Blackjack Odds, Probability and House Edge
Blackjack is an exciting casino game that over the years became one of the most popular and sought-after gambling games in the entire world. The reason for this is that applying the right blackjack strategy when playing can reduce the house edge from 8% to as low as 0.5% giving players a better chance at winning big at the blackjack tables.
House Edge vs. Payout Percentage
The casino house edge is calculated by taking all the bets made playing blackjack and multiplying by the percentage of money wagered the casino will get to keep. House edge calculations always assume that the player is playing optimal blackjack strategy.
The house edge is always expressed as a percentage that, coupled with the casino payout percentage, will always total 100%. The payout percentage (sometimes called return percentage) expresses the percentage of the money wagered that the players will get to win back.
When calculating the payout percentage, it is always assumed the player is playing optimal blackjack strategy, and it refers to the overall average return for the total blackjack hands played.
Let us assume a casino offers a 97% payout percentage for their Atlantic City Blackjack. This means that the house edge will be calculated as 100 minus 97 = 3% house edge.
3% house edge or 97% payout percentage means the same thing. They are just opposite mathematically theoretical numbers expressing the same thing. In both cases, on average, the casino will profit $3 for every $100 the player wagers.
Of course, such calculations are based on averages of tens of thousands of hands played. There can easily be a situation where one player will play, and due to a combination of applying bad blackjack strategy or no strategy at all, they will have a payout percentage, for example, of 56% while another player using the correct strategy combined with a lot of luck will have a payout percentage for example of 134% thus making a profit of $34 for every $100 they wagered.
House Advantage in Banker Games
Many casino games such as roulette, baccarat, craps and blackjack are defined as “bankers’ games” because the player plays against the house (the dealer or croupier is the house representative in the game), and the house has an unequal chance against the player.
The game is structured in such a way that gives the house a greater overall chance of getting some of the money the player wagered regardless of how they are playing.
In blackjack, the dealer will win all bets made by losing players regardless of the value of the dealer’s own hand. So the player must beat the dealer to collect their payout, but the dealer only needs the player to bust out in order to collect the player’s bet.
True Odds vs. Casino Odds
The house has another advantage that it derives from being the one setting the payouts for each game. All casino games, including blackjack, have true odds and have the odds the casino is willing to pay for the game. As a player, you have no choice but to accept the odds the casino is offering.
The best way to illustrate the difference between the true odds and casino odds is by taking a single regulation playing dice with numbers ranging from 1 to 6. The true odds of throwing, for example the number 2 are 1 in 6, so a player has a chance of 16.666% to have the die land on 2.
However, most casinos will not pay 6 to 1 if you made a wager on the die landing on 2. They would probably only pay 5 to 1 or even 4 to 1, thus increasing their advantage by taking all of the player’s money when they lose but not paying the player the true odds of a wager when the player wins.
Low House Edge
Notwithstanding the overall advantage that the casino has over players in most casino games, blackjack is a game that usually has one of the lowest house edges of all casino games. For example, if compared with Keno, which has a 25% to 29% house edge or American roulette, which has a house edge of 5.26% for single number bets, it is clear that blackjack is a very player-friendly game.
The reason for this is that blackjack is not just a game of chance but also incorporates a strong element of skill. Players that adhere to basic blackjack strategy would usually be playing a game with an average house edge of 0.17% in a single deck game and up to 0.66% in an 8 decks game.
The fewer decks are used, the lower the house edge. Single deck blackjack games would normally have lower payouts for hitting a natural blackjack in order to provide the casino with some edge over the player.
It is important to check the house edge on your chosen blackjack variant as some types of blackjack have rules that are more favorable for the casino, which increase the house edge to 1% or higher.
The odds of Busting
When making decisions in blackjack, it is important to understand the probability of going bust by getting a hand total that exceeds 21. Understanding what are your odds of busting when you hit (draw an additional card) on different hands values can help you make the right strategic decisions and help you win more hands.
| Total Hand Value | Odds of Busting when Hitting |
|---|---|
| 21 | 100% |
| 20 | 92% |
| 19 | 85% |
| 18 | 77% |
| 17 | 69% |
| 16 | 62% |
| 15 | 58% |
| 14 | 56% |
| 13 | 39% |
| 12 | 31% |
| 11 or less | 0% |
The Effects of Number of Decks on House Edge
Blackjack is considered to be a very player-friendly game that offers a very low house edge and a high payout percentage for the player. The reason for this is that blackjack is not just a game of chance but also a game of skill, so when players apply basic blackjack strategy, they lower the house edge to lower than 1% on most blackjack variations.
