Blackjack

• The objective of blackjack
• The cards and the “fluctuating” ace
• Playing the game
• Insurance and “even money”
• Blackjack basic strategy
• Generic basic strategy table
• Rules
• Rule values
• Some useful stats
• Blackjack volatility
• Is blackjack “streaky”?
• Blackjack practice
• Blackjack resources on the web

The objective of blackjack

The aim of casino blackjack is to beat the dealer; blackjack is not about making 21 or getting as close to 21 as possible - both of which are frequently cited as the aim of the game.

The cards and the “fluctuating” ace

Cards 2 through 10 have their face value; jack, queen and king are all valued at 10. The ace has a unique “fluctuating” value of both 1 and 11, depending on the other cards in the hand: if the current total is ten or less, the ace is valued at 11 and the hand is referred to as “soft” - meaning it cannot be busted with the draw of any one card; for totals of eleven or more its value is 1, and the hand is now “hard”, meaning that it CAN be busted. For example: 2/4/A = soft 17; 7/3/A = soft 21; 7/4/A = hard 12.

This “fluctuating” ace value can cause confusion in the early stages of acquaintance with the game.

Playing blackjack

The player receives two cards face up while the dealer receives one face up and one face down - the down-card referred to as the “hole card”; to begin with, the dealer usually (but not always, depending on the rules) checks his hand, known as “peeking”, to see if he has a “blackjack” - a combination of ace and ten-value card; if he has, and the player hasn’t, play is over for that hand and the dealer scoops up the money. If the player has a blackjack, he’s immediately paid out at a ratio of 3:2 (for example, $15 for a $10 wager).

If neither dealer nor player has a blackjack, the player then decides how he wants to proceed with his hand. There are five options:

“Stand”: the player is happy with his hand and takes no more cards.

“Hit”: the player requests additional cards, until he is happy with the hand or exceeds twenty-one and busts.

“Double down”: depending on the precise rules of the game, after receiving his initial two cards the player may make an additional bet, to value of his initial wager, and take one more card. He may take no more than that one extra card. If the rules allow it, he may also double down after splitting. Although it’s often possible to double down on absolutely ANY two initial cards, there is an “optimal” doubling strategy, varying depending on the rules of the game, and which should always be followed to the letter - see “basic strategy” further down the page.

“Split”: If the two initial player cards are of the same rank they may be split into two hands, at the cost of an extra wager equal to the first. Both hands are then played out independently of each other. As with doubling, optimal splitting strategy should always be followed to the letter.

“Surrender”: this is quite a rare rule whereby the player may give up his hand, immediately after the dealer has peeked for a blackjack, and receive half his initial wager back.

Once the player is happy with his hand, and assuming he doesn’t bust (exceed 21), the dealer then plays out his own hand, drawing to a total of either “hard 17” or “soft 17” depending on the house rules (see blackjack rules below for definitions of hard 17 and soft 17). In the final analysis, the higher hand wins - unless the dealer busts, in which case the player’s non-busted hand wins automatically. In the event that the player busted his hand, the dealer is not required to play out his own hand and wins automatically himself. In the case of a tie (also known as a “push”), the bet is returned.

Insurance and “even money”

“Insurance” is a side-bet, advertised on the baize of all blackjack tables as “insurance pays 2 to 1” - see below:

insurance

If the dealer has an ace as his up-card, “insurance”, payable at the price of half the original bet, is offered to the player. If the dealer has a blackjack, the insurance bet wins at 2 to 1, the original bet loses and the player ends up breaking even for that hand. If the dealer does NOT have a blackjack the insurance side bet loses and play continues.

In the event that the player has a blackjack himself when the dealer has an ace up the player can take “even money” and accept immediate payment of 1 to 1 on his blackjack. This is a popular move for many players as it seems to represent a guaranteed win, preferable to risking a push in the event the dealer also has a blackjack. However, as is the case with many insurance policies, the “insurance” bet in blackjack is ALWAYS bad; NEVER take insurance, not even when you have a blackjack and are tempted to take the guaranteed win. Like many others in the casino, insurance is a sucker-bet. For more details, see the article on insurance.

