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: Double?

**The opportunity to double your bet in return for agreeing to accept only one more card is a very powerful option for the player, if it’s utilized correctly.** I can’t tell you how often I see players double hands like 7 or 8 against a dealer’s up card of 6 and then bemoan their fate when they lose. Yes, the dealer is very vulnerable with a 6 showing, but placing an extra bet changes the mathematics of the hand, so all doubles must be well-considered. For example, in a six-deck game where the dealer stands on A-6, doubling a hand of 8 against the dealer’s 6 has a total return of 10.3% whereas just hitting the hand returns 12.3% and the risk is lower!

**That said, there comes a time when it is worthwhile to double an 8 against a dealer’s 6 and that’s when there’s a higher proportion than normal of 10s left in the deck.** That point is determined, of course, by the true count. As the true count gets more positive, it becomes more profitable to double. Conversely, as the count goes negative, it becomes a better play to hit some hands, rather than double.

**Just as you’re using flashcards to learn the hit/stand variations, make up, a set for doubling.** Here are the numbers you need:

### Basic Strategy Variations Six decks, dealer stands on A-6

There are slight differences in the GameMaster’s index numbers published here and the optimized numbers on the

BlackjackInfo Advanced Blackjack Strategy Cards.

These differences are usually due to the use of risk-averse calculations by the GameMaster. I maintain that for the majority

of players (who are not playing near the maximum Kelly fraction of their bankroll), straight indexes are preferable to

risk-adjusted ones. In any case where risk-averse indexes differ from straight indexes, even by several points,

the decisions are quite close and the effect of choosing one index style over another is minimal.

**Soft Doubling**

A-2 vs. 4 | Double at 3. | (Got this? Basic strategy says to HIT A-2 against a 4, but if the true count is 3 or higher, you should double.) |

A-2 vs. 5 | Double at 0. | (Don’t get confused here. Basic strategy says DOUBLE A-2 against a 5, but if the count is at all negative, just hit it; double only when the count is 0 or higher.) |

A-2 vs. 6 | Double at -1. | (or higher. As long as the count remains above -1, you’ll double; once it goes lower than -1, you’ll just hit — then hopefully leave the table if the count doesn’t improve.) |

A-3 vs. 4 | Double at 1. | |

A-3 vs. 5 | Double at -1. | |

A-4 vs. 4 | Double at 0. | |

A-7 vs. 2 | Double at 1. | |

A-8 vs. 4 | Double at 5. | |

A-8 vs. 5 | Double at 2. | |

A-8 vs. 6 | Double at 1. | |

A-9 vs. 5 | Double at 6. | |

A-9 vs. 6 | Double at 5. |

**Hard Doubling**

8 vs. 5 | Double at 6. |

8 vs. 6 | Double at 3. |

9 vs. 2 | Double at 2. |

9 vs. 3 | Double at 0. |

9 vs. 7 | Double at 6. |

10 vs. 9 | Double at -2. |

11 vs. A | Double at 1. |

### Homework

Make up a set of flashcards for these variations and begin working them into your game.

I am a fairly successful speed count player switching over to the Hi Low system. I see that the Hi Low system is much more powerful system. In many of the variation decisions it is unclear in several cases if the count is true or running. Please advise if possible. Also I am an Atlantic City BJ player with 8 decks. Are the above rules almost the same as 6 decks?

Michael

The strategy indexes are all for true count. The only time you can use the running count is for the decision of 16vT where the index number is 0. (A true count of 0 or more is the same as a running count of 0 or more.)

You can safely use the same strategy and index numbers between 6 and 8 decks.

Here in the Mid-South and Gulf Coast – Dealers hit A,6 – they do not stand.

How does this process affect “doubling?”

For a basic strategy player, see the Strategy Engine for the correct plays when the dealer hits soft 17.

If you’re asking how the strategy variation index numbers change, many of the index numbers are the same between the 6D S17 game and the 6D H17 game.

Most of the few differences are only a single point here and there.

The most important index change between the games is 12v6. In the S17 game, the index is -1. (Stand at -1 or higher.) In the H17 game, the dealer is more likely to bust with a six showing, and the 12v6 index falls all the way to -4. (Stand at -4 or higher.)

My Advanced Strategy Cards have optimized index numbers for all of these games.

Ken Smith, do you sell the individual advanced strategy card for 6 deck blackjack where the dealer hits on S17? I can’t find it as one of your individual cards and don’t have any interest in purchasing a full set of 6 to get 5 I don’t need.

Sorry, I don’t currently sell the advanced cards individually. My entire stock is already packaged in sets.

I found it available on a different site. Thanks!

Why do some of your indices differ from Wong’s when using the same benchmark rules? For example you that the index for a hard 8 v a 6 is a double at TC 3, whereas Wong says it is at TC 1. There are quite a few other examples that differ greatly from yours can you explain why.

Index generation is trickier than it sounds, and some indexes are close calls over a range of numbers.

I’m not sure what process the GameMaster used when creating his, but seeing small differences in some numbers is not surprising. He did say that his numbers were risk-adjusted indexes. (My opinion of RA indexes is that for the vast majority of players, they are not appropriate. Almost noone plays close enough to Kelly betting to make them relevant.)

