1) The rules of the game
Black Jack is a card game. Nowadays it is mainly offered in casinos. The version of Black Jack played in private circles in the past was called 17 and 4. Despite a certain relationship between the two games, I will briefly explain the rules of Black Jack here, namely in the casino version I play:
Up to 10 players can sit at a Black Jack table. They are joined by the so-called dealer. The dealer deals the cards and pays out the winning bets, just as he collects the losing ones. He also has to monitor who has placed or not yet placed their bet, who is allowed to double or split and who gets paid out or can insure their Black Jack. In short, he is the game master.
At the beginning of the game, therefore, each of the players, participants, may place his or her bet. This bet must be between the minimum and the maximum bet, which is displayed above the table. The stakes are placed in multiples of the minimum stake. The reason for this will become clear later.
After the bets are placed, the dealer begins the dealing process. He places one open card on the table in front of each player in turn. Then he gives himself a card that is visible to everyone and then another open card to each player. Now he asks the players in turn what they intend to do.
The players’ options naturally depend on the aim of the game. The aim of the game is to get as close to 21 as possible. In doing so, the values of the cards are usually the value printed on them. This is true for the cards 2 to 9. But the cards 10. jack, queen king all have the same value. This value is 10. And the ace is also the most valuable card in this game. It counts as 1 or 11, depending on what the player prefers. A very special hand is any 10 + an ace. This is the so-called Black Jack. Not only does it, quite obviously, score 21, it actually counts for more than 21. It even counts for more than 21. A Black Jack is paid out immediately by the bank, and even with one and a half times the stake. However, this only happens if the banker does not have a 10 and an ace in front of him. In these exceptional cases, it could still achieve a tie. In the case of a tie, the so-called “stand-off”, the bet remains unaffected. It is neither won nor lost. This applies in all cases where the player and the banker have the same hand in the total.
The player therefore has a few options, subordinate to the aim of the game, depending on his own hand.
These options are as follows:
If the player is satisfied with his hand, he can simply say “rest”. The dealer moves on to the next player. Of course, hands that lend themselves to “rest” are usually particularly good hands. But even with bad hands you should often remain standing with the best possible strategy, because another “hit”, i.e. buying, does not promise you any improvement. Resten means as much as “to stand still”.
“Hit” could also be loosely translated as “buy”. If you decide to hit, you get another card from the dealer. This card is an improvement if you get closer to 21. However, it is a deterioration if you exceed 21. Then the bet is lost immediately. Example: The player has an 8 and a 4, making a total of 12. He decides to buy, dreams of a 9, would be highly satisfied with an 8, and immediately loses everything on any 10, i.e. on, 10, Jack, Queen or King.
If the two cards have the same value, there is the option of placing the basic bet again and continuing the game with two hands. After that, the same options arise again. However, the dealer will place another card on each of the split cards in any case. Example: The player has two 8s. He decides to split, i.e. he has to put another bet on the table in the amount of his basic bet. After that, the dealer places a card on the first 8. If the player is then satisfied with the hand, the dealer does the same with the next hand of the same player.
Note: Here, too, there are already different rules that are applied from casino to casino. The differences are: Are you allowed to continue splitting if you get the same card a second time? Another is whether you are allowed to double later after splitting (see point “double”). In addition, there are differences as to whether you are allowed to split 10s at all, and in particular whether you are allowed to split “any tens”, i.e. also a 10 and a queen or a king and a jack. This option does not entail any particular risks for the casino, since splitting 10s is generally very bad. The last difference is whether you get only one card after splitting two aces or as many as you want.
The standard variant of doubling is that after the first two cards you may (not must) double your bet if the sum of the two cards is 9, 10 or 11. This option was obviously invented for the benefit of the player, in that it is a “may” and not a “must” decision. So it can only be favourable or neutral. But still: the casinos vary the rules here as well. There are casinos that allow a “double any two cards”. This can tempt reckless players to double even with bad hands. On the other hand, this variant also has an advantage for the good player, as is to be expected: there are the so-called “soft doubles”. These are the doubles where the player has an ace and another card except a 10. So if you have an ace and a 6, for example, you could “safely” double. The hand is already worth 17 if you want it to be. It can get better if you buy an ace, a 2, a 3 or a 4. And it can only get marginally worse if you buy a 5 or higher (a 10 is neutral). But you can’t sell out in any case.
So, casinos that offer the “double any two cards” also give the professional player a favourable option if used correctly. The other rule variation is, as indicated above, the “double after split”. So you are still allowed to double after the split? Of course, this rule variation also only offers advantages to the player if it is offered and he knows how to use it correctly.
Insurance, almost all of which is of course English so far, is an option that was basically invented for the benefit of the casino. The rule itself is that the player may insure his bet if the banker has an ace as the first card in front of him.
