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Blackjack


Blackjack table
• 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
• A few hands worth a second glance
• Doubling explained
• Splitting explained
• Some useful stats
• The “cut card effect
• Blackjack volatility
• Some blackjack misconceptions
• 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 (** see below) - 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).

(** In the European game the dealer receives only one card at the start of play, known as “European no hole card”; see the ENHC explanation below.)

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 the 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 the basic strategy section 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 fully 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.


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, as well as my basic strategy master for almost all possible rule combinations.)

The rules for the game this strategy applies to are: DOA, DAS, OBO (see the rule definitions below). The player totals are listed down the left and the dealer upcards are along the top, with hands divided into hard totals (ace counts as 1), soft totals (ace counts as 11) and pairs. As such, for a hard total of 13 vs a dealer upcard of 6, this is listed in the first chart at the intersection of the 13 down the left hand side and the 6 along the top, where the “S” tells you that the correct play is “stand”.

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

Hard totals
2345678910A
17SSSSSSSSSS
16SSSSSHH HHH
15SSSSSHH HHH
14SSSSSHH HHH
13SSSSSHH HHH
12HHSSSH HHHH
11DDDDDDDDDH
10DDDDDDDDH H
9HDDDD HHHHH
8HHHHHHHHHH

Soft totals
2345678910A
A8SSSSSSSSSS
A7SDDDDS SH HH
A6HDDDD H HHHH
A5HHDDDH HHHH
A4HHDDDH HHHH
A3HHHDDHHH HH
A2HHHDDHHH HH

Pairs
2345678910A
AsPPPPPPPPPP
10sSSSSSSSSSS
9sPPPPPSPPS S
8sPPPPPPPPPP
7sPPPPPPHH HH
6sPPPPPHH HHH
5sDDDDDDDDH H
4sHHHPPHHH HH
3sPPPPPPHH HH
2sPPPPPPHH HH


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 / “no peek” - 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 / “peek” - Original Bets Only. The dealer checks (“peeks”) 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.

• 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 when done in accordance with correct strategy - 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 / “peek”) 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 particularly 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%
• RSA: add 0.08%
• 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 - and 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.


A few hands worth a second glance


Here is a small collection of comment-worthy hands:

• 15 vs 10

Although not the most expensive mistake, standing rather than hitting this hand does cost quite a bit and it's also an extremely common error. Standing on 16 vs 10 is an even more typical play but it costs much less overall. If you always misplay 15 vs 10 you sacrifice an additional 0.14% of house edge, raising the overall casino advantage from 0.5% to 0.64%. This is a heck of a large increase for just one hand.

Other hands, such as 14 or 13 against 10, are even more expensive if misplayed, but players tend to hit them, and so play them correctly, more often.

• 10/10 vs 10

Some players love to split tens. This is always a bad play, but splitting them against a dealer 10 upcard is the single most expensive of all basic strategy errors (discounting purely masochistic plays such as doubling on 20), costing fully 1.32%. This is almost treble the house edge for optimal play, and it increases it overall to almost 2%.

• A2 vs 5

If splitting 10/10 v. 10 is the worst mistake, hitting A2 v. 5 is the least bad. It makes very little difference whether you double or just hit. But again, doubling is the marginally better play, so why not make it? If you want the precise EV numbers, the hit yields 0.137333, and the double yields 0.139852. To put that in context: on a £5 bet, the doubling is worth an average profit of £0.70 or 70 pence, and hitting gains £0.69, or 69 pence.

• 8/8 vs 7

This hand is intuitively a no-brainer: you've got a total of 16 against a dealer 7; stand, and you have nothing; hit, and you have a good chance of busting; split, and you have two decent starter cards to hopefully make two good hands. Pull a pair of 10s and you've now got two 18s. If the dealer draws a 10 on his 7, you win both hands. The mathematics bear out the intuition, also - this hand carries the single biggest difference between all best and second-best plays in blackjack: hit, and you lose on average about half your bet (-0.408); split, and overall you're a winner (0.218).

Yet I still see players standing on this hand; standing is the worst of the three options.

• 5/5 vs ?

