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Chances of Winning Blackjack

Blackjack is unlike many other casino games because the player is activly involved in the outcome of his hands (rather than betting on a random event over which he has no influcene). As a result, a player's chances of winning depend on not only the random outcome of the draw, but also upon the decisions he makes during the game—to hit or to stand, to exercise options such as doubling or splitting.

Over the course of several rounds, the chances of winning each hand will also be skewed by the cards that have been removed from the deck. The player's net loss or gain (the amount in money, rather than a tally of hands won or lost) over a session will be affected by how much he wagers, and at which times he elects to increase or decrease the wagered amount. Finally, house rules can be imposed to change the parameters of the game and restrict the player's options.

With all of these factors in effect, it's not possible to affix a specific number to all situations or all styles of play—but there are three figures that are often cited:

• Most casinos expect each blackjack table to have a hold of about 20%—that is, they expect to be able to keep about 20% of the wagers made. Correspondingly, the average player can expect to lose about 20% of his stake over the course of every session.
• The "core odds" reduce the house's advantage to 10.99%. Based on the assumption the player will elect to hit or stand by the same criteria as the house, the house will win roughly 10.99% more hands than the player.
• The net odds—which consider the amount of money won or lost rather than the core number of hands, generally work out to an 8.89% advantage to the house (given a two-deck game played by the most common set of rules).

An interesting, if somewhat premature, note on these figures is that the house expects to earn more than double (20% as compared to 8.89%) what the odds would seem to indicate it will—and that these expectations generally hold true. This demonstrates how the player's decisions can affect the outcome of the game—and that the average player will lose more than double the mathematically probably amount because of uninformed decisions.

The basic, intermediate, and advanced strategies described in the strategy section of this site can further impact the odds. By using basic strategy consistently, the player can decrease the house's advantage to less than 1%. By adding the intermediate and advanced strategies, a player can make the game completely even (hence fair) and, in rare situations, even turn the odds in his favor by a fraction of a percentage.

What are Odds?

In its simplest sense, odds are the chances a given outcome will occur given the possible alternatives. The easiest metaphor is a coin toss: if a coin is tossed in a truly random fashion (nothing influences the outcome), it is just as likely to come up heads as tails. If it is tossed 10 times, you can expect it to come up heads 5 times, and tails 5 times.

Granted, it is possible, even with true randomness, that the toss will result in heads ten times in a row—which is why odds consider likely rather than certain outcomes. In the long run, mathematical probability will bear itself out in practice—if a coin is tossed 1,000 times, it is likely to come up heads 500 times (though, in practice, it will be plus or minus a few). Thus, it's not necessary to spend several years flipping a coin millions of times to determine the likely outcomes, or rig a supercomputer to simulate the same—though some stubbornly have.

Casino games are carefully designed to exploit the odds, always taking an advantage for the house: a player will never be paid a wager that is strictly equal to the true odds. A good example of this practicee is roulette, in which a wager on a single number pays 35 to 1 even though the odds of winning are 1 in 37.

Blackjack, however, foils the computation of odds based on random events because there are a number of influences that prevent it from being completely random—most significantly the player's choices during the course of the game. In such cases, the odds are set to turn a reasonable profit from the average player. (Actually, they're set to turn a reasonable profit from the reasonable intelligent player, an exorbitant one from the average player, and flat-out milk a "sucker.") This is why an attentive player who makes the right decisions can come out ahead.

The odds of the hand's outcome are determined not only by the initial hand dealt and by the number of hits that are added. This can vary greatly, because a player can take as many or as few as he desires—a player may opt to hit every hand he is dealt until it exceeds 21 and lose 100% of the time.

We can, however, be reasonably certain of the dealer's behavior, as he is forced to play by certain rules, regardless of his instincts, superstitions, or desires. Most often, the rules require the dealer to stop taking hits when his hand reaches a total of seventeen or greater, and no sooner. Before the cards are dealt, it's possible to predict the chances that the dealer's hand will have the following outcomes:

These odds are computed according to mathematical probabilities. More detailed information is available (here) on the method for calculating these odds.

The outcome of the player's hand, meanwhile, will depend on the way his hands are played. If he chooses exactly the same course as the dealer, the outcome of his hands will be exactly the same as is shown above. If he plays according to a different set of rules, the results will be different, and by comparing the two tables, that player's individual likelihood of winning can be computed. If however, the player is erratic, and he chooses to play his hands differently each time with no predictable rationale, no mathematical model can be used to compute his chances of winning.

Determining the core odds

The "core odds" of the game assume that the player will follow the house rules for hitting his hands. In this example, to stop taking hits when his hand reaches a total of seventeen or greater, and no sooner. In this case, all things seem to be equal, and the player should have a 50% chance of winning or losing each hand. This would be true only if the player's wager was returned the dealer busts his hand—but one rule of the game that is never varied is that a player who busts loses his wager, even if the dealer busts afterward.

With this in mind, all the totals for hands remain equal—so a player's 20 will beat a dealer's 19 equally as often as a dealer's 20 beats a player's 19, and the dealer will bust as often as the player while the other stands on a viable hand. The only remaining difference is that the dealer will bust of the instances in which the player busts—which is 33.15% likely to happen in 33.15% of the time, for a core odds value of 10.99% of all hands played.

Again, the core odds shown here apply only to a player who strictly adheres to the same rules as the dealer in playing his hands, which is clearly not the best approach. The strategy section of this site will demonstrate a system that can virtually eliminate the house's advantage over the player—and the intermediate and advanced sections will turn the tables further in the player's advantage.

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