Blackjack Basic Strategy House Advantage
- Basic Strategy Blackjack Test
- Blackjack Basic Strategy House Advantage Administrators
- Blackjack Basic Strategy House Edge
- Basic Strategy Blackjack Game
- Blackjack Basic Strategy Engine
- Basic Blackjack Strategy Chart
- Appendices
- Miscellaneous
- External Links
Introduction
To be clear, perfect blackjack basic strategy will not give the player an advantage over the house, it will, however, make it as close to an even game as you can find in the casino. Related: The Truth about Other Players Decisions in Blackjack. Just like that the player no longer has an advantage in single deck blackjack when playing perfect basic strategy. The casino does not like losing and will not lose for long. Other rule changes that have affected the house edge include letting players only double on a total of 9-11 or 10-11. The house has an advantage in blackjack simply because the player has to draw first and if he busts, the player automatically losses regardless if the dealer subsequently busts in the same round. This is the casino's solitary advantage in blackjack and if everything were equal, the house edge in blackjack would be about 8 percent.
- The house edge is a statistical way of measuring the casino’s advantage over the player.
- Apr 11, 2008 Typical blackjack players give about a 1.5% advantage to the house due to the mistakes they make playing their hands. But even those who get their entire basic strategy down cold still have a 0.5% disadvantage in the typical multi-deck game.
Blackjack switch is a blackjack variant which allows the player to do what is normally considered a classic cheating manoeuver, trading cards between two hands. The player must make two bets of equal size and is allowed to switch the second card dealt to each hand. Of course, nothing good comes without a trade-off. In this case a dealer 22 results in a push against all non-busted hands and blackjacks pay even money.
The game goes by the name Blackjack Exchange at the Bregenz Casino in Austria.
Rules
- All rules are based on conventional blackjack unless otherwise noted.
- Six or eight decks are used.
- Dealer usually hits a soft 17. I hear in Ontario, Canada, the dealer stands on soft 17.
- The player must make two bets of equal size.
- Cards will be dealt face up.
- Dealer will peek for blackjack with an ace or ten up. If the dealer has a blackjack all player hands will immediately lose, except a player blackjack will push.
- The player may switch the second card dealt to each hand. For example, if one hand has 5,10 and the other has 10,6, the player may switch the 10 and 6 to have two hands of 11 and 20. The player may also switch cards to form a blackjack.
- If the player switches to a blackjack, it counts as 21 points.
- Player may double on any 2 cards.
- Player may double after a split.
- Player may resplit up to four hands.
- Winning player blackjacks pay even money.
- A dealer total of 22 will push against any player total of 21 or less. A player blackjack will still beat a dealer 22.
Russian Rules: Same as the rules above, except early surrender allowed (sometimes not against an ace), dealer does not take a hole card, and dealer stands on soft 17.
Playing Strategy
The following tables show the basic strategy under the 8-deck Las Vegas rules after the switch decision has been made. The reason for the differences compared to conventional blackjack strategy is the push on 22 rule.
If 6 decks are used the player should double 9 against a 5.
At this time I have not created a strategy for the Russian rules or Ontario rules.
Simple Switching Strategy
The following is the 'Cindy Liu Simple Switching Strategy,' appropriate under the Las Vegas rules. It is based on the following list of hands in order of strength:
- 21
- 20
- 19
- AA
- 11
- 10
- 9
- 18 or 8
- 8,8 with 2-8 up
Following is how to use it.
Against a dealer 7 or 8, balance the hands, by making the weaker hand as high as possible, using the above scale of hands, if you can.
Against any other dealer up card, maximize the strength of the higher hand, using the scale above, if you can.
If you can't achieve one of the desired hands in the list, then make the strongest hand possible from the following list, in order of strength:
- 7 or 17
- any hand that should be split
- any 12
- any 13
Exceptions:
- With A,A + 3,8 — keep the aces together.
- With A,A + 2,9 — keep the aces together if the dealer has 2-6
- With A,A + 2,8 — keep the aces together
The simple strategy, compared to optimal strategy, results in a cost of errors of 0.17%. It results in an error once every 18.6 hands, and an error with an expected value of more than 10% once every 82 hands.
Advanced Switching Strategy
The following is the 'Cindy Liu Advanced Switching Strategy,' appropriate under the Las Vegas rules. To use it, add up the points for each hand for both ways to play them, and play the one with the greater number of points. In the case of a tie, use the the simple strategy.