In this case, the player can re-insure half of his bet if the banker has the ace. If the bank then buys a 10 to go with the ace, the player would lose his bet but get paid the insurance. The insurance, as the name suggests, is such that you get your bet back in full. So, if the player insured and the bank actually bought a 10, thus reaching blackjack, the player would be at par. All the stakes balance out.
Now, at this point I feel obliged to offer a little mathematical digression:
The insurance is taken out with half the stake. The payout for the insurance stake is the full stake, so the payout for the insurance number is twice the stake. So the payout ratio is 3.0. You have a basic stake of 10 euros. You insure the stake with 5 euros if the banker has an ace in front of him. You lose the basic stake if the bank buys the 10, because the Black Jack cannot be beaten. In return, the insurance sum is paid with 10 euros. The complete basic stake pays the insurance bet. You get back the entire stake, i.e. the entire 15 euros. If you now divide the 15 euros paid out by the 5 euros insurance stake, you get a 3.0. That is the payout ratio for the insurance bet.
Now we ask ourselves the question: How many cards are there for which I receive this payout? As is easy to count, there are exactly four. The 10, the jack, the queen, the king. However, there are not four in the whole deck. There are four out of thirteen. Because the other cards available are the 2, 3, 4, 5, 6, 7, 8, 9 and the Ace. That’s nine cards. So the division “favourable by possible” results in a 4/9 (also to be read in the chapter “how does an odds arise”). The correct payout ratio, i.e. the fair ratio, would therefore be a 9/4. However, you only get a 2/1 or, inflated (the mathematician calls such a thing “expanding”), an 8/4. The bank therefore has an advantage, provided the player insures himself.
Here are some comments on this: Not all casinos allow the player to insure himself. On the surface, this may seem like a protection for the player, as he is not tempted to make a bad bet. Nevertheless, for the professional player it is an option that can give him an advantage. This is because the professional player counts the cards and knows when the ratio of cards has shifted in his favour.
Another note: Many players “insure” their best hands. Black Jack in particular is usually insured. A 20 is also often insured. The players think like this: Either I win the game because the bank doesn’t buy a 10. Or I win the insurance because the bank does buy a 10.
This is a typical example of “sensory deception”. The bet that the bank will buy a 10 with its ace does not improve because you have a good hand yourself. These bets are independent of each other. If you have a blackjack, it cannot lose anyway, even if the bank buys a 10. So you will get paid out one and a half times your stake as often as the event “the bank doesn’t buy a 10” occurs. And that is often enough to justify not insuring. It is not much different with any other hand, even a good one. A 20 can lose even if the bank doesn’t buy a 10. And so on. Insurance is fundamentally bad. But for the professional player it represents an option that can also give him an advantage when the opportunity arises.
f. Special rules
There are already enough special rules presented above. One additional special rule that comes to my mind is the so-called “surrender”. In concrete terms, “surrender” means that after looking at the first two cards and the dealer card, i.e. when the dealer asks you what you intend to do, you can also choose this option. The dealer then takes half of the bet, and you as the player get the other half back. However, you then no longer take part in the game. Surrender = loss of half the stake.
From a casino point of view, this rule is like many others: The amateur players make even more mistakes because they give up the wrong hands, i.e. “surrender”. The professional player can also use this rule to his advantage.
Since I am referring to the book by Edward Thorpe, in which a few numbers and consequent playing strategies were not quite “right”: As I discovered at the time, Black Jack was also played in the 1960s with another kind of “special rule”: The dealer also dealt his second card, but this one was face down. And if he had an ace, after all the players had placed (or better still not placed) their insurance, he looked at his face-down card without turning it over. If he then turned it face up, it was clear that it was a 10, if he left it face down, it was clear that it was not a 10. This resulted in a completely different playing strategy against the ace, since one never had to fear the Black Jack.
So, in summary, the conclusion remains: in sum, all rules are set up in such a way that they give the casino an advantage or at least maintain it, even with rules that are designed in the player’s favour. Why the banks do not always and also not uniformly offer the options that would basically be to their advantage is that virtually every rule can be exploited in the professional’s own favour. The casino might not care about that either. Only: The bad player loses anyway. And he gambles anyway. So why give him another option? You can tempt him to make even more mistakes, but he can’t lose more money than he has with him anyway. On the other hand, you give every professional gambler another option that he can use to the disadvantage of the casino. So one simply leaves it alone again. This is how the different casino rules came about.
g. The further course of the game
So all the players have made their decisions. Those who have overbought have already lost, those who have 20 or 21 are waiting anxiously, those who have 13 or 14 are waiting rather resignedly, but what are they all waiting for? Well, for the dealer, of course. The dealer now deals his cards (where does this funny expression “he lays his cards” come from?). He has to follow absolutely fixed and uniform rules: “Dealer must hit to 16 and must stand on 17.” The dealer must buy if he has 16 or less, he must stand if he has 17 or more. If he has over 21, he is sold, as is the player. If he sells out, he must pay out all bets still remaining at the table (without odds; 1 to 1; exactly the amount bet can be won; exception: the Black Jack). Special case: If he buys a “soft 17” or also a “soft 18” with an ace, i.e. he could continue to buy without risk, he must stand.