I spent many hours fine-tuning the indexes on my advanced card set, and they are straight indexes, not RA. For this game my index for doubling 8v6 is TC +2, which happens to fall right in between Wong and GameMaster.

The good news is that even a 2-point difference in some numbers will not affect your results much, because the EV in these close call cases varies only slightly from one index to the next. The decisions where the differences are more pronounced are generally going to also be those where everyone agrees within a point plus or minus.

Thanks for the detailed answer Ken its appreciated. I always thought counters played more aggressively than the kelly due the fact that extremely high counts are rare. It was my understanding then that it is best to get your max bet out at TC 4 or 5. Don Schlesinger for example plays an extremely aggressive spread where his units go up to two as the TC increases slightly. Is this not a normal betting spread for a counter? Do you recommend playing a half Kelly? Or is this all personal preference depending on how high you want your ROR to be.

The Schlesinger spread you mention would be pretty normal. Optimal spreads will usually get your top bet on the table at +5. How you get there does influence your results, but really not all that much. Any ramp that gets you from your small bet at < +1 to your top bet at +5 is going to perform pretty well. My comments about RA indices and Kelly are based on the fact that almost all players undercount their bankroll, considering only the cash they have on hand at the moment for gambling. In truth, their effective bankroll is much bigger; they can replenish funds from other income sources, and they probably also have other assets that could be counted. Once you get into a large enough bank that these factors don’t overwhelm the accounting, you can probably safely afford to bet more than you can easily get away with anyway. If you still are in a place where these calculations have value for you, then yes, betting half Kelly is a pretty good target in my opinion. There’s still plenty of excitement in that.

I got into an argument with my dad about progressive loss betting systems. His argument was that in a casino where the minimum was extremely low and the maximum was extremely high the casino could be beat.

For example, say a casino offered a game with a 10 dollar minimum and a 1,310,720 dollar maximum (I know a casino would never offer this game but just assume they did for the purposes of the example). This would give you a 1-18 spread if you were to double your bet after every loss, not including splits and doubles. My dad argues that he could beat this casino because the chances of him losing 18 hands in a row is incredibly rare.

Assuming one plays perfect basic strategy the chances of losing this many hands in a row is approximately 1 in 262144. Is there a better way to explain this then to say that the potential small wins do not account for the possibility, however small it is, of losing 1,310,720 dollars.

Anyone have any ideas how I can convince my dad in an intelligent matter that he’s wrong?

First, your numbers need some work. Basic strategy blackjack is roughly 43% win, 49% lose, 8% push.

If we ignore the pushes, you lose (49/92)% of the time.

Losing 18 in a row happens (49/92)^18 = 1/84072.

So, you walk in to the casino with ridiculous bet limits with $2,621,430 in your pocket, and make your first $10 bet.

On average, by doubling after every loss you will lose your entire bankroll once every 84,072 tries.

When you do not lose 18 in a row, you win $10. 84,072 * $10 is only $840,720.

And actually you’ll do worse than this, because you are refusing to split even when it helps your win percentage on some hands. (Not doubling is awful too, but doubling never increases the win percentage, but it sure makes you a lot of money over that kind of action!)

Hello and thank you for this great website.

I play in France with 6 decks game and I am still in need for practise.

Just in relation with the message that talked about doubling your bet after each loss : is it right to consider you have 43% chances to win every single hand before it is dealt ?

In my mind, the chances of winning a hand depend on the true count just before that hand is dealt. Is it right to think so ? That is, when the true count is +2 for example you would have more chances to win a hand than when it is 0 ?

That would seem likely, but it turns out to not really be the case.

See this page: Win/Lose/Push by True Count.

You do lose fewer hands, and most of the difference is offset by pushing more often. Win percentage is surprisingly flat over the range of true counts.

Thanks very much for your reply.

I am getting back to study and practice. Your lessons and exercises are very helpful, thanks for sharing all of this, because it makes us understand that it is not only people with a gift that can make it, but hard work and patience will pay off.

I have one more question if you don’t mind, please :

I read the French version of KO Blackjack. Do you agree with the fact that it is sufficient to keep the running count and not the true count to have the edge over the casino ?

I think I will start that way because it’s simpler.

Yes, KO is a very effective yet simple counting system. It allows you to use just the running count because of the way it is structured (starting count, key count, and an unbalanced set of tag numbers). It’s an ideal first counting system, and you may never have to leave it behind.

Thanks Ken. I’m just a poor student so I account for every dollar, as such I have a set amount set in stone as my bankroll. Thanks for the comments they are very helpful

Most of the deviation play amount to minute practical differences. For the vast majority of players would resources be best spent on focusing on a large enough kitty and supporting the psychology to contain a x10+ spread when normally you would play at best a x8 or x4 spread?

Yes, increasing your spread will have a much more dramatic impact on expected win than learning and using all the strategy variations. The advantage of card counting comes primarily from betting more when you have the advantage. Changing your strategy based on the count is just the icing on the cake. Focus on building your bank and increasing your spread first.

Do this Hi-Lo indexes apply with the European blackjack rules??

(no peek, dealer stands at soft 17, double any 2 cards, double after splits, no surrender, 4/6/8 decks)

Yes, the index numbers will be fine for a European no-peek game, with one adjustment: Ignore any index that has you doubling or splitting against a dealer ten or Ace.