If a player has to sit and think about whether he should play this hand as a starting total of 10 which, behind 11, is the second best non-complete two card starting total in the game, or split that 10 into two hands with a starting card of 5, which is the second-worst player upcard, that player should probably consider stopping thinking about blackjack right there and then. I can't attribute even the fuzziest logic to this decision. I can see how a player, looking at 10/10, can argue himself into the wrong play of splitting: “I could have two starting cards of 10, and 10 is a great starting card”. This ignores the fact that although 10 is certainly a great starting card, two of them together making a 20 is far better, but the fuzzy logic is perceptible. But I can't see any way of arguing yourself into splitting one great starting hand into two awful ones. I cannot see any redeemable aspect of this play, other than “I've got too much money and the casino hasn't”. Yet this uniquely kamikaze move is one that I've personally seen players make.

Don't make this huge mistake.

• “Even money”

This is the archetypal mistake, taking the even money payment option on your blackjack when the dealer has an ace showing. In fairness to the players who take it (almost all), it's not an expensive error, costing an average of just over one hundredth of a percent overall; it also reduces the volatility of the game slightly, as you always receive a one-to-one payment, as opposed to sometimes receiving three-to-two, sometimes nothing.

Still, refusing even money makes you more money overall than if you take it; why would you go out of your way to make less?

It's quite easy to work out why even money is bad: there are thirteen possible ranks of cards for the dealer to drop on his ace: ace, 2, 3, 4, 5, 6, 7, 8, 9 and the four 10s. If you take even money you receive one unit for each of the thirteen ranks, so 13 in total. If you don't take even money, you receive a one and a half unit payment for the first nine ranks, or 13.5 total (9 × 1.5 = 13.5) and you tie against the four highest cards. 13.5 is more than 13, which is why not taking even money is correct. I also touch on this subject in the insurance page.

I once saw a player ask for even money when the dealer had a 10 upcard! With only four aces in each 52-card deck this would be a hugely expensive play. Since it's against the rules, on this occasion the casino saved the player from himself and refused the request.

• A6

Soft 17, whatever the dealer upcard, causes trouble for many players, who seem to see the magic number “17”, which we know the dealer must hit to, and assume that the job is done. Actually, it never is - it is never correct to stand on soft 17. You should always take another card, unless the dealer has 3, 4, 5, or 6, in which case you should double if soft doubling is allowed.

Standing on soft 17, like 8/8 v. 7 above, is actually the worst option of the three when the dealer shows 3 through 6.


Doubling explained


The reason that doubling is correct in certain circumstances is that it's worth more to put out an extra bet and accept the restriction of receiving only one more card than it is to just hit as normal and maintain the option of taking as many more cards as you want - “extra money and one card only” beats “no extra money and as many cards as you want”. Many players baulk at the prospect of doubling at all, and it's true that several correct double plays are not at all intuitively obvious. I hope that the two sections below put to rest any and all fears about doubling.


• Hard doubling

Hard doubling, or doubling when you have a two-card score of 9, 10 or 11, often carries a certain intuitive logic with most players which doesn't need much explaining. With 11 you have an almost fifty percent chance of making 19 or better and almost one third chance of making 21. With 10 the chances are a lower but still good. With 9, many players start to hesitate: the best you can make is 20, if you hook an ace, and the more likely 10 only gives you 19. Any smaller and you're stuck with 18 or less. Consequently, many players shy away from doubling down on 9, particularly against a dealer 3. In fact, players will hesitate about doubling even on 10 or 11 when the dealer shows either a low or a high card, particularly a 2 or a 9.

Here are the values of the “dodgy doubles”, along with the values of the hit alternative:

• 9 vs 3: you average about thirty percent more value when you double
• 10 vs 2: this really is a no-brainer; doubling carries twice the value of hitting.
• 10 vs 9: doubling is about twenty five percent better than hitting.
• 11 vs 2: another no-brainer - twice as much value in doubling.
• 11 vs 9: doubling is about fifty percent better than hitting.
• 11 vs 10: again, about fifty percent more value in the double.

None of the above decisions is remotely marginal. The closest is 10 vs 9, where the double yields fully twenty five percent more value than the hit. Never be afraid of these doubles. Never be swayed by players who tell you they never double when the dealer shows a 2 because “the deuce is the dealer's ace”. If basic strategy says to double, put your faith in the numbers and push that extra chip into the box.


• Soft doubling

Soft doubling, or doubling when you have an ace plus 2 through 8, seems to be a mystery for many players. People who otherwise play sensibly, hitting their 15s and 16s against dealer high cards and not hitting bustable hands when the dealer card is low, seem to go all to pieces when faced with soft hands. As I mentioned above, many players routinely stand on A6. Worse still, I've seen players stand on A5, a hand which cannot be “hurt” with the draw of another card and doesn't even carry the “but I've got 17” erroneous logic of standing with A6.