This form of equal treatment, although urgently needed, gives rise to two curious cases: For example, the dealer has 16, all players have 15 or even less. So theoretically, the dealer would have more than any of the other players and would win all the stakes. However, according to the rules, he still has to buy. If he then sells out, he has to pay out all the stakes.
The other: The dealer has an ace, buys a 6 in addition, has 17, plus “soft”. But now all the players at the table have 18, 19 or more. In this case, the dealer is not allowed to buy and must pay out all bets immediately.
2) The Basic Strategy
The basic strategy gives you a guide as to what is the best decision in a given situation with a neutral count (what this is in the next section, but in principle the count is always “neutral” for those who do not count cards).
a. Hit or rest strategy
The buy strategy (or: when to hit or rest) looks quite simple: Against the small cards, that are the dealer cards 2, 3, 4, 5, 6 you buy until you could sell. After that you have to stand still, to rest. Since this danger already exists at 12, you should stand still at 12.
However, there is a small subtlety here: with 12 against the 2 you still have to buy. That is minimally better than standing still. And against the 3, buying at 12 is not a mistake. It is almost exactly as good as standing.
Against the cards 7 to Ace you generally have to play like the bank. That means you have to buy until you have at least 17. So at 16 you should buy, which often surprises beginners. They intuitively think the risk is too high, because you are already overbought at 6. So 6, 7, 8, 9, 10, Jack, Queen King you lose immediately. Nevertheless, it is correct.
Here, too, there is the peculiarity that buying at 16 against the 10 is irrelevant. One can just as well stand. Again, this knowledge is occasionally new or even counterintuitive even to experienced players.
I have studied many things in detail through intensive study of this game. Whenever I came across such a peculiarity, I was forced to think about it. And then, of course, one finds the reasoning (I only emphasise this here because even many professional Black Jack players sometimes did not know these subtleties. They learned the basic strategy, maybe even the adjusted strategy. But sometimes they didn’t know how to make the moves). So I always liked to ask the question then: Against which bank card is it more important to buy with 16: Against the 7 or against a 10? And the (often unknown) answer is: Against the 7. And it is so much more important that you can call resetting with 16 against the 7 a gross mistake, while resetting with 16 against the 10 is absolutely neutral, i.e. not a mistake.
For the sake of argument, of course there is no difference in terms of improving one’s hand. There is the same amount of favourable and unfavourable cards in the deck. The difference comes here: if you buy a favourable card against the 7, it very often also brings the profit of the bet. While an improvement against the 10 is usually still not enough. Intuitively, this becomes clear very quickly: the most represented card in the deck is a 10, which is in 4 times as often as any other. So the dealer will often buy a 10, with the 7 as well as with the 10. He makes 17 out of the 7 and has to stand. On the 10, he also buys a 10 and has 20. So if you only buy a 2 against a 7, you already have 18 and are a clear favourite. Against the 10, the 2 is of little help. Often enough, the set is still lost.
There is another subtlety in buying. That is the soft hands. And it is of course immediately obvious that with all soft hands you can’t sell out and you don’t have a hand yet (everything under 17 is not a hand, because all the hands always win only if the bank sells out; from 17 you have a hand. Because it can at least occasionally happen that you get a standoff, even if the bank doesn’t sell), must buy. No ifs, ands or buts. The questions always come up when you have a soft 17 or a soft 18. You could safely buy there too, but you can also lose something. If you buy a 5, 6, 7, 8, 9 with a soft 17, the hand becomes worse than it was. From my point of view, however, it is obvious that the multitude of improvement possibilities more than outweighs that.
Again, the reasoning: What you can lose is very little. In the case of soft 17, almost nothing. Because you only lose this minimal stand-off chance that the bank scores exactly 17. And a s tand-off is not even a win. The chance of that is small in every way and the loss is also minimal. So in an English book on Basic Strategy you would definitely find this sentence: Always hit on soft 17.
What is curious here is that newcomers or inexperienced players become unsure whether they should buy, especially with soft 17 against the 7. The thought that leads to the mistake is obvious: It could be that you yourself experience a deterioration and the bank then buys the 10 in exactly this game, as it of course happens most often. But that is not even the curious aspect. That is yet to come: against no card is it more important to buy with the soft 17 than against the 7. The gain in equity is by far the greatest. And that often enough causes confusion, but it is no less true because of that.
