House edge means the percentage of the player's bet the casino wins on average. This is worth figuring out since the size of house edge has everything to do with how likely you're to win. Educated players always find the games with the least house edge possible and therefore win the most - or at least lose the least.
House edge is a percentage which is worked out for all casino games, both online and at land-based casinos. The game of blackjack has a house edge of 2-3%, if the player isn't using a strategy. When it comes to blackjack's house edge, one thing to keep in mind is that the number of decks used will alter the house advantage. Single deck blackjack has the lowest casino edge of 0.16%, which gives the player better odds. Double deck games have a considerably low edge at 0.46%.
For example, if house edge is 1.89%, the player loses $1.89 on average out of every $100 bet he makes. Obviously the player doesn't lose that amount on every single bet; you might win two hands and then lose six hands in a row but in the long run the loss will be about $1.89 per bet. One of the goals of Gaming the Odds is to teach you all about perfect blackjack strategy and to minimize the house edge. You can find several house edge percentages for blackjack game variations below in order to help you to find the best games.
The Amount of Decks
Firstly, what kind of an effect the amount decks has on casino's advantage? The table below displays the house edge for a standard blackjack game: blackjack pays 3:2, the dealer stands on soft 17, doubling is allowed for any two cards and splitting to four hands is allowed.
| Number of Decks | House Edge |
|---|---|
| Single Deck | -0.03% |
| Two Decks | +0.25% |
| Four Decks | +0.38% |
| Six Decks | +0.42% |
| Eight Decks | +0.44% |
Under those rules it would actually be profitable to play according to basic strategy with a single deck. It's always optimal to play according to basic strategy but in the vast majority of cases you're still going to have negative expectation.
Game and Rule Variations
Blackjack Games
Let's move on to the next table, which features other blackjack game variations and their house edges. In order to make it easier to compare these games, all the house edge percentages are for six-deck gamesunless otherwise stated.
| Game | House Edge |
|---|---|
| Atlantic City Blackjack | +0.42% |
| Blackjack Switch | +0.58% |
| Double Attack Blackjack * | +0.61% |
| Double Exposure Blackjack | +0.67% |
| European Blackjack | +0.62% |
| Multiple Action Blackjack ** | +0.42% |
| Pontoon Blackjack | +0.45% |
| Spanish 21 | +0.37% |
| Super Fun 21 | +1.40% |
| Three Card Blackjack | +2.10% |
| Vegas Downtown Blackjack | +0.62% |
| Vegas Strip Blackjack | +0.53% |
* Played with a specific amount of decks (which isn't six).
** Multiple hands played but probability equal to standard blackjack.
The table above was made to give you some idea of which games are better to play than others. It's also important to remember that some casinos may operate with slightly different rules which either increase or decrease the house advantage of the game.
Blackjack Rule Variations
What about other rule variations, then? I'm going to list some of the more common blackjack rule variations and their house edges. The tables below consists of changes made to standard blackjack rules:
| Dealer Hits Soft 17 | |
|---|---|
| # of Decks | House Edge |
| Single Deck | +0.15% |
| Two Decks | +0.45% |
| Four Decks | +0.59% |
| Six Decks | +0.63% |
| Eight Decks | +0.66% |
| Player Can Only Double 9-11 | |
| # of Decks | House Edge |
| Single Deck | +0.11% |
| Two Decks | +0.36% |
| Four Decks | +0.48% |
| Six Decks | +0.52% |
| Eight Decks | +0.54% |
| Player Can Only Double 10-11 | |
| # of Decks | House Edge |
| Single Deck | +0.26% |
| Two Decks | +0.48% |
| Four Decks | +0.58% |
| Six Decks | +0.61% |
| Eight Decks | +0.63% |
| Dealer Doubles on 17 | |
| # of Decks | House Edge |
| Single Deck | -0.03% |
| Two Decks | +0.25% |
| Four Decks | +0.38% |
| Six Decks | +0.42% |
| Eight Decks | +0.44% |
| Player Can Resplit Aces | |
| # of Decks | House Edge |
| Single Deck | -0.06% |
| Two Decks | +0.20% |
| Four Decks | +0.32% |
| Six Decks | +0.35% |
| Eight Decks | +0.37% |
| Blackjack Pays 6:5 | |
| # of Decks | House Edge |
| Single Deck | +1.36% |
| Two Decks | +1.62% |
| Four Decks | +1.75% |
| Six Decks | +1.78% |
| Eight Decks | +1.80% |
A couple of conclusions: first of all, the last section ('Blackjack Pays 6:5') shows you how unprofitable it is to play those games. Never play a game where blackjack pays 6:5.
