
Progress Publishing Co. 

Blackjack Basic Strategy 
Blackjack Basic Strategy
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Blackjack Play before Basic Strategy
House Advantage against preBasic Strategy methods
A History of Basic Strategy
Basic Strategy for a Single and Multiple Decks
Insurance Bet
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Blackjack Play before Basic Strategy
Like other casino games Blackjack became a popular game when Nevada Gambling Act legalized gambling in 1931. From 1931 till the early 1960s the Blackjack popularity was lagging behind the popularity of Craps and Roulette due to the players’ perception that the game was impossible to beat. The players correctly understood the reason behind the toughness of the game – the rule that a dealer wins when both a dealer and a player bust. Nevertheless, the players played the game trying to get the best of it anyway they could. There were three general categories of players before the arrival in the mid1950s mathematicsbased Basic Strategy.
“Hunch” Players
Some players were just “hunch” players making decisions on the basis of their feelings and intuition. Such players, obviously, could make opposite decisions in identical situations in different rounds of play due to the opposite “hunches” at the moment. It is impossible to estimate precisely the house percentage against that kind of a guess work. It can be easy over 10% against a “hunch” player, but probably less than 15% according to Peter Griffin's rationale in his “Theory of Blackjack”.
“NoBust” Strategy
Other players, instead of feelings, wanted to follow Logic in their decisionmaking process. In result, many of them chose to follow “nobust” strategy. Since the root of the Blackjack evil for a player is in the loosing busted hands to the busted hands of a dealer, some players decided no to bust at all by standing on all hard hands from 12 to 16. The table below shows the high probabilities of busting for these hands.
Player's Stiff Hand  12  13  14  15  16 
Probability of Busting  48%  52%  55%  58%  61% 
Basic calculations, however, show fast that this seemingly correct on the surface Logic is wrong and leads to the horrible player’s disadvantage. The problem with this approach is that the dealer does not bust often enough to justify player’s standing on 1216 hands. A player gets 1216 hands 38.7% of the time and a dealer busts roughly 28%. That means that a player wins 38.7x28 = 10.8% of the time. On the other hand a dealer does not bust 72% of the time ending up with 1721 hands. That means that a player loses 72x38.7 = 27.8% of the time. In result, just by standing on hard 1216, a player guarantees the house an advantage equal 27.8%  10.8% = 17%.
“Mimic the Dealer” Strategy
There were other players who decided to imitate the dealer. Since the dealer was a consistent winner the Logic of mimicking the dealer in playing decisions seemed to be the right strategy. According to that strategy a player always hits hard hands 1216 and never hits soft 17 (A6) and soft 18 (A7), never doubles, splits, takes insurance or surrenders. That strategy has an obvious problem – a player can never mimic the dealer completely, because player’s busted hands will always lose to the dealer’s busts when both have busted hands in the same round of play. The simple calculations will show precise house advantage over “Mimic the Dealer” strategy. Both the dealer and a player bust 28% of the time. They bust at the same time 28x28 = 7.84% of the time. That means that in the average series of 100 hands a player loses 7.84 bets due to the dealer winning busted hands. However, a player’s Blackjack is paid at 3 to 2 ratio while the dealer’s at even money. A player has a probability of untied blackjack equal [(2x4x16)/( 52x51)]x[1(2x3x15)/(50x49)] = 0.0469 or 4.69% of the time. That means that a player will get extra half a bet 4.69% of the time reducing in the process the house advantage by 4.69x0.5 = 2.34 bets. The end result is: the house advantage against “mimic the dealer” strategy is 7.84 – 2.34 = 5.5%.
