This free course on blackjack and card counting was created by the GameMaster, publisher of the GameMaster Online website. It is reproduced here in its entirety with permission of the author. His 24-lesson course is an excellent introduction to winning blackjack.

To start at the beginning, visit the Welcome page.

### Basic Strategy Variations

**Casinos that offer single-deck Blackjack games are very aware that it can easily be beaten by a counter who uses a big bet spread, so trying to play the game with a 1-12 spread like I recommend for 6-deck games will likely get you a one-way ticket out of the casino, pronto.** That’s not to say you’re going to get “backed-off” if you bet more than 5 chips on a hand, but I think it’s fair to say making $$$ at a good SD game requires a bigger bag of tricks than needed against a 6-deck game, so altering the play of your hand according to the count is a logical place to start.

**If you know how to count cards, you can use the count to tell you how much to bet on each hand, but you can also use the count to help you play each hand more accurately, too.** If you’ve studied my course up to this point, you know one of the key factors in playing a winning game of Blackjack is to leave the table when the True Count drops to -1 or lower, but that tactic isn’t very practical at a single-deck game, because only a few rounds of hands are dealt before the shuffle.

**Consequently, you have to sit through a lot more “negative” decks, but the good thing is that a shuffle is never too far away.** Yet, at the same time, we all know the casino’s edge increases as the count drops, so we want to neutralize the effects of that as much as possible. Because you’ll be sitting through many more negative counts at a single-deck game, what we need to do is learn the plays for hands like hitting 12 against a dealer’s 5 and so forth. We also want to avoid doubling and splitting pairs in low counts and we’ll hit instead. But we don’t want to guess at important plays like that, so we’ll need to learn Basic Strategy variations for “lower” numbers, like -2, -3 and so forth. A realistic range for most single-deck games is a True Count of -6 to +6 and that will cover 85% of all the hands you’ll ever play, assuming 63% penetration which is about as good as it gets. In a later lesson, I’ll talk about the importance of penetration, but for now, trust me on this.

**Some players prefer to learn just the indices for the most common hands, with the idea that they’ll get a hand like A, 4 against a 5 less than 100 times in every 100,000 hands of play, but they’ll have a 16 against 10 much more often.** In his book, “Blackjack Attack”, Don Schlesinger devoted a chapter to what he calls “The Illustrious 18” that are, in his opinion, the most important Basic Strategy variations. I’m not big on reproducing other authors’ original works, so I’ll refer you to the book for a complete listing if you feel you’d rather not memorize all of the variations I’ve listed here. Another idea worth considering is to not learn the indices below -2, with the rationale that you’ll likely be betting the minimum in such a count, so any playing mistakes will, in the long run, cost you very little. Or, you might want to learn only the indices where you’ll be placing extra bets on the table, as in doubles and splits, with the idea that, if I’m going to be putting more $$$ on the table, I’m sure as hell going to play the hand correctly.

**But I’m of the opinion that if something about this game can be learned, it should be learned.** (Okay, I know I’m a fanatic for this stuff, but what can I do?) If single deck games will be where you’ll spend most of your time, then it’s probably worth the effort to memorize the 90-odd indices presented here. But if this isn’t your primary game, a range of -2 to +6 with some judicious editing will probably suffice. Don’t forget that some of these indices are similar to those for a multi-deck game, so you won’t be starting from scratch. Learn those numbers you think are important for where and how you play.

**Rather than talk you through each hand’s variation, as I did in the multi-deck section, what I’ve done here is produce a Basic Strategy Matrix that shows an “index” number for each appropriate play.** Don’t worry if you have a problem understanding it, because I’ll explain it all at the bottom.

**Basic Strategy Variations Matrix**

Single Deck, H17, Da2, no das, no surrender

**See the matrix. (Use your back button to get back here.)**

### Using the Matrix

(GM Note: The Basic Strategy for this game is available from BlackjackInfo.com: 1D, H17, DA2, NDAS Basic Strategy)

The general rule for understanding the Basic Strategy Variations Matrix is this: **If the number in a slot is 0 or a minus, then that play is a Basic Strategy move that you should make as long as the count is higher than the number shown.** For example, with A, 6 vs. 2, you will double as long as the count is 0 or higher. If the count is minus, just hit. In the case of 9 vs. 4, you’ll double as long as the count is -2 or higher (remember that -1 is “higher” than -2). For a hand of 9,9 vs. Ace, you’ll stand as long as the count is 0 or less. If the count is higher than 0, you split the 9s.