Standing with A7 does seem to have more solid intuitive logic about it: 18 is a decent hand against a low dealer upcard, and in fact it carries positive expectation against all dealer upcards except 9, 10 and ace. However, it remains the case that doubling down on A7 against dealer 3, 4, 5 and 6 is still more profitable than standing.

Some soft hands are very marginal. The difference in value between hitting and doubling with A2 against 5 and A4 against 4 is extremely small. Still, if there's more value to be had by doubling, however small the difference may be you should always double.

One hand that even today causes me to scratch my head is A5 against 4. This double to me somehow just looks awkward. And yet doubling this hand yields almost twice the value of just hitting.

Correct soft doubling adds fully 0.09% to your game; if the house edge is 0.5% and you never soft double, your house edge increases to almost 0.6%. That's a substantial difference. Always soft double when it's correct to so do, trust the arithmetic and don't try to over- analyse your way out of it.


Splitting explained


Doubles require an extra bet. When you split, sometimes more than one bet is needed. In fact, if you can split multiple times and double after split it wouldn't be impossible to have ten bets riding on one hand - five splits and five doubles. Although that's an extreme scenario, having at least three bets on one hand, where a double opportunity presents itself after a split, is very common.

Although every double is not intuitively obvious - some players will watch you in open-mouthed amazement when you double A6 against dealer 3 - the concept of doubling is pretty easy to get your head around: you're in a strong position and you can take advantage of that strength with an extra bet. Splits are not so obvious, because the “I'm strong” concept in doubling is often absent. Some splits are fairly obvious: with two 8s against dealer 7, your current total of 16 looks pretty grim, whereas splitting it away into two hands with a fresh downcard of 8 for each looks very promising against the dealer card.

But what if you've got a pair of 3s against dealer 7 rather than two 8s? Nothing looks particularly strong here for the player, and the dealer has a good upcard. Why not just hit and lose one bet rather than splitting and losing two? Extend that to a pair of 8s against a dealer 9 and the logic really seems to fly out the window.

Crucial to understanding splits is that you're often in a lose/lose situation - neither the split option nor the non-split alternative yields a positive outcome. However, when it's correct to split, as in a pair of 3s against dealer 7, although neither hit nor split is positive for the player splitting is better because it's less negative - you lose less in the long run.

A useful way of getting your head around tricky splits is to think about exactly what your starting total is with and without splitting. For example, in the case of a pair of 3s, forget all about the “3” aspect and consider that your starting total without splitting is 6. This is the worst of all the upcards for both player and dealer. If you now look at the hand as a split, you have two hands with a starting total of 3. The 3 is not a particularly good starting card but it's a lot better than 6. Since, perhaps surprisingly, it's actually over two times less bad for the player than the 6, then putting out that extra bet for the split is the correct play.

This way you can rationalise the most perplexing splits, the 8s against dealer 9 and 10. With those two hands, our intuition really does work against what the numbers tell us is correct. This is the way the thought process goes: “If I split my 8s at best I'm going to make two hands of 18; the dealer's going to make 19 (or 20 with the 10 upcard) and I'm going to lose two bets rather than one.”. So put that intuition aside and think about what you've got right now - 16 - and what you'll have if you split - two starting 8s. It's true that an 8 doesn't fair well against a dealer 9 or 10, but it's vastly better than starting with 16. 16 against dealer 9 has an EV of about -0.50; 8 against nine is around -0.20, so two hands starting with an 8 against the dealer's card have a combined value of -0.40. The numbers for two 8s against dealer 10 are even closer, but it's still slightly better to split, because you lose less money.

The same is true of all these “awkward” splits - two 9s against 8 or 9, two 7s against 7, two 6s against 2 and so on. Putting out the extra bet and splitting doesn't turn a losing hand into a winner, but overall the value is higher and loses less in the long run.

To show that it's not all doom and gloom with the splits, here are all the hands that go from being losers to winners when you split: 3s vs 5 and 6; 6s vs 5 and 6; 7s vs 4, 5 and 6; 8s vs 2, 3, 4, 5, 6, and 7.

The icing on the cake is those hands that go from being winners to bigger winners by splitting: 9s vs 2, 3, 4, 5, 6 and 8.

As with doubling: when basic strategy says to split, always do so.


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!


