Blackjack: Strategy and Odds

Copied with permission from the Wizard of Odds

How to Play Blackjack

Blackjack can be played with one to eight ordinary decks of cards. Cards of rank 2 through 10 are scored according to their face value. All face cards are 10 points. Aces are semi-wild and can be worth either 1 or 11 points. The highest hand in blackjack is an ace and any 10-point card and is called a blackjack. A winning blackjack pays 3:2. If both player and dealer have a blackjack the bet is a push. Aside from a blackjack, a winning hand pays even money. The player wins if his hand has more points than the dealer, without going over 21. Thus, a 21-point hand is the highest and is why the game is sometimes called 21. If either the player or dealer go over 21 it is called a break or bust and a busted hand automatically loses. If both the player and the dealer bust the player loses, where lies the house advantage. If the player and the dealer tie, the bet is a push.

A round of blackjack begins with each player placing a bet in the circle or logo directly in front of him. Then the dealer will give each player and himself two cards. Player cards are usually dealt face up. One dealer card is dealt face up (the up card) and the other face down (the hole card). If the dealer has a ten or an ace as the up card it is possible he has a blackjack, in which case all player hands will lose except those with another blackjack. In the U.S. the dealer will check for blackjack immediately, if one is possible, and will collect all losing bets immediately if he does have a blackjack.

In the event the dealer has an ace as the up card he will allow the players to insure their hands against a blackjack. This is much like any insurance policy in which you are betting something bad will happen. The insurance bet in blackjack pays 2:1 if the dealer has a blackjack. If the dealer has an ace showing and a player has a blackjack the dealer may ask "even money?" This is because if the player has a blackjack the net result of both the blackjack and the insurance bet will be an even money win regardless of whether the dealer has a blackjack. After all players have had a chance to accept or decline insurance the dealer will check the hole card.

After it has been established that the dealer does not have a blackjack the players in turn may play their hands. The following options are available.

Stand: If the player is satisfied with his hand as-is he may stand pat. To signify you wish to stand, wave your hand as if to wave the dealer away. In a single deck game, tuck your cards face down under your bet.

Hit: If the player wishes to take another card he may continue to do so until he either stands or busts. To signify you wish to hit, tap the table with your finger. In a single deck game, scrape your cards lightly against the felt.

Double: If the player feels he needs one and only one more card then he may double his bet and be dealt one more card, good or bad. This option is only offered on the first two cards, and sometimes on the first two cards after splitting. To signify you wish to double, place another wager next to your original wager of equal value. In single deck, place your cards face up by your bet.

Split: If the player's first two cards are of equal point value he may split them into two hands. In this event each card is the first card of a new hand. The player must also make another wager, of equal value to the first wager, for the second hand. Splitting after splitting is allowed; however, resplitting aces is often an exception. The player may usually split up to 2 or 3 times if another splitting opportunity arises. Doubling after splitting is usually but not always allowed. To signify you wish to split put the additional wager next to the original wager. In single deck, place your cards face up by your bet.

Surrender: Finally, some casinos offer the player the option to surrender on the first two cards. If the player does not like his prospects he may forfeit half the bet as well as his cards. This option is generally only offered after the dealer checks for blackjack, known as "late surrender."

After all players have played their hands, from the dealer's left to right, the dealer will play his hand. The dealer has no free will but must always play by certain house rules. Usually the rule is that the dealer must hit until he reaches a score of 17 or more. Some casinos stipulate that if the dealer has a soft 17, an ace and any number of cards totaling 6, he must also hit. If the dealer busts, all players that did not bust automatically win.

Blackjack Basic Strategy

The most important thing to know about blackjack is the basic strategy. This strategy is simply the best way to play every possible situation, without any knowledge of the distribution of the rest of the cards in the deck. At the top of the page is the basic strategy for four or more decks when the dealer hits on soft 17, which is the most common game. Below are links to more basic strategy charts for other rules. If you only memorize one table I would suggest the one above. It can be played effectively under any rules.

To use the basic strategy look up your hand along the left vertical edge and the dealer's up card along the top. In both cases an A stands for ace. From top to bottom are the hard totals, soft totals, and splittable hands. Rule variations can have an effect on some borderline situations. The most flexible rules are the number of decks, whether the dealer hits or stands on a soft 17, and whether doubling is allowed after splitting.