Blackjack basic strategy

In order to achieve the best possible payback you have to make correct playing decisions; is it a stand or a hit? A hit or a double? A double or a split?

In the same way that a European roulette inside bet has its own unique mathematical expectation, −0.027 or −2.7%, so does each of the 550 possible three-card combinations in blackjack. However, since blackjack offers up to five choices for how to play each of those combinations (hit, stand, double, split and surrender), the actual expectation is dependant on whichever option the player ultimately selects. The option with the highest expectation for the player is clearly the correct way to play the hand.

For example, take 3/3 against a dealer 7;

Hit: −0.15, or −15%.
Stand: −0.47, or −47%.
Double: −0.89, or −89%.
Split: −0.05, or −5%.
Surrender: −0.5, or −50%.

Of the five options, splitting is the best - or rather, the least bad, since all have negative value for the player - at −5%. As such, the correct play for 33 v. 7 is “split”.

The correct playing decisions are collectively referred to as the “basic strategy” for the game, and the strategies vary based on the number of decks and the rules.

For more details then you could ever want on the expected value of every possible three-card combination, one to eight decks, see the BJ Math expected value table list and choose from any of the ten tables available.

Generic basic strategy table

The table you see below is a “generic” basic strategy designed for the multi-deck game. Although the games recommended in the subsequent articles have different rules and different adherent strategies, I would recommend that you learn this generic strategy as it forms the basis of all the subsequent variations. (For comprehensive strategy charts covering almost all online games available, see the Basic Strategy section in the menu.)

The rules for the game this strategy applies to are: DOA, DAS, OBO (see below for definitions);

H = hit, S = stand, D = double and P = split.

Hard Totals
blackjack generic basic strategy hard totals

Soft Totals

Pairs

Blackjack rules

The payouts of online blackjack games vary enormously, from as low as under 99% to as high as over 100%. What makes the difference is the many different rules blackjack games use and the number of decks involved. However, since for the purposes of this site the only games under consideration are single-deck games we can dispense with a very large percentage of everything else on offer and concentrate on rules. The following is a list of all current rules used in online blackjack, plus an explanation:

• S17 - Soft 17, sometimes incorrectly referred to as “stand 17”. The dealer must stop drawing cards when his total is at least soft 17. A “soft” hand is a hand in which the ace, with a double value of both 1 and 11, is valued at 11, and as such cannot be busted with the draw of any subsequent card. For example, if I am dealt a six followed by an ace, the total stands as 6 + 11 = 17. There is no card in the deck that can bust that hand - a subsequent ten card would give a total of 6 + 1 (value of the ace switched from 11 to 1) + 10 = 17. If the dealer drew those same initial cards - a six followed by an ace - his total would be “soft” 17 and would take no more cards under the S17 rule.

• H17 - Hard 17, sometimes incorrectly referred to as “hit 17”; the dealer must stop drawing cards when his total is at least hard 17. Using the same example as above of a six followed by an ace, in a “hard 17” game the dealer WOULD be required to draw another card to his initial 6 and ace. If the third card were a 10, the total would stand at 6 + 1 + 10 = 17, and he would take no more cards.

• ENHC - European No Hole Card. Rather than dealing himself two cards, the dealer draws just one, then waits for the players to complete their hands before drawing his second card. The practical implication for the player is that if the dealer’s initial card is a ten or an ace he may end up with a blackjack, resulting in the additional loss of any extra bets (doubles or splits) the players make. As such, ENHC restricts the players’ doubling and splitting options.

• OBO - Original Bets Only. The dealer checks for blackjack before any play commences, so that only players’ initial bets are lost to blackjack - doubles or splits don’t come into play. An alternate format is for the dealer to wait until the players complete their hands before checking for blackjack, but only collecting the initial bet and returning to the players any doubles or splits in the event of a dealer blackjack. The result is the same. An early version of Cryptologic used this format.

• “Full-peek” - Exactly the same as Original Bets Only. The dealer “peeks” for blackjack prior to commencement of play

• D9 - Double 9. The player may double down only on an initial two-card total of nine, ten or eleven.