The “cut card effect”


The cut card effect is the slight increase of the house edge in games where the dealer deals to a cut card, compared to games dealt from a continuous shuffle machine or any other setup where the cards are reshuffled after each round. The use of a cut card results in fewer rounds containing cards that favour the player - the 9s, 10s and aces - than when no cut card is used. Intuitively this doesn't seem to make much sense.

Let's say that on average the cut card is placed at a depth that yields fifteen rounds of play: the dealer starts dealing from the top of the shoe, the players receive fifteen rounds of cards, the cut card comes out, play for that shoe ends and the dealer starts the next shuffle. Now let's assume that, over the course of fifteen rounds of a particular shoe, there has been a marginal predominance of the bigger cards - the 9s, 10s and aces. These cards have the effect of requiring fewer cards to be dealt per round of play because the hands will need less cards to be complete.

To clarify this, imagine first a round of play where players see only 2s, 3s and 4s: hands using these cards will need as many as six or seven cards for completion. For example, with the dealer showing a 2, a player hand might be 2, 3, 2, 4, 3, and no hand will require less than three cards. Now imagine a round of play which is served by only 9s, 10s and aces: now, with only one exception (9s vs 9, which would be a split) no more than two cards per hand will be required, with the players standing on 19, 20 and blackjack.

Consequently, when those small cards predominate they have the effect of getting us to the cut card more quickly. The big cards are all waiting in the shoe to be dealt, but we don't get to them because the cut card comes out. However, when the big cards predominate, given that they result in fewer cards per round, we get to the cut card more slowly - and since we've been dealt a predominance of big cards, there are now small cards waiting to be dealt.

In summary: rounds of big card predominance result in an extra round of play which contains small cards, but this is not offset, when small cards predominate, by an extra round of play containing big cards. The cut card thereby manufactures additional play containing small cards. And small cards are bad for the player.

When a shuffle machine is in use there is no cut card, so this extra round of bad small cards doesn't exist. Voilà: the "cut card effect".

The effect is small, reducing the house edge by about 0.02%, or one in five thousand. If the house edge with a shuffle game is 0.5%, the same game dealt with a continuous shuffle machine is 0.48%.


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 a tad over 16.

Your results will fall within one standard deviation approximately 67% of the time; within two, 5%, and within three, just 0.030% 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 (one standard deviation) = 2.13.

Your 35-unit loss is therefore a little over two standard deviations; we know that results fall within two SDs 5% of the time.

As such, a 35-unit loss out of 200 initial hands will occur, on average, a little more than 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.


Some blackjack misconceptions


• “Blackjack is 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.



Previous
two hands
Outcome of this hand
Win %Lose %Push %
win, win43.247.88.9
win, lose43.247.88.9
win, push43.247.88.9
lose, win43.347.88.9
lose, lose43.247.98.9
lose, push43.347.88.9
push, win43.347.88.9
push, lose43.247.88.9
push, push43.247.98.9

(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.)


• “The dealer always wins because he plays last”

This one really in endemic - almost all players who feel able to express an opinion on the subject will tell you that the casino has the advantage in blackjack because the dealer plays last. The logic here is that the dealer doesn't always have to play out his hand, on those occasions when all hands have been busted, and so wins by default. This would imply that the casino has more of an advantage with fewer players, as with a full table it's very unlikely that all hands will be busted, whereas with just one player the dealer will often win by default when that one player busts.

The true reason that “the casino always wins” at blackjack, or to be more precise “the casino has an advantage”, is simply that the rules are configured in such a way as to ensure this happens - the dealer playing last is neither here nor there. To clearly understand this, simply exaggerate one player-friendly rule, for example the natural blackjack payoff of 3:2. If we simply increase that 3:2 payout to 2:1, or paying double rather than one and a half, the player now has moreorless a 1.5% edge rather than a 0.5% disadvantage. This is irrespective of the fact that the dealer plays last. In fact, a single deck game with good rules yields in itself a very small player advantage, without any unusual rule changes or additions, and notwithstanding the fact that the dealer plays last as usual.


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


• Blackjack forum online

Arnold Snyder's blackjack forum is a goldmine of information for both professional and casual blackjack players, provided by blackjack expert and author Arnold Snyder.

BJ hype vs reality deals with the inexperienced player's need to separate the wheat from the chaff when evaluating the vast amounts of advice available on the subject. How to weed out the charlatans and learn from the experts.