**It’s a lot easier to use the matrix if you’ve memorized the Basic Strategy for this game but if you haven’t yet done that, you really should learn it before you get into this advanced mode of play.** For each player hand and dealer’s up card combination you will see either a specific action, such as hit, stand, double, etc., or a number. The number is an “action point” based upon the True Count and it keys the variation. As to what the proper variation is for a situation may get a little confusing, but if you study the hand in question, you can usually figure it out. A good example of this is A, 7 versus a dealer’s 2. In the matrix, you’ll see the number 1 in that spot, so do you hit or stand or do something else? Well, “something else” is the answer, so you should double, just as you do with A,7 vs. 3, 4, 5, and 6. Logic plays a role here, so if a play sounds illogical, it’s probably the wrong one. Would you really hit A,7 against a 2? Of course, you might stand, but that’s already the Basic Strategy play, so doubling is all that’s left. Consequently, what this is telling you is that you should double A,7 against a dealer’s up card of 2 when the True Count is 1 or more. If the True Count is less than 1, use the Basic Strategy play, which is to stand. Against a 3, Basic Strategy says to double A,7. But the index for that is -1, so that’s telling you to double A,7 vs. 3 only if the True Count is -1 or higher. If it’s not, then you should stand.

**Let’s talk about another variation that may cause some confusion: 8, 8 vs. 10.** The notation in that box is “Stand@6”, so if the True Count is 6 or more, you will not split the 8s, but stand instead. Another hand that draws a lot of questions is 7, 7 vs. 10. Yes, Basic Strategy is correct when it says to stand with 7, 7 vs. 10 in a single-deck game, mostly because the dealer either has a good hand, like a 20 or s/he is “stiff” and we’re hoping for a dealer bust. Because you already have 2 of the four 7s in the deck in your hand, the odds are greatly reduced that you can beat a dealer’s 20 by catching another 7, so the mathematics work out that you’re better off standing and praying. But it’s a close call, so if the count is below 0, you should hit. This means that if the running count is -1 or lower, you should hit 7,7 versus a 10, not split. If the count is 0 or higher, stand.

**Now, take a look at the Hard Totals section, where I have 2 different types of 16s: a 10,6 and a 9,7. ** In the 10, 6 row there’s a “4” under the dealer’s 10 and a “0” in the 9,7 row. This is what’s called a “composition-dependent” play and I included it for several good reasons. First of all, 16 vs.10 is a relatively common hand and you can see by the numbers that there’s quit a difference between how the two 16s should be played. What the variations matrix’s saying is that you should stand with 9,7 at 0 or higher, but stand with 10,6 only when the True Count is 4 or more. This is quite a departure from what we do with a 16 vs. 10 in a multi-deck game, where we stand only when the count is more than 0 (i.e., a running count of 1). Just a side note here: there’s a lot of confusion about this play in my multi-deck section, but what I do is stand with 16 vs.10 when the running count is 1 or more, otherwise I hit it. What you do when the count is exactly 0 doesn’t really matter because the expected value is the same for either play. The same is true for a hand of 9,7 vs. 10 in a single-deck game.

**Anyway, why would we stand with 10,6 vs.10 only when the True Count is at 4 or more?** It all has to do with the total number of 10s in a single deck, which is sixteen and you already have one of them in your hand and the dealer is showing one as his up card. That’s two less 10s that can bust you and two less 10s the dealer can have in “the hole”, so it sways the decision away from standing toward hitting more aggressively. Look, a hand of 16 is never going to be great, regardless of how you play it, so all we’re really doing is trying to minimize the damage. Hitting 10, 6 vs. 10 until the True Count is 4 or more helps with that process.

In the row for 6,6 you’ll see a notation under the dealer’s card of 7 like this: Split@<0 and that means, "split a pair of 6s versus 7, if the count is below 0."
**I don’t want you to leave without me telling you the most important variation of all, which is the Insurance bet. ** You hopefully know that proper Basic Strategy tells us to never take insurance (even when you have a ‘natural’ and the dealer’s up card is an Ace, in spite of what everybody else tells you), but in a single-deck game, the insurance bet becomes profitable at a True Count of 1.4 or higher.

