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Counting cards simulator // Blackjack

Counting cards simulator

Simulating Blackjack with MATLAB
December 24, 2016 – 10:10 am
Blackjack Card Counting on the

Figure 1. Start of an atypical but important example: You are dealt a pair of 8s, and the dealer’s up card is a 4.Blackjack is the most popular casino game in the world. Using a basic strategy, a knowledgeable player can reduce the casino's advantage to less than one-half of one percent. Simulating blackjack play with this strategy in MATLAB® is both an instructive programming exercise and a useful parallel computing benchmark.

Blackjack is also known as "21." The object is to get a hand with a value close to, but not more than, 21. Face cards are worth 10 points, aces are worth either 1 or 11, and all other cards are worth their numerical value. You play against the dealer. You each start with two cards.Figure 2. The final outcome. Your cards are dealt face up; one of the dealer's cards stays face down.

You signal "hit" to receive additional cards. When you are satisfied with your hand, you "stand." The dealer then reveals the hidden card and finishes the hand. If your total ever exceeds 21, you are "bust, " and the dealer wins the hand without drawing any more cards.

The dealer has no choices to make, and must draw on hands worth less than 17 and stand on hands worth 17 or more. (A variant has the dealer draw to a "soft" 17, which is a hand with an ace counting 11.) If neither player goes bust, then the hand closest to 21 wins. Equal totals are a "push, " and neither wins.

The fact that you can bust before the dealer takes any cards is a disadvantage that would be overwhelming were it not for three additional features of the game. On your first two cards:

  • An ace and a face card or a 10 is a "blackjack, " which pays 1.5 times the bet if the dealer does not also have 21
  • You can "split" a pair into two separate hands by doubling the bet
  • You can "double down" a good hand by doubling the bet and receiving just one more card

Figure 4. Histograms for each player.Basic Strategy

Basic strategy was first described in the 1956 paper "The Optimum Strategy in Blackjack, " published in the Journal of the American Statistical Association by four authors from the Aberdeen Proving Ground. It is now presented, with a few variations, on dozens of web pages, including Wikipedia. The strategy assumes that you do not retain information from earlier hands. Your play depends only on your current hand and the dealer's up card. With basic strategy, the house advantage is only about one half of one percent of the original bet.

Figure 3. Four players in a parallel simulation. Figure 5. The Standard and Poor’s stockmarket index over one year versus 100 hands of blackjack per day for the same time.
Source: www.mathworks.com
Interesting facts

Mike Aponte also known as MIT Mike is a professional blackjack player and a former member of the MIT Blackjack Team. Aponte was one of the leaders of a team of MIT students that legally won millions at blackjack tables around the world by counting cards. He is one of the main characters, "Jason Fisher," in the best selling book, Bringing Down...

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