BJ basic strategy explains the logic behind basic strategy and presents comprehensive strategy charts; Snyder also offers a simplified version similar to my own “super simple strategy” - be assured that no copying was involved on either side.

Calculating the house edge for any rules set gives the effect on the house edge of the number of decks in play and all possible rule variations. The various rules are categorised by single, double and multiple decks.

Every option is good makes the point that no option is bad for the player, as any such can be used when correct and otherwise disregarded. He illustrates the point with the surrender option.

Shouldn’t you hit?” is an account of a round of blackjack in which four professionals played the exact same hand in four different ways, and each one was correct.

Betting and risk for the basic strategist gives precise expected return and risk numbers for the basic strategy player based on hands per hour, total hours played and standard deviation. This sort of information is almost invariably reserved for professional card counters, and it's a valuable resource for casual players who want to keep their play under control.

Interview with Ken Uston, flamboyant card counter from the 1960s and '70s whose exploits in team play and legal battles with the casino establishment gained him something of a legendary status within the game.

The MIT team: interview with Johnny C, manager of the Massachusetts Institute of Technology card counting team which took on Resorts International in Atlantic City in the late 70s and spread out into Las Vegas and ultimately abroad. A fascinating and absorbing read.


• About Casino Gambling

Blackjack basic strategy presents basic strategy in explanatory rather than the usual chart format, an approach which may be preferable for some players.

Rule variations is a brief explanation of the effect of rules changes on the house edge, with a small number of examples given.

Dealer bust percentages lists the average dealer bust rate for each of the ten upcards.

Blackjack continuous shuffling machine talks about the advent of the CSM, the reasons behind its introduction to the game, how the machines work and their effect, both negative and (slightly) positive, on the basic strategy player.


• Wizard Of Odds

Blackjack strategy and odds is the blackjack homepage of Michael Shackleford's excellent site, with links to the mountains of information available, along with the tools and calculators he has developed. If you were limited to just one blackjack resource across the entire internet, this would be the one to go for.

Blackjack house edge calculator produces house edge numbers for almost any conceivable set of rules. The house edge figure constantly recalculates as you reconfigure the rules.

Expected return for every play is a page of blackjack expected value charts for all play decisions for all initial three-card combinations. You need to hover the mouse over the charts to expand them to full visability.

Expected return using basic strategy is a chart giving the EV of every basic strategy play, along with two other charts listing the EV of the first two player cards and just the first card, again assuming the player uses optimal basic strategy.

Dealer probabilities from upcard lists the probability of all possible dealer outcomes (17 to 21 and bust) based on the dealer's starting card, for one to eight decks and both hard and soft 17 dealer drawing rules.

Standard deviation in blackjack is a comprehensive explanation of the topic, including a useful table which lists the probability of a given loss based on a given number of hands played.

Risk of ruin in blackjack gives the probablity of losing a given number of hands based on total hands played.


• BJ Info

Blackjack basic strategy engine generates basic strategy charts for any subset of rules.

Interview with “LV Bear”, a professional blackjack player and something of a cheerleader for the rights and fair treatment of professionals and “ploppies” (a rather disparaging word for uninformed gamblers) alike.

Interview with “MIT Mike” Aponte, a member of the MIT blackjack team, in which he details some of the fun, games and capers that were had by that famout / notorious team of blackjack advantage players.

Interview with Stanford Wong, one of the most highly-regarded authors of blackjack books, in which amongst other things he talks about his work with tournament blackjack and how he decided upon the curious pseudonymn he goes by.

Ken Smith’s blackjack blog, with posts on a wide range of blackjack issues.

Discussion forums, now for some reason no longer active, but archived as a useful source of information.

Blackjack tournaments, Ken's tournament homepage with links to all the relevant information.


• BJ21

Free discussion forum, Stanford Wong's public message board. There are also “green chip” and “black chip” forums available for a subscription fee.

Advantage casino play, in which David Matthews talks about the beginnings of blackjack and how advantage play developed.

The “Hail Mary” bankroll technique, betting large amounts in relation to your overall blackjack bankroll with a view to increasing it as quickly as possible.

Blackjack games to avoid, such as blackjack 6:5, continuous shuffle machines and hand-held multiple deck games effectively masquerading as single or double deck.

6 to 5 blackjack payout describes the circumstances of the genesis of the 6:5 blackjack payout, looks at negative player reaction and analyses casino blackjack returns with a view to establishing the profitability of the short-pay game.


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