It is mainly because the stand-off is not particularly tempting. It is, after all, only half the swing one can have. Beyond that is the fact that for any given improvement, you immediately get a huge positive equity. If you just think about the minimal improvement that comes from an ace. Suddenly you have 18 and most of the time you win. There is also the circumstance, which has already been explained above: Even if, on the surface, you get worse if you buy a 5. One would then have and would only have to, but urgently, continue to buy now. In short: Basically, the 7 is a very favourable card for the player, which most players (also good) often do not know. But it is only good for the player because he has to make a hand under all circumstances, which increases the risk of selling considerably, but when you have made one, it usually wins.
So the strategy: always buy soft 17. And most importantly against a 7. Buying with the soft 18, on the other hand, could cause a little more difficulty. This soft hand is already worth something. You can actually get worse here, and not even insignificantly. Apart from the fact that you would even win against a 17 if the bank were to make one, you can also achieve the stand-off against the 18. And if you deteriorate, you can “give up the hand”. Nevertheless, I can tell you the strategy, but these moves are quite rare, and you often shake your head if you do what the strategy says. With a soft 18 you have to buy against a 9, 10 and against the ace. Intuitively, I actually find it both plausible and easy to remember. You have 18, the banker (probably) makes more, so you have to buy. Against all other cards, however, it’s a clear “rest”.
The reasons for the basic strategy of buying can of course be applied to other cards. It is quite obvious that all the cards where the bank then has a hand when it buys a 10 and thus has to stop immediately, give the player a certain strategy. You know what the bank is doing, so to speak. The 10 is in the stack 4 times as often as any other. The 7 makes 17, the 8 18 and so on. In this respect, you have a goal that you want to achieve.
If the bank has a 2 or any other card below 7, you absolutely don’t know what it will do. The effect that they, with the still most common combination of drawing a 10 and then another 10, naturally also “plays into the player’s cards”. The bank sells out much more often, that’s clear. But the fact that the hand the bank makes when it makes one is an arbitrary one is an additional demotivation for buying on the player side. Even a 20, if one should reach it, is still most often “killed” by the bank card 2 (except of course by the ace, where the black jack is threatening). Why just by the 2? In this sense, the 2 is obviously simply the most flexible card. It is the one furthest away from a hand, which increases flexibility.
b. Double Strategy
i. Normal double strategy
The “doube strategy” or doubling strategy is in principle quite simple and moreover not nearly as important as the hit strategy. Doubling situations are quite rare anyway, and the difference between doubling and not doubling is usually not even that big. Nevertheless, you should of course, as a professional player anyway, but also as a casual player, do it “correctly” if possible.
In contrast to the hit strategy, average players don’t make that many mistakes. When it comes to doubling, it’s probably the case that you intuitively do it right.
So here is the strategy: Never double against ace and 10. Doubling with 11 against 10 is extremely close to being wrong, but still. Intuitively, I think it is immediately clear: you can reach a 21 from the 11 with 4/13, but you can still lose even if the banker draws an ace! This not only costs (crucial) percentages, there is also nothing more frustrating than losing with 21.
If you are interested here why I had calculated everything myself: Edward Thorpe had declared in his book that doubling against both the 10 and the ace was strictly correct. My farsightedness at the time was not sufficient to attribute this to the rules used in America, according to which, as you can read above, it is already certain that the banker has no Black Jack, since he had already “controlled” the card, even if it had a 10. It’s just that the error seemed so serious to me that I didn’t even feel like bothering with it any more. Since this instruction was simply wrong, subsequent results would also be wrong.
In practice, by the way, it looked like this: one evening I was sitting at the gaming table in Baden-Baden, had 11 in front of me and the bank had an ace. I remembered Edward Thorpe’s recommendation that I should definitely double this set. At the same time, I had not only remembered but of course easily calculated that one should never insure. So I should double, but not insure? That seemed totally illogical to me. So I insured my set first, which probably caused some astonishment, not only from the croupier. Then, when it was my turn, I slavishly followed my book recommendations and doubled my sentence. My train of thought was something like this: “Either I get a 10 or the bank does. If both, it doesn’t hurt.” The croupier then said that if I wanted to double, I would also have to double the insurance. Well, I accepted that, it sounded logical. No question that I then received a small card myself as well as the bank, so I lost both sets. When I got home, I was naturally preoccupied with this decision. I never opened the book again afterwards. The result was clear: the instruction was wrong, it was not a double with 11 against the ace, and that too “by far”.
Against all other cards, if you don’t want to bother thinking, it’s simply right to double with 10 or 11. You get the 10 relatively often and then have an almost unbeatable hand. 20 or 21 are a dream, that is and remains so. The percentages that you gain with this are quite small, not only because of the relatively rare occurrence of the constellation. Nevertheless, doing the right thing remains the premise, quite clearly.
For particularly meticulous players, I would of course like to mention that doubling with 9 against 4, 5 and 6 at the bank is also correct. However, this gain is really only marginal. It is greatest against 6, against 5 and 4 it becomes progressively less important. Mistakes that are made often enough are not doubling with 10 against the 9. The players then feel the 9 is too good a card and don’t dare. It is nevertheless correct, but the gain from doubling is also small here. With the adjusted strategy, I myself almost regularly refrained from doubling when the count was in the red. It is simply too unimportant and quickly becomes completely ineffective.