Some obvious situations have been left out to keep the chart as small as possible. I have more basic strategy charts for other numbers of decks, as well as European blackjack.

The best way, I have found, to memorize the basic strategy is notice patterns and to try to understand why you should play every situation as the chart says. Then make flash cards and go over and over them until you know it cold. Do not deal out cards to yourself because the soft totals and the pairs will not occur often enough to test your knowledge.

Many people do not believe in the basic strategy because they once took the advice of someone who knew it and then lost the hand. Let me make something perfectly clear, you will not win every hand with the basic strategy! In fact, you won't even win half your hands. However, I can personally testify that while you will have short term ups and downs, over the long run you will roughly break even using it.

Rule Variations

Rule variations will have an effect on the player's expected return. The numbers below show the effect on the player's return under various rules and after taking into consideration proper basic strategy adjustments. These changes are relative to the following Atlantic City rules: 8 decks, dealer stands on soft 17, player may double on any first two cards, player can double after splitting, player may split to 4 hands.

Rule	Effect
Blackjacks pay 2 to 1	+2.27%
Five card Charlie*	+1.46%
Suited blackjacks pay 2 to 1	+0.57%
Player 21-points is automatic winner	+0.54%
Early surrender against ace	+0.39%
Early surrender against ten	+0.24%
Player may double on any number of cards	+0.23%
Late surrender against aced 10 after splitting aces is a blackjack	+0.19%
Player may draw to split aces	+0.19%
Six card Charlie*	+0.16%
Player may resplit aces	+0.08%
Late surrender against ten	+0.07%
Seven card Charlie*	+0.01%
Late surrender against ace	+0.00%
Dealer must stop with six cards	+0.00%
Late surrender after splitting	+0.00%
Split to only 2 hands	-0.01%
No-peek: ace showing	-0.01%
Player may double on 9-11 only	-0.09%
No-peek: ten showing	-0.10%
Player may not resplit	-0.10%
European no hole card	-0.11%
Player may not double after splitting	-0.14%
Player may double on 10,11 only	-0.18%
Dealer hits on soft 17	-0.22%
Blackjack pays 6-5	-1.39%
Player loses 17 ties	-1.87%
Blackjacks pay 1 to 1	-2.27%
Player loses 17,18 ties	-3.58%
Player loses 17-19 ties	-5.30%
Player loses 17-20 ties	-8.38%
Player loses 17-21 ties	-8.86%
Dealer bust on 22 is a push	-9.53%

Note: A "Charlie" is an automatic winner. For example the five-card Charlie rule means the player automatically wins with 5 cards, as long as he didn't bust.

The "no peek" rule applies when (1) the dealer does not peek for a blackjack or does not deal a hole card at all, (2) the player doubles or splits, (3) the dealer gets a blackjack, and (4) the player loses the total amount bet. This is the case under normal European rules. However, at many Internet casinos the rules are bizarre and the dealer peeks for blackjack with an ace but not a 10, or vise versa. Thus, I break down the no peek rule according to the up card.

Insurance

Do not take insurance, even if you have a blackjack. Card counters can get away with making smart insurance bets when the deck is rich in tens but the non-counting player should always decline it. The following table shows the house edge on the insurance bet depending on the number of decks used.

House Edge on Insurance
Number of Decks	House Edge
1	5.882%
2	6.796%
4	7.246%
6	7.395%
8	7.470%

Bad Strategies

Three popular bad strategies encountered at the blackjack table are never bust, mimic the dealer, and always assume the dealer has a ten in the hole. All three of these are very bad strategies. Following are my specific comments on each of them, including the house edge under Atlantic City rules (dealer stands on soft 17, split up to 4 hands, double after split, double any two cards) of 0.43%.

Never bust: For my analysis of this strategy I assumed the player would never hit a hard 12 or more and based all other decisions on maximizing expected value under this assumption. This results in a house edge of 3.91%.

Mimic the dealer: For my analysis of this strategy I assumed the player would always hit 16 or less and stand on 17 or more. The player as well as dealer stood on soft 17. The player never doubled or split, since the dealer is not allowed to do so. This results in a house edge of 5.48%.

Assume ten in the hole: For this strategy I first figured out the optimal basic strategy under this assumption. If the dealer had an ace up I reverted to the proper basic strategy assumption of assuming the dealer did not have a ten. Then I went back and used this strategy under regular playing conditions. This results in a house edge of 10.03%.