Casino Blackjack House Advantage

4/13/20224/13/2022

The house edge in blackjack is low relative to other games, with it being as low as 1% when a basic blackjack strategy is implemented. In blackjack, the house edge comes from the dealer having a hidden card about which the player has to make assumptions. In addition, if the player busts, the dealer wins, even if they then bust in the same round. Casinos have a mathematical advantage, otherwise referred to as the house edge. The reason is that players make a bet depending on the dealer’s first card. For example, players hit a card and bust about 28% of the time. And, even though the dealer goes bust as well, we will lose in this scenario. The casinos don't beat the players because they get lucky, they beat the players because the odds are stacked in their favor. This built-in advantage is called the house edge. In numbers, it's the the percentage of the player's bet that the casino keeps as profit, over the long term. For example, in roulette house.

Blackjack Casino House Edge
Casino Blackjack 21
Casino Blackjack House Advantage Reviews
Casino Blackjack Online

Playing and mastering blackjack are two entirely different things. Mastery of blackjack starts with understanding the house edge and recognizing how it can impact your game. Understanding the house edge is vital for becoming a player that is capable of taking on the house. Without further ado, let’s delve into how to reduce the house edge!

This guide will also show you the ins and outs of the house advantage, blackjack odds and blackjack strategy. You’ll be ready to sit at the table and take on the dealer after you’ve read this!

What is the House Advantage?

The house edge is the mathematical advantage that a casino has over its players. This edge varies from game to game, and is normally represented as a percentage and denotes the amount of return that the house can expect to receive over time. It also represents the percentage of losses that the player will likely incur.

Let’s say that the house has an edge of 5% in a particular game. If a player bets €100, then the house will likely earn €5, while the player will likely lose €5. This does not mean that the player can’t win more or turn a profit – it merely means that the house will take some money at the end.

What Percentage is the House Edge in Blackjack?

The house edge in blackjack is low relative to other games, with it being as low as 1% when a basic blackjack strategy is implemented.

In blackjack, the house edge comes from the dealer having a hidden card about which the player has to make assumptions. In addition, if the player busts, the dealer wins, even if they then bust in the same round. Learning blackjack odds and strategy makes this less of an issue.

Blackjack Odds

Admittedly, learning blackjack odds is a little more difficult than it is for other casino games. This is down to the randomness of the draw and the number of different combinations. Nevertheless, there are some ways of determining the odds of drawing specific cards. The initially probability of drawing a card of any value is 7.69%, based on there being 13 different possible options.

However, seeing as Jacks, Queens and Kings all have a value of 10 in blackjack, the odds of drawing a card valued at 10 is 4/13, which is a probability of 30.7% in percentage terms. As a result, the house edge can be reduced simply by having an idea of the odds of drawing certain cards. For example, if you happen to draw a Jack and a King, then you know that the odds of drawing yet another 10-value card are much reduced.

Reducing the House Edge in Blackjack

There are a variety of ways to reduce the house edge in blackjack. As previously mentioned, the simplest is to learn a basic blackjack strategy and commit it to memory before you play. A basic blackjack strategy is a set of rules, usually presented in a chart, which tells you how to play your hand after it is dealt. For example, if you are dealt a soft 17 (Ace, six), the chart compares it to the dealer’s upcard and informs you of how to act. In some cases, using a basic strategy can reduce the house edge to just 0.5%! If you want to lower the house advantage, studying the basics of blackjack strategies is a good place to start.

In addition to basic strategy charts, several strategies have been developed to reduce the house edge in blackjack even further. Unlike the basic charts, which only focus on the total value of your hand, these strategies look at what cards make up your hand and give specific actions depending on the cards – they’re called composition-dependent strategies.

Here’s an example. If you have 16 and the dealer has 10, depending on the composition of your hand there are a number of different options. For instance, if you had three separate hands that all equaled 16, with the first comprised of a 10 and a six, the second of nine and seven, and the third of four, five, and seven. If you followed basic blackjack strategy, you’d hit on all these hands, but with a composition-dependent strategy, you don’t hit on the final hand. This is because it is made up of low-value cards that would otherwise be needed to make a pat hand (under 21) from 16. The blackjack odds of drawing a low-value card are much lower than with the other two hands.

In most cases, by using a composition-dependent strategy along with the existing basic strategy charts, it’s possible to reduce the house edge to as little as 0.18%, which is practically nothing!

Hopefully, you’re now fully informed of what the house advantage is, how it applies to blackjack, and the steps you can take to reduce it. If you think you’re ready to put the new knowledge to the test, why not play on one of our online blackjack tables!

Slot machines are a popular type of casino game.

Games available in most casinos are commonly called casino games. In a casino game, the players gamble cash or casino chips on various possible random outcomes or combinations of outcomes. Casino games are also available in online casinos, where permitted by law. Casino games can also be played outside casinos for entertainment purposes like in parties or in school competitions, some on machines that simulate gambling.

Categories[edit]

Overhead view of a casino floor with table games (bottom) and slot machines

There are three general categories of casino games: gaming machines, table games, and random number games. Gaming machines, such as slot machines and pachinko, are usually played by one player at a time and do not require the involvement of casino employees to play. Tables games, such as blackjack or craps, involve one or more players who are competing against the house (the casino itself) rather than each other. Table games are usually conducted by casino employees known as croupiers or dealers. Random number games are based upon the selection of random numbers, either from a computerized random number generator or from other gaming equipment. Random number games may be played at a table or through the purchase of paper tickets or cards, such as keno or bingo.