Number of Decks in Play
In most blackjack variations there is a direct effect of the number of decks in use on the house edge. Some blackjack variations have a fixed number of decks in use, as the use of any other number of decks would not sit well with some of the rules.
However, many blackjack versions can be played using a different number of decks. The change in the number of decks in use has a direct effect on the house edge and can lower or increase it, depending on the number of decks in use.
In general, the fewer decks are used, the lower the house edge and vice versa. The fewer decks are in play, the higher the payout percentage the player can expect from the game when playing optimally using basic blackjack strategy.
Why Number of Decks Matters
The reason that the number of decks has such an effect on the house edge is that the number of decks has a direct effect on the player’s chances of hitting a natural blackjack.
The main reason for this is that when fewer decks are in use and the player is dealt a 10 valued card as their first card, there is a higher probability of the second card dealt to the player being an ace which will result in the player having a natural blackjack.
In addition, there is a lower chance of the dealer having a natural blackjack against the player’s natural blackjack. Such a hand will result in a tie, and the player’s bet will be pushed (returned to the player).
The Real Percentages
Let us take, for example, a fixed set of rules and see how the house edge changes the more decks are in play.
The Rules:
- Double on any two cards
- Dealer hits soft 17
- Double after split allowed
- Resplit up to 4 hands
- No Surrender
- No hitting split aces
- Player’s original bet only lost when dealer showed blackjack
- A cut card is in use
Below is a table that lists the house edge that corresponds to the number of decks in use when playing by the blackjack rules listed above:
| No. of Decks in Play | House Edge |
|---|---|
| Single Deck | 0.17% |
| Double Deck | 0.46% |
| Four Decks | 0.60% |
| Six Decks | 0.64% |
| Eight Decks | 0.66% |
Effects of Blackjack Rules Variations on House Edge
The game of blackjack has over the years spun over 100 documented variations. Some variations have very fixed rules that never change, while others are more flexible, and the casino can decide to include some rules and not others when they offer a particular blackjack variation.
Changes in blackjack rules have an obvious effect on the house edge the casino enjoys and the potential payout percentage the player can receive.
Number of decks
As a general rule, when fewer decks are in use, the house edge is reduced due to two main factors:
- Fewer decks increase the likelihood of a player hitting a natural blackjack. When a player is dealt a 10 valued card, they have a better chance of the second card dealt being an ace when playing fewer decks.
- Fewer decks decrease the chance for a dealer’s blackjack vs. a player’s blackjack, which will result in a push.
Resplitting
Most casinos will allow resplitting a post-split hand that again shows cards of the same value. Some casinos limit the total number of split hands allowed (for example, they will allow resplitting up to 4 hands), while other casinos will allow unlimited splits. As a general rule, the more resplits are allowed, the lower the house edge on the game. Therefore the more favorable it is to the player.
Dealer hits soft 17
All blackjack variants have a fixed set of rules that govern the dealer’s actions. One of the key actions a dealer can take is to hit or stand on soft 17. This decision is not left up to the dealer and is predetermined by the rules of the game. As a general rule, it is better for the player if the dealer stands on soft 17 as it drops the house edge by around 0.2%.
Late surrender
This rule allows the player to surrender their hand after the initial two cards are dealt if they believe their hand does not stand a chance of winning or resulting in a tie with the dealer. When employing late surrender, the player loses half their original bet, with the other half pushed. This rule is favorable to the player as it lowers the house edge by up to 0.1%.
Double after split allowed
In most games, doubling down after a split is allowed. These games would have a house edge that is lower by about 0.12% than the house edge of the same game when doubling after a split is not allowed.
Resplitting aces/ Hit resplit aces
In most games, players are not allowed to resplit aces and can have one more card dealt for each split hand. They are not allowed to hit, double or resplit. However, when these actions are allowed, they make the game more favorable to the player. Allowing hits after ace splits reduces the house edge by more than 0.1%, and allowing to resplit aces lowers the house edge by around 0.03%.
Changes to natural blackjack payouts
In most blackjack games, when a player has a natural blackjack, the payout is 3:2. However, in some games (especially single deck games), a natural blackjack pays at 6:5 or 1:1. When playing a 6:5 game, the house edge increases by about 1.4% and when playing 1:1 game the house edge increases by about 2.3%.