Let's look at an example. Suppose you have 8+4 and A+8 against a dealer 6, where the underlined card is the second one dealt. So you can play (1) 12 and soft 19, or (2) 8-8 and soft 15. Which pair of hands is better? According to the table, the 12 is worth 0 points and the soft 19 is worth 1, for a total of 1. For the alternative, 8-8 is worth 1 and the soft 15 is worth 1, also for a total of 2. So the odds favor switching to 8-8 and soft 15. Note that the simple strategy would incorrectly advise the player to not switch. My Blackjack Switch appendix 1 shows that the combined expected value of 12 + soft 19 is -0.2108+0.3634=0.1526, and 8-8 + soft 15 is higher at 0.1461+0.0365=0.1824.
The cost of mistakes in the advanced strategy, compared to optimal strategy, is 0.08% only. The player will make an incorrect decision once every 24.5 hands, and a mistake with an expected value over 10% once every 250 hands.
Basic Strategy Blackjack Test
I also have a printer friendly version (PDF) of both switching strategies, as well as the basic strategy.
Arnold Snyder Switching Strategy
The Big Book of Blackjack by Arnold Synder contains an easy and intuitive switching strategy. Out of respect for copyright, I won't say more than that about how it works. According to Cindy Liu, the Sndyer strategy results in a cost of errors of about 0.2% compared to optimal strategy. Besides that, I highly recommend the book for breaking new ground in blackjack, which is not easy to do any more.
Switching Calculator
My Blackjack Switch calculator, courtesy of Jing Ding, will advise when to switch in any situation. The calculator is based on the Playtech rules and an infinite deck assumption.
House Edge
Under the standard Las Vegas rules, with six decks, the dealer hits a soft 17, and a switched blackjack counts as 21 points, the house edge is 0.58%, assuming optimal strategy. Follow are the effects on the house edge of some rule variations:
- Eight decks: +0.02%
- Switched blackjack automatically wins: -0.40%
- Blackjack automatic winner: -0.21%
- Dealer stands on soft 17: -0.30%
The house edge under the Russian rules is 0.20%, assuming early surrender against an ace is allowed.
Side Bet
There is also a Super Match side bet based on the player's initial four cards. The following table shows the paytable, probability, and return of each hand:
Super Match Side Bet
| Hand | Combinations | Probability | Pays | Return |
|---|---|---|---|---|
| Pair | 136401408 | 0.352205 | 1 | 0.352205 |
| 3 of a kind | 7577856 | 0.019567 | 5 | 0.097835 |
| 2 pair | 5941728 | 0.015342 | 8 | 0.122738 |
| 4 of a kind | 138138 | 0.000357 | 40 | 0.014268 |
| Nothing | 237219840 | 0.612530 | -1 | -0.612530 |
| Total | 387278970 | 1 | -0.025485 |
The lower right cell shows a house edge on the side bet of 2.55%.
C4
The Casino Bregenz in Austria offers Blackjack Switch under the name Blackjack Exchange. They add a side bet called the C4, which is based on the poker value of the player's initial four cards. The table below shows a house edge of 14.32%, based on six decks.
C4 — Six Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Four of a kind | 500 | 138,138 | 0.000337 | 0.168425 |
| Straight | 20 | 3,649,536 | 0.008899 | 0.177988 |
| Flush | 12 | 5,647,896 | 0.013772 | 0.165269 |
| Two pair | 10 | 5,871,528 | 0.014318 | 0.143177 |
| Three of a kind | 8 | 7,502,976 | 0.018296 | 0.146368 |
| All other | -1 | 387,278,420 | 0.944378 | -0.944378 |
| Total | 410,088,494 | 1.000000 | -0.143152 |
With four decks, the house edge of the C4 is 18.02%. With eight decks it is 12.40%.
Other Switch Pages
- Printer friendly basic and switching strategies (PDF).
- Appendix 1: Expected value table for each initial hand, for purposes of making accurate switching decisions.
Acknowledgements
My thanks to Cindy Liu for both her simple and advanced switching strategies, Jing Ding for his switching calculator, and to Gabor for his mathematical contributions.
External Links
- German translation of this article.
- Interview with the inventor of Blackjack Switch Geoff Hall
Written by: Michael Shackleford
Most players understand that the casino holds an advantage in blackjack. This advantage is known as the house advantage or house edge, and is usually under 1% in most blackjack games, provided players play using the optimal basic strategy under the rules of the game they’re playing.