### Learning the Basic Strategy Variations

**Once you’ve chosen the Basic Strategy variations you want to learn, you should make a set of flash cards for them.** Exactly how to do that is explained in Lesson 14 of “The GameMaster’s Blackjack School” and I cannot over-emphasize their value. Make up a set and carry them with you, or at least study them intently before each playing session if single-deck Blackjack isn’t your “primary” game.

Hi , thanks for this lessons.

I have a question : which method is used in the Basic Strategy Variations Matrix( for counting 1 deck )? the hi/lo or the‘Hi-Opt 1′ ?

it’s written that for counting one deck it’s better to use ‘Hi-Opt 1′ but i’m not sure on which of this 2 system is based the matrix that i have to learn

Thanks Lorenzo

I believe those indexes are for Hi-Opt 1, and I am really surprised at how much they differ from Hi-Lo.

This is another aspect of the GameMaster School that I did not closely audit when publishing.

I definitely need to take a closer look at them and make sure they are good numbers for Hi-Opt I, and make that clear. Thanks!

Are matrix numbers available for the new single deck ‘6 to 5’ games? Particularly with doubling allowed only on 10 and 11, and doubling allowed on splits. Or maybe a ‘best practices’ substitute?

Thanks for the online BJ course.

Steve

Two things:

1) It’s going to be tough to beat 6 to 5 counting. The starting house edge is just too high.

2) There are no changes in either the strategy or the index numbers due to the rule changes. (Just ignore the ones you cannot use because of rule restrictions.)

But you should seriously be looking at the 6-deck games that pay 3:2 instead of playing the single deck 6:5 games.

hey can you really go through a card game in 10 seconds? I can’t even flip the cards in a deck in under 20 and thats when i’m not even looking at the cards

Remember you are flipping through the deck 2 cards at a time. Still, the GameMaster’s time of 10.5 seconds is very fast. I don’t think I was ever that fast, but frankly, it’s not something I have practiced in a long while. I know my speed is just fine at the real game.

I’ve never been to a casino, I’m actually not old enough, how long do you have to decide what to do on each hand? And do you have any tips for keeping track of the count while at the same time adding and subtracting new totals?

Most decisions at the table are made pretty quickly, but you won’t be bothered about it unless you take more than 20 or 30 seconds to decide.

As for how to keep track? Practice, practice.

If you play the game with no variation, only change your bets can you still achieve an advantage or is variation play integral for this to occur?

Yes, you can profitably play without strategy variations. Bet variation yields the majority of the profit, with strategy variations just being the extra on top.

I was wondering how much it’s actually realistic to make assuming you make no major mistakes and you keep track of the count. Saying that the casino has a 1 % advantage they’ll win 51 hands and we’ll win 49. We say that we only have 2 bet sizes, 5 and 10, min and max. We say that we’ve been counting and betting higher when the count is high and lower when it’s low and we’ve come out with 51 L: 41 min + 10 max = -305. 49 W: 24 min + 25 max = 370 so on average for 100 hands we’ll have earnt 370-305 = 65. Saying we take the standard approach of initial money 40x max bet our initial capital is 400. 65/400 = aprox. 16% increase per 100 hands so if you take a conservative approach of 100 hands per hour you’ll have doubled your money in 6 hours. 16*6=96.

I just wanted your input on wether these numbers are reasonable and realistic or if not then what your thoughts are on eventual profits and how much you yourself would expect to make on an average night

Your estimates have a lot of problems. Even your first calculation of 51 vs 49 yields the wrong answer… That would be a 2% house edge, not 1%. But honestly, you can’t even come close to understanding blackjack with a simple wins/losses idea. It’s too complex for that kind of simplification.

My advice? Ditch all the manual calculations. If you want concrete numbers, either run the sims yourself using something like the CVData software, or buy a book like Blackjack Attack where all this work has been done for you.

The bottom line is far less lucrative than your estimates. Assuming decent conditions, a card counter’s advantage is usually around 1% of his total action. In 100 hands, your profit is probably a couple of your minimum bets. And you’ll need to spread far more than $5 to $10 to make any profit at all. (The house edge can’t be overcome with such a small spread.)