used probability and statistics theory to calculate a way to reduce the house advantage.

• Strategy was impractical because it required a computer and is illegal to use computer devices in a Casino

• The Decision Equation:

• The equation compares the expectations of the player, if they first draw a card or then if they stand on their hand. It means that at different values of the hand their expectancy varies for the count of the hand.

Edward O Thorp•Known as the father of card counting

•PhD. in mathematics

•Published card counting results in New York Times top-seller book “Beat the Dealer”

•His book’s success caused losses at the Casinos

•Casinos tried to change the rules of the game due to Thorp’s “ten count” but were unsuccessful and decided to revert back to the old rules.

Rules• A player is playing against only the dealer, not other players

• Each player places their ante on the table

• Each player is dealt one card face down followed by the dealer

• Then each player receives one card face up followed by the dealer

• Each player then has the opportunity to up their bet

• Next each player, one at a time, can hit to take additional cards, until they reach 21, bust, or decide to stay. Some may opt to stay with their original two cards

• The dealer then tries to reach 21. On most tables the dealer must stay on a hand of 17 or above.

• A player wins by beating or equaling the dealers value.

Basic StrategyIf sum of cards add up to:

• 16 or less you hit • 17 or more you stay

• Most dealers play by this basic rule, but it will be posted on their table.

Hit Stay

Card Counting• Card Counting keeps track of the cards that have been dealt by assigning

a numerical value to specific cards.

• These values are added to find a rolling count which allows the player to predict if a high or low card will be dealt next.

• The total count is found by dividing the rolling count by the number of decks played.

• The method of card counting is not illegal because it does not use any electronic devices or other aids to keep the count. It is all in the player’s own head, but it is still frowned upon in casinos because card counters can have an advantage over the house.

Card CountingCard Face Value Value

2-6 +17,8,9 0 (neutral)

10, J, Q, K, A -1

• As the cards are dealt the player has a rolling count of the card values. After every card the player will add +1, 0, or -1 to the rolling count.

Ex. If the following cards: 6, 2, 7, A, 8, 4, 10 The rolling count is: +1

• The higher the count the higher the chance of a high card (10, J, Q, K, A)• The lower the count the higher the chance of a low card (2, 3, 4, 5, 6)

Random Facts• In one deck of cards there are 550 possible combinations of hands

a player can receive in the initial deal

• Card counting has inspired many books and movies

• Players position at the table is referred to as bases• First player to the dealers left is sitting at first base and so on

• Napoleon loved twenty-one

• Blackjack was banded in the U.S. at the turn of the 19th century until Nevada legalized gambling in 1939.

• The idea of blackjack team play was invented by Al Franesco

MIT Team• Initially formed after a mini-course in January 1979 called "How to

Gamble if You Must“

• Used technique developed by Al Francesco

• At one time, had almost 30 members that could play the various positions in team play (spotters, gorillas, and big players, who would all bet according to a system to stay under the radar)

• Their story is told in the book “Bringing Down the House” and the recent movie “21.”

Our Experiment• Our experiment imitated a game of blackjack using basic strategy. We

then put the cards in the same order and played using card counting strategies, using six decks of cards, which is the most common number of decks used in casinos.

• We set up an excel document and recorded the exact card dealt and the players hand totals (including the winner).

• For the card counting strategies we recorded the rolling count (RC) and total count (TC)(rolling count divided by the number of decks used) to base our decisions in hitting or staying.

• The additional rules we implemented for our card counting strategy were as follows: • If TC is +/- 1 or less, use basic strategy• If TC is +/- 2 or greater, use counting strategy• If TC is +/- 3 or greater and your total hand = 17 or 18, use count • If total hand is 19 or greater, stay

Our Results• Using basic strategy Player 1 won 51% of the time. Player 2 won 59%

of the time.

• Using card counting strategies Players 1 and 2 both won 65% of the time.

• The range of the rolling count on the table was from -8 to 11• When the rolling count is highly negative (-8), the player should

expect low value cards, while when the rolling count is highly positive (11), the player should expect high value cards.

• The range of the total count on the table in the card counting game was from -1.33 to 1.83• The total count tells the player the same thing as the rolling count,

but it is now in relation to how many decks are currently in use.

• Below is a chart of the complete results of our experimentMicrosoft Office

Excel 97-2003 Worksheet

ConclusionWe found that card counting does improve your chances of beating the house. There was a 14% increase in the number of wins. However, we found that the longer you play the more accurate the count will be. We also found that when we played with only two decks of cards no significant results were found between playing with basic strategy and card counting. The card counting only has a significant effect in the long run, not immediately. You cannot quickly learn simple card counting strategies and expect to receive a big pay out over a few hands in Vegas. Card counting is all based on probability and it is not guaranteed you will receive the predicted card. The method is far from perfect though there are those that have used it to win big.

Your Test

Keep the CountThe rolling count on the table is 0.

The rolling count on the table is now -3.

Keep counting…Just kidding! (But the answer is -2)

Referenceshttp://web.ebscohost.com/ehost/detail?vid=1&hid=16&sid=8b67e188-1dd4-4597-8b62-969c830702ce%40sessionmgr9&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#db=a9h&AN=36903986

http://www.jstor.org/stable/2281431?seq=6&Search=yes&term=Blackjack&term=Optimum&term=Strategy&list=hide&searchUri=%2Faction%2FdoBasicSearch%3FQuery%3DOptimum%2BStrategy%2Bof%2BBlackjack%26wc%3Don%26dc%3DAll%2BDisciplines&item=1&ttl=45&returnArticleService=showArticle&resultsServiceName=doBasicResultsFromArticle

http://www.blackjackman.com/history.html

http://www.jacobsongaming.com/The_Blackjack_Zone.pdf

http://www.gypsyware.com/blackjackLegends.html

http://lightoxygen.blogspot.com/2009/03/top-10-interesting-blackjack-facts.html

http://en.wikipedia.org/wiki/MIT_Blackjack_Team