• D10 - Double 10. The player may double down only on an initial two-card total of ten or eleven.

• DOA - Double On Any. The player may double down on the first two cards of any initial hand.

• DAS - Double After Split. The player may double down on the first two cards of any split hand.

• LS - Late surrender. The player may “surrender” half his initial bet, assuming the dealer doesn’t have a blackjack. The dealer will check for blackjack before the option is offered.

• RSA - Resplit Aces. If the player is dealt an ace pair and goes on to receive a third ace on one of them, he may split to a third hand.

• DSA• - Draw To Split Aces. When aces are split, usually only ONE card is dealt to each ace. In DTSA, the player may request additional cards to his aces as if he were playing a non-split hand.

All these various rules can be combined to give an almost unlimited variety of games, and each individual rule adds to or takes away from the player’s expected overall return, i.e. some rules are advantageous to the player and some are not. Doubling is ALWAYS advantageous - hence DAS and DOA are player-friendly, whilst the restrictive D9 rule is not. Since ENHC (European no hole card) also limits the doubling / splitting options it is less player-friendly than the far more common OBO (original bets only) rule. LS (late surrender) is very mildly advantageous to the player when used correctly, as is RSA.

Most of the above is reasonably logical if you think about it: since doubling / splitting is good for the player, rules that restrict those options are bad. The two rules which really AREN’T intuitively logical are S17 and H17: Soft 17 is better for the player than hard 17, because although in hard 17 the dealer busts more frequently he also makes a final hand total which is slightly larger, and as such beats the player’s final total more often.

Rule values

Here are the actual percentage values for each rule. Failing any other option, you can input these values into any game to establish the overall return.

A single deck game with the following rules - S17, DOA, no DAS, no surrender, OBO - has a house edge of almost exactly zero, which equates to a player average return of 100% assuming accurate play - the perfect gambling game!

• H17: subtract 0.2%
• DAS: add 0.14%
• D9: subtract 0.08%
• D10: subtract 0.18%
• LS: add 0.08%
• ENHC: subtract 0.11%
• DSA: add 0.19%

So for example, suppose your game is single deck, H17 and DAS. From your 100% return figure, subtract 0.2% for H17 and add 0.14% for DAS. 100 - 0.2 + 0.14 = 99.94% overall return.

Ascertaining the exact rules is not always easy. I recently enquired of a “reputable” casino the number of decks employed in their two multi-deck games. The service representative I spoke to didn’t know but promised to get back to me on the matter. She never did! For the purposes of this site this is not an issue, since all the games under consideration are fully explained. It’s worth bearing in mind when setting off on your own, however, that these things frequently necessitate some serious research before the details come to light.

Some useful stats

• Win/lose/push:

Depending on the exact rules, using correct basic strategy the player will win 43.2% of his hands, lose 47.9% and push 8.9%. Factoring out the pushes, the player wins 47.5% of all resolved hands and loses 52.5% - or five hands out of every 100. The extra value to the player comes from natural blackjacks that pay 3:2, plus correct doubling and splitting. The 3:2 blackjack payoff approximately five hands in every hundred garners the player an extra 2.5%, while correct doubling adds 1.6% and splitting makes up the remainder, at about 0.4%. As such, the player’s initial disadvantage of five percent on “hands only” is reduced to 5 - 2.5 - 1.6 - 0.4 = 0.5%, for the average multi-deck game.

• Bust rate:

The dealer busts on average 28% of all hands; the player busts 16% of the time if using correct basic strategy.

• The “best” and “worst” of incorrect plays:

Deviations from basic strategy cost you money; the most expensive deviation in its own right is hitting instead of splitting 8/8 v. dealer 7, costing you fully 58% of your bet compared to the correct play. Overall, since this hand is fairly rare, the cost is just 0.025%. The worst possible deviation overall is splitting 10/10 v. dealer 10. This hand is so common that the overall cost is 1.32%.

Splitting 10/10 v. 10 increases a generic multi-deck house edge of around 0.5% to 1.82%!