Another question I occasionally asked other professional players was something like this: If you have 21, which bank card do you prefer to have it against? The answer comes hesitantly to not at all. But it is: against a 9. It also makes sense quite quickly upon brief reflection: the bank cannot reach 21 by buying one card, so it needs at least two cards. But the margin to 21 is smallest with the 9, insofar the banker most often has to stop before, after which you win immediately. The main reason is, of course, that the bank must immediately rest on the largest number of concrete numbers and you have won directly: These are the 8, the 9, all four 10s and the ace. If the bank has any other card, there are fewer, and with 10 and the ace at the bank, the reason is obvious: you can even lose.
ii. Soft doubles
Just for the sake of completeness I would like to mention this strategy here: Soft doubles are only possible against the bank cards 2, 3, 4, 5 and 6. Against these cards doubling is more effective the higher your hand already is. This is also a fact that is less known, and if known the reasons for it are often unknown. However, as always, it arises quite easily through good thinking.
Doubling with ace and 2 is much less favourable than doubling with ace and 5. This may be surprising, considering only the fact that with the same number of cards you also make the same hands. From soft 13 you make a 17, 18, 19, 20 and 21 respectively with 4, 5, 6, 7, 8. From soft 16 you make the same hands with the cards Ace, 2, 3, 4, 5. All these cards are equally represented in the deck. The reason lies a little deeper: the hand Ace 2 is much better than the hand Ace 5 when you have it in front of you without the doubling option. Because: if you were to buy an Ace, a 2, a 3 or even a 4 at soft 13, you would be allowed and urgently need to keep buying. You would still have no hand and would have no selling cards, so the hand remains “soft”. This improves your chances considerably compared to the hand Ace 5. With Ace 5 there is only the ace where you would be giving away marginally if you stood still. Otherwise, the other options are: Either you make a hand or you have to stand still. And that is more or less the same whether you double or not (with the exception of the ace).
In summary, this means that logically you would have the same equity if you double the hands. There simply cannot be any difference. The difference is in the initial equity of the two hands if you do not double. And this is usually so positive with ace 2 that you would reduce this positive equity if you were to double. The equity is still slightly positive with ace 5. It has to be positive for doubling to be theoretically justified (who wants to double their loss?). But it cannot be improved by buying without doubling, in contrast to the Ace 2 hand.
So, having first established that the aces with the larger side card are to be doubled, if at all, we would now have to determine which hands are suitable at all. For this we have to do a little preliminary thinking.
First of all, the small bank cards are more favourable for you in ascending order. So the 6 and 5 are most favourable for you (the difference between 5 and 6 is marginal. The reason soon becomes clear: 6 is higher and would therefore be less favourable for the bank in terms of selling. But there is just one of thirteen cards, namely the ace, after it has a 17 and may/must stand. This circumstance reduces the selling risk again). The 4, 3 and 2 become less favourable for you in descending order. The higher the banker’s card and your own side card, the more likely it is to be a double. This is a basic rule that can help avoid making big mistakes. This leads to a realisation that is really the only semi-effective one: ace 6 and ace 7 are the most important two double hands. They don’t take away much in terms of effectiveness, because although you would get the better hand with the soft 18 with the most common card, the 10, you would win much more often. On the other hand, you have more to lose. Because the cards 4 to 8 make a 0 out of your previously quite good hand. Of course, this rule still only applies to bank cards 2 to 6.
The other doubles are all unimportant, even if correct. Ace 2 is never a double, the hand itself is too good to double, as explained above. Ace 3 is a double only against 5 and 6. Ace 4 is double against 3, 4, 5 and 6. And Ace 5 against 2 through 6. Ace 6 and Ace 7 also against all, 2 through 6, as explained above.
c. Split Strategy
The split strategy is actually also quite simple once you understand a few basic concepts. Overall, learning it was a bit like school for me: if you have enough clues, the strategy can usually be deduced intuitively. Learning and remembering is replaced by a form of “oversight”.
The nightmare for the players at the table is, of course, always when the banker has a 10 or an ace in front of him. In this respect, it is hardly worth thinking about a split against one of these two cards. The only exception is the 8-card split. I’ll say straight away, though, that I don’t even look to see if it’s right or wrong. I know it’s almost indifferent (memory says split is marginally better). It’s a bit like choosing between plague or cholera.
You have, unsplit, a 16. That 16 is, philosophically, the furthest thing from a hand. Philosophically only because, purely mathematically, 16 is closer to 17 or 20 than 12 or 14. Nevertheless, it is further away because, in order to get a hand, you would have to buy. However, this buying involves the risk of selling. And this risk is higher at 16 than at 15, 14 and so on. A 16 would be a solid surrender against the 10. Surrender would be all hands (according to the rule description above) where the equity is below -0.5. The 16 against the 10 has an equity of -0.55. If you were allowed to surrender, you should do so, because you would then turn the -0.55 into a -0.5 (you would get half of your bet back).
