Abstract
Blackjack is the only game offered by casinos, where it is proven that players can beat
the dealer on the long term. Many books and articles have been published about this theme,
however most of them are written to make You lose money. The only way of having a moderate
advantage over the dealer is to count cards remaining in the shoe, placing variable bets
and deciding when to stay or buy, double or split. An analysis on how this works is
described in this document. It is assumed that the reader of this document is familiar with
the rules of Blackjack and that she has a basic understanding in probability calculation and
terminology. A program to calculate the best strategy can be downloaded from this site,
so that everybody can verify results and test it against their preferred counting method.
Why do casinos still offer Blackjack if players can beat the dealer?
Because most people don't know how it works. So they still continue to lose their money. Casinos know that, and those few who really are capable to exploit the rules are of no consequence. In order to have a moderate advantage over the Blackjack dealer, You must keep track of the cards which have gone. Or the other way, You must know which cards are still in the shoe. This means that You have to count cards. If You find articles about winning Blackjack methods without card counting, forget them! It often seems as if authors of such articles and books do not even understand the sources they are copying.In order to win, gamblers must not only know when to buy or stay, double or split, they also must know when to place minimum stakes and when to bet high. Without this knowledge there is no way to win on the long term.
There is absolutely no way to win on the long term playing Blackjack without counting cards.
Probability and expectation
Let me explain what is meant by "On the long term". As an easier understandable example lets choose Roulette. There are 37 pockets in European casinos (38 in the US), of which 18 are red, 18 are black and one (two) are green. The probability that the ball rolls at the seeded number is 1/37=2.7% (1/38=2.6%). The probability that the ball rolls at the seeded color is 18/37=48.6% (18/38=47.3%).On the long term this means that after N games a seeded number should be hitten k times, where k=N/37±x (k=N/38±x). If this experiment is repeated very often, the relative deviation x/N from the theoretical probability will decrease with the number of games, whereas the absolute deviation x can increase.
An other very important term is expectation: This is the percentual gain or loss. The expectation can be calculated for a single decision or for an entire strategy. It is the (probability for winning * gain) - (probability of loss * stake). Expectations are the far more interesting numbers in this article.
Experienced gamblers
The terms probability and expectation are quite theoretical because an average gambler will never play that many games in order to get significant statistics over his decisions. This also means that there are no experienced gamblers, or to say it in other words: through gambling You can not aquire the knowledge how to find the right decision. All self-assessed experienced gamblers lost and will lose their money. In order to get statistical significant results, millions and millions of games would have to be played. This is only possible through computer simulation. A gambler playing Roulette can't do many wrong decisions but he also can't do many right ones either (except quitting to gamble of course). On the other side a gambler playing Blackjack has many more possibilities, giving him plenty of opportunity to do the wrong decisions. And the majority of Blackjack gamblers do make the wrong decisions, and thus feed their dealers because they do not know what the right decisions are.Many articles have been written about playing Blackjack in order to beat the dealer. Most notably is the book from Edward O. Thorp: Beat the Dealer, (1962). Innumerable others followed. The serious ones present one or more counting methods to find out the best strategy when betting high, stay or buy, double or split. This article presents no existing or new counting method but a program to calculate the best strategy upon the momentary card distribution in the shoe. This program is very small (less than 60kB of source) and has no graphical user interface. Thus it is easily adoptable on hand-held computers and embedded systems. As casinos do not allow any kind of computers, a graphical user interface would be of no usage anyway.