At the other end of the scale, the least expensive basic strategy deviation is to double A/2 v. 5 rather than hit. The overall cost of this mistake is a miniscule 0.00023%, which would increase the 0.5% house edge to 0.500023%.

If you’re masochistic enough to make severe basic strategy deviations, here is a short list of the effects:

• Never double: adds 1.6% to the house edge.
• Stand on stiffs (12 - 16) against dealer 7 - A: adds 3%.
• Hit stiffs against dealer 2 - 6: adds 3.2%.
• Always take insurance: adds 0.23%.

As such, if you never double, hit and stand incorrectly and always take insurance, you add an extra 7% to the house edge!

Volatility in blackjack

Blackjack, like all gambling games, is subject to the ups and downs of Dame Fortune; fortunately, there is a simple statistical formula we can use to measure it, using "standard deviation".

Standard deviation in blackjack is calculated as follows:

• Take your total initial hands played
• Find the square root
• Multiply the square root by 1.15.

Here’s an example, using 200 initial hands:

(sq.rt.200 = 14.14) × 1.15 = 16.26

The standard deviation of 200 hands is therefore 16.26.

Your results will fall within one standard deviation approximately 68% of the time; within two, 95%, and within three, 99.7% of the time - which covers almost all eventualities.

Playing a typical multi-deck blackjack game with an expectation of −0.5%, you will on average lose one unit for every 200 played. Supposing you end up losing 35 units out of 200 hands played - how probable / improbable is that?

The difference between your expected loss (1) and your actual loss (35) is 34.

34 ÷ 16.26 (one standard deviation) = 2.09.

Your 35-unit loss is therefore a fraction in excess of two standard deviations; we know that results fall within this figure 95%s of the time, and therefore outside it, 5% of the time.

As such, a 35-unit loss out of 200 initial hands will occur on approximately one occasion in twenty.

If you don't have a calculator with a square root function, there should be one in your computer: Start menu / programmes / accessories / calculator.

Is blackjack “streaky”?

One of the many myths about blackjack is that the game is inherenetly “streaky”, meaning that wins tend to follow wins - and losses follow losses - more than would be expected in a random game. As such, many blackjack authors advocate progressive betting systems - increasing after a win and decreasing after a loss - in order to capitalise on these apparent non-random tendencies.

In an attempt to give the lie to the “streak” argument once and for all, blackjack player and author Stanford Wong made a “streak study”, recording the results in his book Professional Blackjack (see “Search For Streakiness”, pages 239 - 244). A computer simulation of 20 million hands recorded wins, losses and pushes as a function of the previous two hands, for the purpose of highlighting possible changes in the win/lose/push statistics based on preceding combinations.

The results are recorded in the table below; the left hand column lists the nine possible two-card combinations of win/lose/push, and the three columns to the right show the results for the hand following. For example, row one (win, win) shows the percentages recorded for all the hands following two wins.

streaks chart

Table reproduction with the permission of Stanford Wong.

Clearly, there is no difference - no two-card combination results in any significant change in the win/lose/push rate of the subsequent hand. The tiny discrepancies, 43.2 / 43.3 and 47.8 / 47.9, result from the relative “shortness” of the simulation: in order to eradicate ANY differences it would need to have been substantially longer.

“Streaks” in blackjack are no lesser or greater than those predicted by game statistics, and as such cannot be capitalised on by raising / lowering your bets based on the results of the preceding hands.

(There's a review of Professional Blackjack on the resources page. It’s main focus is card counting, but there's of a lot that’s of interest and value to all blackjack players, and I highly recommend it.)

Blackjack practice

The best blackjack practice utilities I can find are, predictably, supplied by Michael Shakelford and Ken Smith:

Wizard Of Odds blackjack practice

It can be customised for number of decks and different rules. If you make a mistake, a box pops up with the correct play.

BJ info blackjack practice

Slightly more customising options, including the ability to switch off the trainer and a “fast” and “slow” setting. The fast setting I find still a tad on the slow side.

Blackjack resources on the web