What does the house edge or advantage mean? It is an expression of how much of each unit wagered that the casino can expect to win on average. In other words, if the house advantage is 1% and you make bets of $100, you can expect the casino to win $1 for every bet you make over the long run. The results of doubling down, splits, blackjacks and everything else are included in that calculation.
Obviously, no bet in blackjack would cause you to lose exactly $1 on any given $100 bet. However, if you played tens of thousands of hands, or looked at the aggregated results of thousands of customers playing at the casino, you would see that the casino was coming out ahead by about that 1% margin. This assumes of course that everyone plays perfect basic strategy. The reality is that casinos make more than that because of players that don’t know about basic strategy or prefer to gamble and bet with their gut when they are feeling lucky.
Blackjack Rules and the House Edge
Not surprisingly, different blackjack rules can have an impact on the size of the house edge. Some rules variations are beneficial to the player, while others increase the casino’s advantage.
The following is a rundown of how different rule changes can affect the house advantage. Credit to The Wizard of Odds for their excellent analysis of how rules affect the casino’s advantage. All rule changes and their effects are rated against a typical game with the following rules: a blackjack game with an eight deck shoe, where the dealer stands on all 17s, the player may double on any two cards, the player can double down after splitting, and the maximum number of hands the player may split to is four. This game would have a house edge of about 0.45%.
Remember, the lower the house edge the better. So negative values below are better for the player while positive values are better for the casino.
Promotional Rules
Many promotional rules are sometimes offered which can offer a lot of help to the player. For instance, if blackjacks pay 2-1, the house advantage is reduced by 2.27%. The following are some possible promotional rules variations that help the player, along with the amount by which they reduce the house edge:
- All blackjacks pay 2-1: -2.27%
- Triple down: -1.64%
- Five card Charlie: -1.46%
- 2-1 on suited blackjacks: -0.57%
- Six card Charlie: -0.16%
- Seven card Charlie: -0.01%
Using Fewer Decks
Most players have heard that blackjack games with fewer decks are friendly to players, but you might be surprised to find that the differences between these games are relatively small. In fact, the player will see almost no advantage unless only one or two decks are being used. Here’s how reducing the number of decks affects the house advantage:
- Six Decks: -0.02%
- Five Decks: -0.03%
- Four Decks: -0.06%
- Two Decks: -0.19%
- One Deck: -0.48%
Changing How the Dealer Plays
One of the biggest rules variations between various casino blackjack games is whether the dealer stands on all 17s, or hits on soft 17s (an Ace with another card or cards that total up to 17). The common rule of standing on all 17s is actually better for the player.
- Dealer hits on soft 17: +0.22%
Player Options
Changing the options available to the player can also have an impact on the house edge. For instance, allowing surrender, the option to hand in your cards and get half your money back before the hand is played, reduces the house edge. Allowing this before the dealer checks for blackjack is known as early surrender, while allowing it only after the dealer has checked for blackjack (and not received one) is known as late surrender. This is the effect of some common player-friendly rule variations:
- Early surrender against an Ace: -0.39%
- Late surrender against an Ace: 0%
- Early surrender against a Ten: -0.24%
- Late surrender against a Ten: -0.07%
- Hit after splitting Aces: -0.19%
- Drawing a Ten after splitting Aces counts as blackjack: -0.19%
However, in most cases, casinos are more likely to eliminate player options rather than give players a helping hand. Here are some rule changes that limit what the player can do, and their associated increases in the house advantage.
- Players can only split to three hands: +0.01%
- Players can only split to two hands: +0.10%
- Players may double down only on 9, 10 or 11: +0.09%
- Players may not double down after splitting: +0.14%
- Players may not split aces: +0.18%
Blackjack Short Pays
Perhaps the worst rules variation that can be found at casinos these days is the short pay blackjack. Traditionally blackjacks will pay 3-2 on your wager, meaning our example $100 bet wins $150. However, some casinos, particularly in Las Vegas, are now dealing blackjack games that offer less than this. While it may seem like a minor change, even a small reduction in the odds paid for a blackjack can have a huge impact on the house edge, turning what looks like a good blackjack game into a poor one. You should be particularly wary of games advertising “player friendly” rules such as single deck blackjack that only pay 6-5 or worse on a blackjack. Here’s how short paying blackjacks increases the house edge:
Blackjack Basic Strategy House Advantage Administrators
- Blackjack Pays 7-5: +0.45%
- Blackjack Pays 6-5: +1.39%
- Blackjack Pays 1-1: +2.27%