Buying would only marginally improve this equity, if at all. What about splitting? And here we are with the cholera. If you split, you would first have to place your bet again. Then you would have twice as much money on a still hopelessly losing hand. The “normal case”: You buy a 10 on both 8s, have two (ridiculous) 18s, the bank buys its 10 and beats you by a long way. Not an enviable situation. Nevertheless, the two 8s are of course still much better than this 16. But double the stake for that? As I said, the difference is marginal. So even if you remember that you shouldn’t split against 10s and aces, you wouldn’t make a big mistake, guaranteed.
But otherwise the 8s are the cards that always have to be split. 16 is just too bad, against that you would have two 8s, that works. So: always split, against 2 to 9 anyway.
The 9s split is also quite a good split. You only have an 18 before, which doesn’t promise too much equity. After the split you have two 9s and quite a good potential to get to 19 with a 10, i.e. to improve. In this respect: always split 9s from 2 to 9 (this is where the mistake is most likely to happen. The normal players don’t dare because the bank card is too good. But it is really important because you lose with the 18 too often just like that). The 7 split is only good from 2 to 7. Intuitively clear: the 14 without split are hopelessly bad. Having two 7s is not great, but still good enough against 2 to 7. Against the higher cards it is clearly not worth it anymore. You have one (but nowhere near as bad as the 16) losing hand, a 14, and turn it into two losing hands, with no improvement. The 7 paired with a 10 makes a ridiculous and always inferior 17.
Note: there was a special rule in some casinos where I played, where you win something with 3 7s. I really played in many casinos and it is indeed advisable to inquire beforehand whether 3 7s are something special. I received a positive answer often enough. There were the following rewards (without claiming to be complete): A glass of champagne; Three 7s count like Black Jack; there is a special chip, a kind of golden chip, which also had quite a high value (I got one of these three times in Austria during a trip on 4 days; a night with the croupier, if female; but that only applied to me). So: ask first and then, of course, never split the 7s….
The 6s split is only good from 2 to 6. The 12s you would have are not a good hand. Two 6s are expandable. Especially against the small cards, where anything can happen to the player.
Two 5s, that really applies without exception, you never split. The 10s you have are a winning hand, at least very promising, normally a double. The split would also be like a double, but you would have two very bad hands (my father famously used to say when we were repairing bicycles that we “made a broken one out of three whole ones.”). It would be much the same if you split two 5s.
The 4s split is almost as bad. “Never split 4s. Nothing more to say about that.”
The 3s are fine to split again. The sum 6 is worthless. On the other hand, two times a 3 is expandable. Of course only from 2 to 7 at the bank. Cards above that become “too dangerous.”
The same applies to 2s as to 3s: Split from 2 to 7 at the bank.
That’s it. Simple, isn’t it?
3) Why does the bank actually win at all?
This aspect is also somewhat disregarded in the literature. One compares the game conditions and realises: All the advantages are on the side of the player. Why should the bank win at all? So why the question should arise at some point in a player’s career, in principle in every game, where is the advantage, for which side is it and how can it be fought, is clear to me. With Black Jack, however, it is not quite so trivial to understand this, as I had to find out again and again during my annoying round of questions. The player has absolutely the same rights as the bank, and even gets a few more options.
It looks like this: If the player has a Black Jack, he gets one and a half times the money. The bank, however, only gets single money for its Black Jack, if insured even none at all. Advantage for the player. The bank must buy at 12, 13, 14, 15, 16, the player may buy. Advantage to player. The player may double on 9, 10 or 11 (or even with “any two cards”), the bank may not. Advantage player. The player may split, the bank may not. Player advantage. If both have the same hand it is a standoff. In a standoff, the bet is neither won nor lost. So this rule is only balanced, fair. Surely there must be a banker advantage somewhere now?
I like to express this advantage like this: All equally good hands are standoff. Only when selling there is no standoff. When the bank and the player are sold, the player’s bet is lost. That gives the bank its advantage.
You can even express this as a percentage: The bank sells at x%, the player at y percent. That makes, in product, x * y per cent. No, wrong. Because these two events are not independent of each other (see also the chapter “Independent events”) because the player’s strategy is designed in such a way that he rarely sells himself against the cards where the bank sells frequently, and against the cards where the bank rarely sells, he sells himself frequently. The bank advantage thus amounts to only z percent.
