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• Odds Of Winning Blackjack At Casino

In this article we discuss several aspects of the odds and probabilities in Blackjack. As a casino game, Blackjack is designed to transfer the money from your pocket into the house's vault, unless some method of advantage play is used. This is where this guide comes in.

We begin this Blackjack guide with a very important assertion – casino games, hence the name, are designed with a built-in house advantage – a casino's edge in odds over a player at any given bet.

Thus, by stepping into a casino, you know that the odds by default are stacked against you to a certain degree. This means that in the long term you will always lose money, unless you skew the odds to even or in your favor.

Casinos believe that as soon as you enter their premises, it is just a matter of time before all your money becomes theirs. And since they want to keep you around for as long as possible, they will attract you with the so-called comps – complimentary items and services given out by the house to encourage players to gamble.

Casinos will do everything they can to make you feel cozy, valued and inclined to prolong your stay at the tables. These “freebies” they give out depend on the game a person plays, for how long, and of course on the size of his bets. Casinos have staff whose job is to manage the comps and contact players to persuade them to visit and play.

As a casino game, Blackjack also falls under this principle and is designed to transfer the money from your pocket into the house's vault, unless some method of advantage play is used. This is where this guide comes in.

We will present ideas which will can help you shift odds to near-even, and in some cases even slightly in your favor. This will be done in the first section of the guide where we will discuss strategies relating to the basic strategy player.

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Later on we will move to the so-called advantage player, where card counting takes place. Whereas the basic strategy player is on relatively even ground with the house, albeit still behind, the advantage players, hence the name, have an advantage over the casino as soon as the game begins.

Regardless of which type of player you want to become, both require the aforementioned “method of advantage play” – strategies, card counting etc., which help skew the odds out of the casino's favor.

Blackjack is one of the most widely played casino games for several reasons – it has simple rules, it is offered by almost every casino and most importantly – offers the best overall odds for the player, even for the non-advtantage one. It is simply a game that falls under the principles of odds and probabilities and can be beaten through lots of experience, knowledge and skill.

Odds and probabilities

Now, one would wonder how come if the stacks are always stacked against the non-advantage players, who make up most of the player mass, there are still many people going to the casinos. After all, if all these people were constantly losing, they would ultimately become discouraged and the majority will stop playing.

Gamblers hope that on any particular night they might be lucky and the odds fall in their favor. For example, although tossing a coin has a 50% chance to turn heads or tails, when you toss it only 20 times, it might land 14 times on heads and 6 on tails. The even probability of tossing tails or heads is true only when you repeat the exercise enough times to ensure a large enough sample pool.

And because many people get lucky at any given moment, they will earn money, fueling their excitement and luring them back in the casino the next night. And although this causes the house to lose money, the casino relies on the fact that players place millions of bets, which irons out the outcome in the long-term and makes the house profitable. In mathematics, this is known as the law of large numbers.

This rule dictates that the more bets are placed, the closer the casino's odds will come to the artificially created built-in house advantage, thus the more hands (bets) a non-advantage gambler plays (places), the smaller his chances to win become.

Thus, players who do not employ advantage methods will be losing money if they continue to play in the long-term, which allows casinos to continue to operate, while basic strategy and advantage players profit from their efforts.

Calculating the house's advantage in blackjack is difficult due to the huge amount of card combinations and also because not all winning bets have the same payout (for example, a blackjack which is a 21-hand with an ace and a 10-valued card, pays 3:2 in most casinos).

The extent and source of the house's advantage varies in different casinos. In blackjack, for example, it is derived from the fact that when the player busts himself by exceeding the count of 21, the house wins the bet, regardless of whether the dealer would also bust when drawing more cards to complete the hand for other players on the table.

Improving or reducing the house's advantage

The house edge depends on the rules the casino has established for the blackjack table and they are posted and easily visible either on, or near the table.

For example, a casino where dealers stand on a soft 17 (S17), instead of hitting it (H17), favors the players' odds, reducing the house's edge by around 0.2%. Increasing the number of decks also increases the house's edge, and vice versa.

The implementation of other rules such as the allowance or disallowance of resplitting, doubling down after split, double on 9/10/11 or only on 10/11 and so on. Casinos typically aim to boost their advantage but also not to discourage players from joining the game and, thus, seek some form of balance. For example, if they offer one-deck blackjack, they typically forbid doubling on soft hands or after splitting, restrict resplitting and so on.

The table above illustrates the house's edge relative to the different number of decks, considering the following set of rules:

– dealer hits soft 17
– double split is allowed
– resplit to four hands is allowed
– no surrender
– no hitting split aces
– double on any two cards
– original bets only lost on dealer blackjack
– cut-card used

As evident, the house's edge experiences the most dramatic jump when raising the number of decks from one to two and grows progressively slowerr as more decks are added.

Hand-held and shoe games, house edge

Single-deck games belong to the so-called hand-held games. Double-deck games could also be hand-held. Although they are still being offered by some casinos, their peak of popularity has passed. Nowadays, casinos more often host shoe games.

