First, a brief history of cards: Playing cards are believed to have been invented in China and/or India sometime around 900 A.D. The Chinese are thought to have originated card games when they began shuffling paper money (another Chinese invention) into various combinations. In China today, the general term for playing cards means "paper tickets". The contemporary 52 card deck used in the U.S. was originally referred to as the "French Pack" (circa 1600's) which was later adopted by the English and subsequently the Americans.
The first accounts of gambling were in 2300 B.C. or so, and yes, the Chinese again get the credit. Gambling was very popular in Ancient Greece even though it was illegal and has been a part of the human experience ever since.
The history of the BlackJack card game itself is still disputed but was probably spawned from other French games such as "chemin de fer" and "French Ferme". BlackJack originated in French casinos around 1700 where it was called "vingt-et-un" ("twenty-and-one") and has been played in the U.S. since the 1800's. BlackJack is named as such because if a player got a Jack of Spades and an Ace of Spades as the first two cards (Spade being the color black of course), the player was additionally remunerated.
Gambling was legal out West from the 1850's to 1910, at which time Nevada made it a felony to operate a gambling game. In 1931, Nevada re-legalized casino gambling where BlackJack became one of the primary games of chance offered to gamblers. As some of you may recall, 1978 was the year casino gambling was legalized in Atlantic City, New Jersey. As of 1989, only two states had legalized casino gambling. Since then, about 20 states have had a number of small time casinos sprout up in places such as Black Hawk and Cripple Creek, Colorado and in river boats on the Mississippi. Roughly 70 Native American Indian reservations operate or are building casinos as well.
In addition to the United States, countries operating casinos include France, England, Monaco (Monte Carlo of course) and quite a few in the Caribbean islands.
The first recognized effort to apply mathematics to BlackJack began in 1953 and culminated in 1956 with a published paper. Roger Baldwin wrote a paper in the Journal of the American Statistical Association titled "The Optimum Strategy in BlackJack". These pioneers used calculators and probability and statistics theory to substantially reduce the house advantage. Although the title of their paper was 'optimum strategy', it wasn't really the best strategy because they really needed a computer to refine their system. I dug up a copy of their paper from the library, it is ten pages long and fairly mathematical.
Professor Edward O. Thorp picked up where Baldwin and company left off. In 1962, Thorp refined their basic strategy and developed the first card counting techniques. He published his results in "Beat the Dealer", a book that became so popular that for a week in 1963 it was on the New York Times best seller list. The book also scared the hell out of the casinos.
Thorp wrote "Beat the Market" in 1967, in which he used mathematics and computer algorithms to find pricing inefficiencies between stocks and related securities. Currently he is using an arbitrage formula to exploit undervalued warrants in the Japanese stock market.
The casinos were so affected by "Beat the Dealer" that they began to change the rules of the game to make if more difficult for the players to win. This didn't last long as people protested by not playing the new pseudo-BlackJack. The unfavorable rules resulted in a loss of income for the casinos. Of course, not making money is a sin for a casino, so they quickly reverted back to the original rules. As Thorp's "Ten-Count" method wasn't easy to master and many people didn't really understand it anyway, the casinos made a bundle from the game's newly gained popularity thanks to Thorp's book and all the media attention it generated. Beat the Dealer is rather difficult to find these days, although I managed to pick up a copy at the library recently.
Another major contributor in the history of winning BlackJack play is Julian Braun, who worked at IBM. His thousands of lines of computer code and hours of BlackJack simulation on IBM mainframes resulted in The Basic Strategy, and a number of card counting techniques. His conclusions were used in a 2nd edition of Beat the Dealer, and later in Lawrence Revere's 1977 book "Playing BlackJack as a Business".
Lastly, let me mention Ken Uston, who used five computers that were built into the shoes of members of his playing team in 1977. They won over a hundred thousand dollars in a very short time but one of the computers was confiscated and sent to the FBI. The feds decided that the computer used public information on BlackJack playing and was not a cheating device. You may have seen this story in a movie made about his BlackJack exploits detailed in his book "The Big Player". Ken was also featured on a 1981 Sixty Minutes show and helped lead a successful legal challenge to prevent Atlantic City casinos from barring card counters.