This advantage is gradually compensated for by the rules that work in the player’s favour. The lion’s share of this is the Black Jack. For a Black Jack comes to 4/13 (the chance of getting a 10) * 1/13 (the chance of getting an ace) and the whole *2, since the order does not matter (ace or 10 first). So 4/13 * 1/13 * 2 = 8/169 and that is, generously calculated, 1/21. And at 1/21 you get half a unit for free. So 1/21 * 0.5 = 1/42, which is 2.38%. The remaining rule advantages always make up only smaller percentages and, depending on whether they are offered or not, the remaining bank advantage ultimately fluctuates between 0.4% and 1.3%.
4) The winning strategy
The fact that there is a winning strategy is solely due to the fact that information about the cards that have already been dealt is available, since they are lying face up, all the cards that have been dealt.
It is obvious that certain cards hold advantages for the player. These cards are, of course, the 10s and the aces. The combination of the two gives the player the dream of half the donated unit, which, as explained above, already “eats up” a large part of the bank advantage. In addition, there are the following advantages: if the bank has one of the small cards 2 to 6, these are the cards that the player would like to see in the bank, namely the 10s. From each of the small cards the bank sells itself, provided it draws two 10s. Although the probability of this is only 4/13 * 4/13, i.e. 16/169, about 1/10, it exists. There is also the advantage that 10s and aces are the player’s favourite cards when doubled. You score 19, 20 or 21 (unless you get an ace on your 11 in the worst case) and usually have a winning hand.
So the best cards for the player are 10s and aces. If they were just a little bit more frequent in the deck, then the minimal advantage of about 1% for the bank would be “used up” in no time and would work in the player’s favour…
Yes, and since you recognise this at some point (also recognised it long before my time), you have to recognise the situations in which the 10s and aces are more frequently present in the remaining pile. The recipe for success is: count, count cards. The very simple counting method is really manageable for everyone, I dare say. You count the 10s and aces with the cards 2 to 6, both of which add up to 5 of the 13 cards. 2, 3, 4, 5, 6 are 5 of 13 and 10, Jack, Queen, King, Ace are also 5. Now you simply count every card 2 to 6 as plus 1 and every card 10 to Ace as minus 1. The 7, 8, 9 are neutral, so they count as 0. You do this in such a way that with a little practice you can record the total hands dealt before the dealer makes his final round. So there are two cards in front of each player and one card in front of the dealer. Then you record the hands, because you also get some time. Each hand is a 0, plus or minus 1 or 2. Then you have a count of -2, let’s say, for the hands that have already been dealt. Then the cards are dealt one by one, not as quickly as during the first deal, because they are dealt on the basis of a decision and not, as in the beginning, anyway (because there are really card artists as dealers who deal so quickly that you wouldn’t be able to keep up). Then you have a count for this one game, for example +1. For the games before, I (and also most of the other professional players I met) had a stack of chips or a chip arrangement in front of you, which shows you the count in this sledge so far (in the so-called sledge, all cards are placed in the beginning, as I said, in the final phase up to 6 packs of cards, for dealing and not visible to the player). So you then add this +1 to the previous count.
The way I counted with the chips was different. Above all, depending on the casino, they didn’t want to make it too conspicuous. This meant that I occasionally counted with only two chips. I set one to a time (practically every chip has some kind of imprint that makes this possible) and then, depending on the sign of the count, I put the other one on top or just leaned against it. Putting it on the chip stood for plus, putting it next to the chip stood for minus.
When the count reached a certain positive number, the game was classified as an advantage game. Part of the strategy was, of course, to play all the games in which you had a disadvantage as small as possible. The fact that you had to play at all was, of course, to keep your place. If you skipped one or two games, the coach would ask you if you didn’t want to play any more, because there would be a lot of players on the waiting list? So you were more or less forced to play the games with a disadvantage. But if you then had an advantage, it was clear that you had to play as much as possible. So that was usually the maximum that was allowed.
A few more things that had to be taken into consideration and, if necessary, included: There was, of course, an absolute count. That was the number you had counted with the chips or whatever. In addition, there was a remaining pile of cards. And this could be of different thicknesses. That’s why we spoke of the “running count”, which was the absolute number, and the “true count”. The true count was the count per deck. So you had to estimate the remaining cards to get the true count. The best way to do this was to count the number of hands that had already gone through in this slide. Each hand at the table of 7 has two cards plus the banker has at least two cards, plus the required purchased cards for the banker and the player, and that gave something like an average of 20 cards per hand played. So 5 hands played were two decks. But you just developed a certain routine in that. You couldn’t look into the slide (there were also different ones that could allow you to do that, but it was a bit embarrassing to look in there), but the cards that were played were usually put in a pile and by the height of the pile you could estimate with experience the cards that were played.
In addition, there was the problem of the ratio between minimum bet and maximum bet. The higher this factor, the more favourable the conditions. It was essential to find this out first. In the Europacenter casino in Berlin, the ratio was 25:1. The minimum bet was 10 DM, the maximum bet was 250 DM. That’s not a very unfavourable ratio, but as has been mentioned several times, the conditions in Hamburg were better in every respect. In Hamburg the ratio was 50:1. 10 DM minimum and 500 DM maximum.