A History of Basic Strategy
The first attempts to develop a correct mathematicsbased strategy to play every hand in Blackjack in every possible situation started as early as 1954 at the Atomic Energy Commission Laboratory in Los Alamos. It is generally accepted that the first successful attempt in devising such strategy was done in 1956 by the mathematicians Baldwin, Cantey, Maisel and McDermott. They relied on approximate version of exact mathematical algorithms and used desk top calculators to derive specific probabilities for playing all possible hands against all possible dealer’s upcards. The accumulated data revealed the best possible decisions for a player to make on the basis of his first two cards and a dealer’s upcard. Those decisions were grouped into Basic Strategy. Basic Strategy was developed for a singledeck game with “standard” Las Vegas Strip rules. It was a zeromemory strategy requiring no memorization of any kind on behalf of a player. That first Basic Strategy produced a close to 0% advantage for a player turning Blackjack into an even money game – a great improvement in comparison with the previous best strategy by Culbertson with the disadvantage of 3.6% for a player. It was published in 1956 in the Journal of American Statistical Association. The book by the same authors “Playing Blackjack to Win” was published a year later in 1957.
Basic Strategy reduces the house advantage against a player by telling a player when and how to use all the options available to him. By correctly standing and hitting with his hard and soft hands, doubling and splitting a player improves his chances and almost completely erases 5.5% disadvantage of a player playing “mimic the dealer” strategy. The table below shows the improvements (according to Griffin) to a player expectation coming from a correct usage of his playing options.
Player’s options  Improvement in advantage 
Correct pair splitting  +0.4% 
Correct doubling down  +1.6% 
Correct standing  +3.2% 
Hitting soft 17 (A,6) and soft 18 (A,7)  +0.3% 
Basic Strategy for a Single and Multiple Decks
Basic Strategy does not turn every bad hand into a winner. It only maximizes a player’s expectation giving a player a best possible result for every particular confrontation between player’s initial two cards and a dealer’s upcard. Few examples will illustrate the benefits of the Basic Strategy for a player.
Suppose a player has (10,5) and the dealer’s upcard is a 10. It is a losing hand regardless of what player does. Both options of hitting and standing produce guaranteed longrun loss. However, the correct decision according to Basic Strategy is to hit instead of standing. Standing with 15 versus 10 gives a player expectation of 0.54 or in percentage terms it is a house advantage of 54%. That means that the average loss on every dollar bet will be 54 cents if a player stands. If a player hits, an expectation will be 0.5 and a house advantage this time is only 50%. A player’s average loss is 50 cents instead of 54. Thus the correct decision of hitting instead of standing improves player’s expectation by 0.04 and decreases house advantage by 4% saving a player on the average 4 cents on every dollar bet. In this example, Basic Strategy does not turn the hand into a winner but, instead, reduces the expected loss.
Assume now that a player has (A,7) and a dealer gets a 5 as an upcard. It is winning hand, which guarantees a longterm win. A player can stand with this hand and enjoy a + 0.22 expectation or 22% advantage over the house. On every dollar bet in this situation, a player wins on the average 22 cents if he stands. But the correct decision according to Basic Strategy will be to double down. That option will give a +0.17 expectation or advantage of 17% to a player, which will produce an average win of 17%x$2 = 34 cents thanks to a doubled bet. Thus the double down option increases player’s winnings by 34 – 22 = 12 cents.
Below are two basic strategies for a single deck and for multiple (4, 6 and 8) decks. The strategies assume standard Las Vegas Strip rules. These rules are: a dealer stands on soft 17, a player can double on any first two cards but not after splits, resplitting is allowed except aces, which can be resplit only once, insurance is available and no surrender.
