Background on Blackjack

So, maybe you read the article on the MIT blackjack teams in Wired magazine, or saw one of the television specials concerning them. A (very rough) version of their story was recently brought to the big screen by the movie 21. A even more recent, albeit smaller film, concerning Blackjack card counting is Holy Rollers. Or, maybe you already gamble on Blackjack in casinos, it being one of if not the most popular games offered there. For whatever reason you would like to know a little more about card counting in Blackjack. I did, and so produced the Blackjack Blastoff program as a result.

The program is meant to provide a full featured introduction to Blackjack card counting. It allows for multiple players, either human or computer, playing different card counting strategies possibly under different rules and conditions. Simulations allow you determine what the expectations are in the long run for the strategies under given conditions.

In this document I intend to provide background information on card counting independent of the program. If you are unfamiliar with some of these ideas this should provide information to make the program more useful to you. It is currently my intention to produce a separate document that will serve more as a user guide to the program itself.

Blackjack advantage play with card counting

A brief history

The original revelation that Blackjack could be played with only a minimal house edge came from a 1953, pre-computer, three year study by four Army mathematicians. They produced the “Optimum Strategy in Blackjack” in a . This amounted to what is now commonly known as Basic Strategy, more on this will follow shortly.

Their article was read by Edward O. Thorp who turned it into what is essentially card counting as we now know it. Thorp brought computers into the game using a IBM 704 to refine the results of the Army team and renamed the result to Basic Strategy. His book “Beat The Dealer” was a New York Times best seller and launched card counting. Casinos began counter measures against card counting in response to Thorp's efforts including using multiple decks which reduces it's effectiveness.

The next New York Times best seller on the topic concerned the MIT blackjack team, “Bringing Down The House”, by Ben Mezrich. From that followed the Wired article already mentioned. “Breaking Vegas” on the History Channel also concerned the MIT teams. The movie “21” is the most recent media event on this topic. Originating professional blackjack team play itself is usually credited to Ken Uston, who began on Al Francesco's team.

The whole idea of card counting is that a higher number than normal of certain cards remaining in the deck, or shoe, creates a situation that is favorable or unfavorable to the player. Thorp's book was the first to publish strategies based on this idea that could be capitalized on to gain an advantage over the casino. The popularity of Blackjack increased considerably with the word out that it could be beat.

Harvey Dubner introduced the first actual point count system, the high-low system. This is what the MIT teams used. It is the most written about system and probably still the most popular. Other systems have been introduced to be more advanced or more simple.

Details on that will follow as we now begin considering card counting in more detail.

The Basic Strategy

Suppose that you are sitting opposite the dealer with a king in the hole and a deuce showing, the dealer also has a deuce upcard. What do you do? Well, either what Basic Strategy tells you to do, or what the count for your strategy tells you to do if you should deviate from Basic Strategy. A usual way to learn these situations is by charts. There are many sources available for Basic Strategy charts. For this section I will use information from the Wizard of Odds who I believe to be a reputable source. The Wizard of Odds Basic Strategy Chart. This tells you that holding a hard twelve against a dealer two that you should hit. For every possible combination of player's hand and dealer's upcard the Basic Strategy will have a recommendation. Counting aside, in the “long run” by not using this choice it will cost you money, it is always the best choice. Again with counting aside, by doing this in the long run the casino will usually have only about a .5% edge although this can vary by the rules in play.

Now, you might think that's fine, I can learn this by rote, but why are these the best choices? These are the best choices because they give you the maximum expected value for the given situation. Let's say the expected value is how much you would get in return, in the long run, for a dollar bet. Then for the example situation of a player 2-10 hand vs. dealer upcard of 2, the expected value for hitting would be -0.2534. So you would expect in the long run to loose a little better than a quarter for every dollar bet in this situation, not very good. So why didn't it say you should hit? The expected value then would be -0.2928, or almost losing 30 cents for every dollar bet. It's not a good situation to begin with and this is not so big a difference but it is not as good. For every $100 dollars bet you would expect to loose $4 dollars more by standing, for every $1000 you would expect to loose $40 more. Remember these things are determined over the “long run”. Going from bad to worst would be doubling down where the expected value would be -0.5068, losing more than 50 cents on the dollar. The Wizard of Odds is again a good source for all of these expected values with Blackjack: Expected return for every play.

OK, you might now say. That shows that hitting is better than standing because it saves you more money. But, why does it save you more money? That would be because for this situation it makes more sense to try and improve your hand rather than leave it as is and hope that the dealer busts. So, Basic Strategy comes down to...

• Trying to improve your hand when the dealer is likely to have you beat and is not likely to bust.

• Stand when you are likely to have the dealer beat.

• Stand when the dealer is fairly likely to bust. These situations would be when the dealer's upcard is a 'stiff' type, 2 to 6 card, which he will probably have to hit and is quite possibly close enough to 21 to bust when he does hit.

• Double down when there is a good chance you will end up with a good hand. Or possibly you will end up with a mediocre hand but by the dealer's upcard there is again a good chance he will bust.

• Split by the same reasoning. You are likely to get two good hands, or two hands against a dealer hand that is fairly likely to bust.

This should give you an idea of why Basic Strategy matters. Without counting cards it is the best you can do in the long run, period. It should also have given you some idea of what makes Basic Strategy tick. How can you improve on Basic Strategy? By card counting, which we will now begin considering.

Card Counting

Again, Thorp's “Beat the Dealer” considered what is now sometimes called EOR, or 'effect of removal'. Removing some cards from the deck favors the player, while removing others favors the dealer. Extending on this leads to point count systems. Assign points to the cards and add or subtract their value as the cards are dealt and you have an idea if the current deck is favorable.

The High-Low point count system

The first point count system to take advantage of this and still quite probably the most popular is the high-low system. In this counting system the 2-6 cards are all valued as +1 point, the 7-8-9 have no effect on count, the 10 cards are counted as -1.

The high-low counting system is a balanced one. That means that if you count all the way through a deck of cards you will end up back at zero. For high-low and balanced systems generally you have to convert the running count to a 'true count'. Changes to basic strategy and to betting are based off of the 'true count'.