BlackJack for Women

Blackjacks Independent Trials vs. Dependent Trials

To facilitate your understanding of an independent trial versus a dependent trial, the following example will be used:

Let us imagine twenty marbles (ten white and ten red) concealed from view in a container. If we extract a white marble from the container, make note of this result, and replace the white marble back into the container, we could not make an educated guess as to what the color of the next marble would be if we were to repeat the same procedure. As long as the marble is put back into the container, the ratio of white marbles to red marbles will not be changed. Thus, the odds of retrieving a red marble are the same as for a white marble.

The same holds true for the games of roulette, craps, keno and slots. Whatever has occurred previously has no bearing on what will occur next. This means, provided there are no mechanical imperfections that if one had thrown ten sevens in a row at the craps table, the probability of a seven occurring again would be exactly the same, or one out of six trials. Conversely, had one not thrown a seven in one hundred trials, the odds would still be exactly the same that one would come up (one out of six trials). This phenomenon is referred to as "independent trials process." It is important to understand and even more important to believe this, or you will always have difficulty second-guessing your intuition in a casino.

Let's go back to our marbles in the container. If we extract a white marble from our container but this time keep the marble outside the container, we will have an advantage in prediction. We now know that there is a better chance of a red marble being extracted on the second attempt because there are nine white marbles left in the container along with the original ten red marbles. This principle of dependent trials, illustrated by this example, is the conceptual foundation for card counting.

It should now be readily apparent that the game of Blackjack can be beaten because it is a game of dependent trials rather than a game of independent trials like keno, craps, roulette, etc. Stated in another way, when as little as a single card has been played from a total deck, the probabilities have been altered until all the cards have been replaced in the deck. For example, when all the aces have been played, it is impossible to get a natural, until the deck is reshuffled. Or, if all the 10's have been played from the deck, one could hit a hand totaling twelve with the certainty that it would not bust.

The knowledge presented herein will allow you to have the necessary understanding to: first, bet a larger sum of money when the player's probabilities of winning are greater, and, second, play your hand in accordance with the best probability of winning. You will, therefore, bet more money when your chances of winning are greater, thereby winning a larger percentage of your big bets and a smaller percentage of your small bets, but your overall winnings will increase. Further, you will know how to make the right decisions on how to play your hand.