Basic Strategy for a Single Deck
H Hit; S  Stand; D  Double Down; P  Split
Player's Hand 
Dealer's UpCard 

2  3  4  5  6  7  8  9  10  ACE  
8  H  H  H  D  D  H  H  H  H  H 
9  D  D  D  D  D  H  H  H  H  H 
10  D  D  D  D  D  D  D  D  H  H 
11  D  D  D  D  D  D  D  D  D  D 
12  H  H  S  S  S  H  H  H  H  H 
13  S  S  S  S  S  H  H  H  H  H 
14  S  S  S  S  S  H  H  H  H  H 
15  S  S  S  S  S  H  H  H  H  H 
16  S  S  S  S  S  H  H  H  H  H 
Hard Hand More or Equal17  S  S  S  S  S  S  S  S  S  S 
A2  H  H  D  D  D  H  H  H  H  H 
A3  H  H  D  D  D  H  H  H  H  H 
A4  H  H  D  D  D  H  H  H  H  H 
A5  H  H  D  D  D  H  H  H  H  H 
A6  D  D  D  D  D  H  H  H  H  H 
A7  S  D  D  D  D  S  S  H  H  S 
A8  S  S  S  S  D  S  S  S  S  S 
A9  S  S  S  S  S  S  S  S  S  S 
AA  P  P  P  P  P  P  P  P  P  P 
22  H  P  P  P  P  P  H  H  H  H 
33  H  H  P  P  P  P  H  H  H  H 
44  H  H  H  D  D  H  H  H  H  H 
55  D  D  D  D  D  D  D  D  H  H 
66  P  P  P  P  P  H  H  H  H  H 
77  P  P  P  P  P  P  H  H  S  H 
88  P  P  P  P  P  P  P  P  P  P 
99  P  P  P  P  P  S  P  P  S  S 
10,10  S  S  S  S  S  S  S  S  S  S 
Basic Strategy for Multiple Decks
Player's Hand 
Dealer's UpCard 

2  3  4  5  6  7  8  9  10  ACE  
8  H  H  H  H  H  H  H  H  H  H 
9  H  D  D  D  D  H  H  H  H  H 
10  D  D  D  D  D  D  D  D  H  H 
11  D  D  D  D  D  D  D  D  D  D 
12  H  H  S  S  S  H  H  H  H  H 
13  S  S  S  S  S  H  H  H  H  H 
14  S  S  S  S  S  H  H  H  H  H 
15  S  S  S  S  S  H  H  H  H  H 
16  S  S  S  S  S  H  H  H  H  H 
Hard Hand More or Equal17  S  S  S  S  S  S  S  S  S  S 
A2  H  H  H  D  D  H  H  H  H  H 
A3  H  H  H  D  D  H  H  H  H  H 
A4  H  H  D  D  D  H  H  H  H  H 
A5  H  H  D  D  D  H  H  H  H  H 
A6  H  D  D  D  D  H  H  H  H  H 
A7  S  D  D  D  D  S  S  H  H  H 
A8  S  S  S  S  S  S  S  S  S  S 
A9  S  S  S  S  S  S  S  S  S  S 
AA  P  P  P  P  P  P  P  P  P  P 
22  H  H  P  P  P  P  H  H  H  H 
33  H  H  P  P  P  P  H  H  H  H 
44  H  H  H  H  H  H  H  H  H  H 
55  D  D  D  D  D  D  D  D  H  H 
66  H  P  P  P  P  H  H  H  H  H 
77  P  P  P  P  P  P  H  H  H  H 
88  P  P  P  P  P  P  P  P  P  P 
99  P  P  P  P  P  S  P  P  S  S 
10,10  S  S  S  S  S  S  S  S  S  S 
Insurance Bet
Basis Strategy does not include an insurance bet. Basic Strategy player should never take Insurance. Insurance is a side bet that the dealer's hole card is a 10valued card. That side bet has nothing to do with and no connection to his original bet. Since Insurance bet pays 2 to 1, it will make sense for a player if the odds of a dealer having a 10 are better than 2 to 1. Suppose a player is in a single deck game, he does not hold a ten among his first two cards and a dealer shows Ace. There are 16 tens left in the remaining 49 cards and 33 nontens. That means that the odds for a hole card being a ten are 33 :16 or 2.06 to 1 against it. These odds are not better but worse than 2 to 1. That's why it is better for a player to ignore a dealer's invitation to take insurance. Suppose a player's bet is $1. Then, in this example a player wins on the average 16 times out of 49 for a total of 16x2= $32. He loses 33 times for a total of $33. The net result is $1 giving a player expectation on Insurance bet equal 1/49 =  0.020408 or a disadvantage of 2.0408%. This negative expectation is the best a player can have with Insurance bet. It will be a lot worse if a player has one or two tens in his hand and if he plays against multiple decks. If a player has one 10 his disadvantage rises to  8.16%. If he has two tens, the disadvantage is 14.2%.
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