Some casino games combine multiple of the above aspects; for example, roulette is a table game conducted by a dealer, which involves random numbers. Casinos may also offer other type of gaming, such as hosting poker games or tournaments, where players compete against each other.

Common casino games[edit]

Notable games that are commonly found at casinos include:

Table games[edit]

Poker (Texas hold'em, Five-card draw, Omaha hold'em)

Gaming machines[edit]

Random numbers[edit]

House advantage[edit]

Casino games typically provide a predictable long-term advantage to the casino, or 'house', while offering the players the possibility of a short-term gain that in some cases can be large. Some casino games have a skill element, where the players' decisions have an impact on the results. Players possessing sufficient skills to eliminate the inherent long-term disadvantage (the house edge or vigorish) in a casino game are referred to as advantage players.

Blackjack Casino House Edge

The players' disadvantage is a result of the casino not paying winning wagers according to the game's 'true odds', which are the payouts that would be expected considering the odds of a wager either winning or losing. For example, if a game is played by wagering on the number that would result from the roll of one die, true odds would be 5 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that the player gets the original amount wagered back. However, the casino may only pay 4 times the amount wagered for a winning wager.

The house edge or vigorish is defined as the casino profit expressed as the percentage of the player's original bet. (In games such as blackjack or Spanish 21, the final bet may be several times the original bet, if the player double and splits.)

A European roulette ('single zero') wheel

In American roulette, there are two 'zeroes' (0, 00) and 36 non-zero numbers (18 red and 18 black). This leads to a higher house edge compared to European roulette. The chances of a player, who bets 1 unit on red, winning is 18/38 and his chances of losing 1 unit is 20/38. The player's expected value is EV = (18/38 × 1) + (20/38 × (−1)) = 18/38 − 20/38 = −2/38 = −5.26%. Therefore, the house edge is 5.26%. After 10 spins, betting 1 unit per spin, the average house profit will be 10 × 1 × 5.26% = 0.53 units. European roulette wheels have only one 'zero' and therefore the house advantage (ignoring the en prison rule) is equal to 1/37 = 2.7%.

The house edge of casino games varies greatly with the game, with some games having an edge as low as 0.3%. Keno can have house edges up to 25%, slot machines having up to 15%.

The calculation of the roulette house edge was a trivial exercise; for other games, this is not usually the case. Combinatorial analysis and/or computer simulation is necessary to complete the task.

In games which have a skill element, such as blackjack or Spanish 21, the house edge is defined as the house advantage from optimal play (without the use of advanced techniques such as card counting), on the first hand of the shoe (the container that holds the cards). The set of the optimal plays for all possible hands is known as 'basic strategy' and is highly dependent on the specific rules and even the number of decks used. Good blackjack and Spanish 21 games have house edges below 0.5%.

Traditionally, the majority of casinos have refused to reveal the house edge information for their slots games and due to the unknown number of symbols and weightings of the reels, in most cases it is much more difficult to calculate the house edge than that in other casino games. However, due to some online properties revealing this information and some independent research conducted by Michael Shackleford in the offline sector, this pattern is slowly changing.^[1]

In games where players are not competing against the house, such as poker, the casino usually earns money via a commission, known as a 'rake'.

Standard deviation[edit]

The luck factor in a casino game is quantified using standard deviations (SD).^[2] The standard deviation of a simple game like roulette can be calculated using the binomial distribution. In the binomial distribution, SD = √npq, where n = number of rounds played, p = probability of winning, and q = probability of losing. The binomial distribution assumes a result of 1 unit for a win, and 0 units for a loss, rather than −1 units for a loss, which doubles the range of possible outcomes. Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold.^[3]

SD (roulette, even-money bet) = 2b√npq, where b = flat bet per round, n = number of rounds, p = 18/38, and q = 20/38.

For example, after 10 rounds at 1 unit per round, the standard deviation will be 2 × 1 × √10 × 18/38 × 20/38 = 3.16 units. After 10 rounds, the expected loss will be 10 × 1 × 5.26% = 0.53. As you can see, standard deviation is many times the magnitude of the expected loss.^[4]

The standard deviation for pai gow poker is the lowest out of all common casino games. Many casino games, particularly slot machines, have extremely high standard deviations. The bigger size of the potential payouts, the more the standard deviation may increase.

As the number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over. From the formula, we can see the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played. As the number of rounds increases, the expected loss increases at a much faster rate. This is why it is impossible for a gambler to win in the long term. It is the high ratio of short-term standard deviation to expected loss that fools gamblers into thinking that they can win.

Casino Blackjack 21

It is important for a casino to know both the house edge and variance for all of their games. The house edge tells them what kind of profit they will make as percentage of turnover, and the variance tells them how much they need in the way of cash reserves. The mathematicians and computer programmers that do this kind of work are called gaming mathematicians and gaming analysts. Casinos do not have in-house expertise in this field, so outsource their requirements to experts in the gaming analysis field.