| Dealer Hits Soft 17 | |
|---|---|
| # of Decks | House Edge |
| Single Deck | +0.15% |
| Two Decks | +0.45% |
| Four Decks | +0.59% |
| Six Decks | +0.63% |
| Eight Decks | +0.66% |
| Player Can Only Double 9-11 | |
| # of Decks | House Edge |
| Single Deck | +0.11% |
| Two Decks | +0.36% |
| Four Decks | +0.48% |
| Six Decks | +0.52% |
| Eight Decks | +0.54% |
| Player Can Only Double 10-11 | |
| # of Decks | House Edge |
| Single Deck | +0.26% |
| Two Decks | +0.48% |
| Four Decks | +0.58% |
| Six Decks | +0.61% |
| Eight Decks | +0.63% |
| Dealer Doubles on 17 | |
| # of Decks | House Edge |
| Single Deck | -0.03% |
| Two Decks | +0.25% |
| Four Decks | +0.38% |
| Six Decks | +0.42% |
| Eight Decks | +0.44% |
| Player Can Resplit Aces | |
| # of Decks | House Edge |
| Single Deck | -0.06% |
| Two Decks | +0.20% |
| Four Decks | +0.32% |
| Six Decks | +0.35% |
| Eight Decks | +0.37% |
| Blackjack Pays 6:5 | |
| # of Decks | House Edge |
| Single Deck | +1.36% |
| Two Decks | +1.62% |
| Four Decks | +1.75% |
| Six Decks | +1.78% |
| Eight Decks | +1.80% |
A couple of conclusions: first of all, the last section ('Blackjack Pays 6:5') shows you how unprofitable it is to play those games. Never play a game where blackjack pays 6:5.
Secondly, games where the player can resplit aces are preferable for the player. Try to find those games. It's also good for the player when the dealer doubles 17.
Blackjack Side Bets
And finally, blackjack side bets and house edges for them.
| Side Bet | House Edge |
|---|---|
| 21+3 Blackjack | +3.20% |
| 21 Madness | +23.00% |
| Bonus Blackjack | +24.00% |
| Match the Dealer | +3.10% |
| Perfect Pairs Blackjack | +4.10% |
| Royal Match Blackjack | +6.50% |
| Super Match Blackjack | +2.60% |
| Super Sevens Blackjack | +11.70% |
| Bust It Blackjack | +7.00% |
No, casinos didn't include the 'side bet' option just to give players a better chance of winning. As you can see, side bets are good for the casino and bad for the player even if they might make the game a bit more exciting.
Favourable Blackjack Rule Variations for the Player
Here's a list of blackjack rule variations favourable for the player:
- The less decks the better. (Games with one deck are the best.)
- Double down on any 2 cards.
- Blackjack pays 3:2.
- Resplitting aces allowed.
- Dealer stands on a 17.
- Early/late surrender.
- Low deck penetration (for card counters).
- Insurance (for card counters).
Favourable Blackjack Rule Variations for the Casino
- Side bets.
- Double down on 10 and 11 only.
- Dealer hits a soft 17.
- The more decks the better.
- Blackjack pays 6:5
- Low deck penetration (against card counters).
- No doubling down after splitting.
- Not allowed to resplit aces.
I suggest trying to memorize these lists and look for games with beneficial blackjack rule variations for the player. Rule variations in favor of the casino should obviously be avoided.
Blackjack House Edge: FAQ
Do bet sizes impact house edge in blackjack?
It makes no difference whether you bet $10 or $10,000 - the house advantage stays the same. The amount you lose or win per bet changes, of course, depending on how big of an edge either you or the casino's got.
Which blackjack game has the smallest casino edge?
Suggesting all games are played with six decks - which is a common size for a blackjack shoe - Spanish 21 has the best house edge for the player according to the blackjack house edge table on top of this page. Standard 21 Blackjack is good too since you can actually have the edge by playing perfect basic strategy with a single deck.
How big is the house edge if I count cards?
This depends on many variables, such as which blackjack card counting systems you're going to use. In case you're using a highly complicated system, play perfectly and manage to find a good game to play, you may have a significant edge (even 3% or 4%).
Additional Resources:
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]
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] | 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.
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.)
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.
Blackjack House Edge
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.
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.
See also[edit]
References[edit]
Blackjack Probability Calculator
- ^'Michael Shackleford is the wizard of odds'. Observer. Retrieved 13 October 2015.
- ^Hagan, general editor, Julian Harris, Harris (2012). Gaming law : jurisdictional comparisons (1st ed.). London: European Lawyer Reference Series/Thomson Reuters. ISBN978-0414024861.
- ^Gao, J.Z.; Fong, D.; Liu, X. (April 2011). 'Mathematical analyses of casino rebate systems for VIP gambling'. International Gambling Studies. 11 (1): 93–106. doi:10.1080/14459795.2011.552575. S2CID144540412.
- ^Andrew, Siegel (2011). Practical Business Statistics. Academic Press. ISBN978-0123877178. Retrieved 13 October 2015.
Blackjack House Edge Definition