In a shoe game, a card shoe (rectangular box) holds multiple decks of cards. The dealer pulls cards out of the shoe and slides them to the appropriate areas in front of the players. Cards are most often dealt face up, which prohibits the player from touching them. Even if the gambler splits their hand, they don't touch the cards and instead just place their additional bet and the dealer does the splitting.

Only in games where cards are dealt facing down can the player hold his cards, but only in one hand.

Almost always you will see shoe games consist of multiple decks, four and more, and on rare occurrences two. Thus, shoe games will logically favor the house's odds.

You may also encounter tables using the so-called Continuous-Shuffling Machines. These devices hold three or more decks and after a couple of rounds the dealer returns the used cards to the machine and shuffles them with the unused cards. Thus, each shuffle refreshes the shoe, making it impossible to count cards, which is why card counters avoid these games.

As for basic strategy players, CSMs don't have such an impact, but they increase the number of hands played per hour, meaning the player will incur larger money losses (why we will explain later).

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Introduction

The following table shows the house edge of most casino games. For games partially of skill perfect play is assumed. See below the table for a definition of the house edge.

Casino Game House Edge

Odds Of Winning Blackjack At Casino

Notes

House Edge

The house edge is defined as the ratio of the average loss to the initial bet. The house edge is not the ratio of money lost to total money wagered. In some games the beginning wager is not necessarily the ending wager. For example in blackjack, let it ride, and Caribbean stud poker, the player may increase their bet when the odds favor doing so. In these cases the additional money wagered is not figured into the denominator for the purpose of determining the house edge, thus increasing the measure of risk.

The reason that the house edge is relative to the original wager, not the average wager, is that it makes it easier for the player to estimate how much they will lose. For example if a player knows the house edge in blackjack is 0.6% he can assume that for every $10 wager original wager he makes he will lose 6 cents on the average. Most players are not going to know how much their average wager will be in games like blackjack relative to the original wager, thus any statistic based on the average wager would be difficult to apply to real life questions.

The conventional definition can be helpful for players determine how much it will cost them to play, given the information they already know. However the statistic is very biased as a measure of risk. In Caribbean stud poker, for example, the house edge is 5.22%, which is close to that of double zero roulette at 5.26%. However the ratio of average money lost to average money wagered in Caribbean stud is only 2.56%. The player only looking at the house edge may be indifferent between roulette and Caribbean stud poker, based only the house edge. If one wants to compare one game against another I believe it is better to look at the ratio of money lost to money wagered, which would show Caribbean stud poker to be a much better gamble than roulette.

Many other sources do not count ties in the house edge calculation, especially for the Don’t Pass bet in craps and the banker and player bets in baccarat. The rationale is that if a bet isn’t resolved then it should be ignored. I personally opt to include ties although I respect the other definition.

Element of Risk

For purposes of comparing one game to another I would like to propose a different measurement of risk, which I call the 'element of risk.' This measurement is defined as the average loss divided by total money bet. For bets in which the initial bet is always the final bet there would be no difference between this statistic and the house edge. Bets in which there is a difference are listed below.

Element of Risk

Standard Deviation

The standard deviation is a measure of how volatile your bankroll will be playing a given game. This statistic is commonly used to calculate the probability that the end result of a session of a defined number of bets will be within certain bounds.

The standard deviation of the final result over n bets is the product of the standard deviation for one bet (see table) and the square root of the number of initial bets made in the session. This assumes that all bets made are of equal size. The probability that the session outcome will be within one standard deviation is 68.26%. The probability that the session outcome will be within two standard deviations is 95.46%. The probability that the session outcome will be within three standard deviations is 99.74%. The following table shows the probability that a session outcome will come within various numbers of standard deviations.

I realize that this explanation may not make much sense to someone who is not well versed in the basics of statistics. If this is the case I would recommend enriching yourself with a good introductory statistics book.

Standard Deviation

Hold

Although I do not mention hold percentages on my site the term is worth defining because it comes up a lot. The hold percentage is the ratio of chips the casino keeps to the total chips sold. This is generally measured over an entire shift. For example if blackjack table x takes in $1000 in the drop box and of the $1000 in chips sold the table keeps $300 of them (players walked away with the other $700) then the game's hold is 30%. If every player loses their entire purchase of chips then the hold will be 100%. It is possible for the hold to exceed 100% if players carry to the table chips purchased at another table. A mathematician alone can not determine the hold because it depends on how long the player will sit at the table and the same money circulates back and forth. There is a lot of confusion between the house edge and hold, especially among casino personnel.

Hands per Hour, House Edge for Comp Purposes

The following table shows the average hands per hour and the house edge for comp purposes various games. The house edge figures are higher than those above, because the above figures assume optimal strategy, and those below reflect player errors and average type of bet made. This table was given to me anonymously by an executive with a major Strip casino and is used for rating players.

Hands per Hour and Average House Edge

Translation

A Spanish translation of this page is available at www.eldropbox.com.