Another problem was when to set the maximum in the first place. And there were obviously different views on this. My numbers showed that I should play the maximum from a true count of +3 per deck. The other pros I met rather claimed that you should only play from 3.5 or 4 per deck (playing means maximum, of course). I guess that was book knowledge. The effects of adjusted strategy were perhaps not considered?
The last aspect was the budget one had. Of course, if you go in with 3000 DM, it doesn’t necessarily make sense to then play one game, or even, if it was possible, two boxes at maximum A box is marked on the game table where a player places his bets. Of course, I very often didn’t go alone, so you had two boxes anyway. In addition, however, you often knew at least one player at the table after a while who either also played quite well or who, if you placed your bet at their bet, which was possible up to the maximum, made the decisions that you yourself would have liked to make, i.e. simply subordinated yourself to the decision. Certainly that also happened when you had played in one place for a while. So the maximum applied per box, not per player. Nevertheless, the budget also played a role. So occasionally, depending on the budget, one had to vary the stakes oneself a bit differently from minimum – maximum, for reasons of common sense.
5) The adapted strategy
So if you wanted to exploit all the elements, you also had to adapt your strategy to the count. I don’t have these details in my head, nor can I read them in any documents (I once had quite a few saved on some old computer). But I’m sure I can’t get to the hard drive any more). Nevertheless, I can both read up on them at any time (these data are on my current computer) and remember well which decisions were close or very close. And from this I could very well deduce the critical decisions that really mattered.
Basically, you have to distinguish between games where you play minimum and where you play maximum. That is quite clear. Nevertheless, the following aspect is often neglected, even by professional players: the minimum games have a much lower stake. This means that the decisions are less important. But: The minimum games occur much more frequently! It used to be that you could play every 10th to 12th game with maximum. So if the ratio was 25:1 and you played every 10th game with maximum, then the betting ratio was still only 2.5:1 in favour of the maximum games, and this number is calculated on the stakes. So one stakes only about 2.5 times as much money in total per evening in the apparently so important games.
Against this background, the decisions of the adjusted strategy also become important in the case of a negative count (of course not at 0, because adjustment was only related to some count other than 0. The basic strategy is calculated on the balanced count or on “no information about it”.
The important adjustments for a negative count here: The limit when one had to buy with 12 and also with 13 against 2 and 3 was relatively low. And also the hit with 12 against 4 became correct relatively quickly (i.e. with only a small negative count). Depending on the quality, one should refrain from doubling and splitting quite early. The problem with negative count is not so much that you make bad hands yourself. You make them often enough anyway, with this count and that count. The problem is that the probability of the bank overbought becomes successively smaller. The bank always makes a hand or sells out. But the player does not know the hand yet and is in the dark. The selling of the bank thus becomes the essential parameter. By the way, one strategy was also very important for adaptation: going to the toilet, ordering a coffee, briefly greeting a friend or acquaintance. It is best to always adjust all these activities to the games with a very negative count and not to play at all.
As far as I know, the adjustments with a positive count were dealt with much more intensively in the literature. Because there was a lot of money in it. Here, one had to urgently refrain from hitting with 16 against the 10, if the count was only slightly positive. The hit against the 9 was also soon overturned. The hit at 15 against the 10 shortly afterwards. In addition, however, there were a few expert moves that I honestly never made: The 10s against the 6 or the 5 could be split if the count was high. But I often didn’t even bother to ask in the casino whether I was only allowed to split 10s of the same kind or “any tens”, i.e. also Jack and King. I simply didn’t do it. But that was also a budget question. With too small a budget, it doesn’t seem to make much sense to me to rip apart a 20 and then have double the money on two still uncertain hands. I guess I’ve also fallen victim to a supposed “security mindset”. Equity is equity. Security is illusion.
Of course, another important adjustment was to insure against blackjack. This can be determined with a simple calculation: If the count per deck is +5, then on average there are four 10s and one ace more in the deck. Normally, the calculation is 16/52 or, shortened, 4/13 for the probability of getting a 10 with a neutral count. At +5, there are four more 10s in the deck calculated on 52 cards. That makes a chance of 20/52 for a 10. You would need a chance of 1/3 to have a good bet, since the insurance is paid twice. So with this (monster) count you would have fair odds of 52/20 and get paid out 60/20 or 3:1 (3 to 1 because the stake, unlike betting, stays put and is paid twice; nevertheless, this corresponds to a payout ratio of 3.0 or 3:1).
The count for insurance therefore only needs to be slightly positive to make it a good bet. A positive count of +1.66 per stack (the true count) would be enough to make the insurance a good bet. I will not calculate why here. For the sake of understanding, our maths teacher always said, for all the tasks he couldn’t figure out himself, “The rest is homework.” That’s how I do it too…