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.

### A Few Words on Single Deck

**In the previous lesson, I taught you how to figure the “true count” for a multi-deck game, but I want to emphasize that the concept of true count also applies to single-deck games as well.** The conversion is done a bit differently, but the result is the same; you end up with a standardized count per remaining deck. If you see just one card in a single-deck game, a 5 for example, you now have a “running count” of 1 and a true count of one. That, of course, is because there’s only one deck in the game to begin with and we determine the true count by dividing the running count by the number of remaining decks. If, after playing several hands the running count is 6 and there’s three-fourths of a deck left to be played, we must divide the running count by .75 in order to determine the true count. In this instance, the true count is 8. If we were at the halfway point of the deck, the true count would be 6 divided by .50 = 12. Got the concept of that? In a single-deck game, you have to divide by fractions, and that isn’t easy to do, so all you single-deck counters need to practice this in order to figure it properly when you play.

### Betting With the True Count

**For each increase of 1 in the true count as figured by the Hi / Lo counting method, the player’s advantage increases by about .5% in the average Blackjack game. ** If the casino has an edge over the basic strategy player of .40% (6 decks, double on any first two cards, double after splitting pairs, dealer stands on A-6), it takes a true count of just about 1 in order to get “even” with the house. Being even means that the player who utilizes proper basic strategy will win as much as s/he loses — in the long run — at a true count of one. A true count of 2 gives the counter an edge of .5% over the house; a true count of 3 gives the player an edge of 1% and so forth.

**It is the edge that a player has on the upcoming hand which determines their bet.** Counters bet only a small portion of their capital on any given hand, because while they will win in the long run, they could lose any one hand. By betting an amount which is in proportion to their advantage (called the “Kelly Criterion”), they are maximizing their potential while minimizing the risk. A lot of people misinterpret the Kelly Criterion by assuming that the amount bet is in direct proportion to the advantage. They think that if you have a 1% edge, you should bet 1% of your “bankroll” and that is incorrect. What they are forgetting is the doubling and pair splitting which goes on in the course of a game and that increases the risk or “variance” of a hand. For a game with rules like those listed above, the optimum bet is 76% of the player’s advantage. Here’s a table of optimum bets which will work well for most multi-deck games:

True Count |
Advantage |
% Optimum Bet |

-1 or lower | -1.00% or more | 0% |

0 | -0.50% | 0% |

1 | 0% | 0% |

2 | 0.5%x76% | .38% |

3 | 1.0%x76% | .76% |

4 | 1.5%x76% | 1.14% |

5 | 2.0%x76% | 1.52% |

6 | 2.5%x76% | 1.90% |

7 | 3.0%x76% | 2.28% |

By using this table, you can determine the optimal bet for any bankroll; just multiply the figure in the last column by the amount of the bankroll. Thus, for a bankroll of $3000, the optimal bet for a true count of 2 is .0038 X $3000 = $11.40.

### Some Practical Considerations

**First and foremost, it isn’t practical to bet in units of less than $1, so a betting schedule must be rounded off. Secondly, it is more appropriate to bet in units of $5 so that you’ll look like the average gambler, plus it cuts down on the calculations you need to make.** Further, it is impossible to refigure your optimal bet while seated at the table, even though it should be recalculated as the bankroll varies up and down. Finally, it just isn’t possible to play only at shoes where the true count is 2 or higher; you will sometimes have to make bets when the house has an edge. All of this rounding and negative-deck play cuts into your win rate, but by knowing the conditions which can cost you money, steps can be taken to minimize their impact on your earnings.

### The Betting Spread

**A single-deck game with decent rules in which thirty-six cards or more are used before a shuffle can be beaten by a 1 to 4 spread.** A two-deck game in which seventy cards or more are used before the shuffle can usually be beaten by a 1 to 6 spread. A game with four decks or more will require a spread of 1 to 12 in order to get an edge. We’ll discuss the evaluation of games in a later lesson, but I wanted to lay the foundation for your money management by giving you an idea of what it takes to play winning Blackjack. The spread is expressed in betting units, so if you play with $5 chips, you’d be spreading from $5 to $60 in a six-deck game. Since a counter should have a bankroll consisting of a minimum of 50 top bets, a spread like this will require a bankroll of $3000.

With a $3000 bankroll, a betting schedule could look like this:

True Count |
Player’s Bet |
Optimum Bet |

0 or lower | $5 | $0 |

1 | $5 | $0 |

2 | $10 | $11.20 |

3 | $20 | $22.80 |

4 | $40 | $34.20 |

5 | $50 | $45.60 |

6 | $60 | $57.00 |

A betting schedule like this allows you to “parlay” your bets as the count rises, thus making you look more like a “gambler”.

**YOU WILL SAVE A LOT OF MONEY AND FIND MORE PROFITABLE SITUATIONS IF YOU LEAVE A TABLE WHEN THE COUNT HAS GONE DOWN TO A TRUE OF – 1. BUT LEAVE ONLY AFTER LOSING A HAND; NO GAMBLER WOULD LEAVE A TABLE AFTER A WIN.
**

So, have I got your brain spinning? If so, just hang in there as I’ll be wrapping all this up in a nice, easy-to-understand package in the coming weeks. As always, get your homework, then you’re outta here.

### Homework

None. How’s that for a break?

I didn’t get the 76% calculation. In the later lessons we learn to calculate the house edge. And we did three examples with the results 33%, 33% and 30%. Ho do we calculate now our bets? 80%-10×0.4%=76%???? for the mentioned above? and why?

The GameMaster is pretty sparse in his explanation of the 76% factor, though he mentions it briefly above.

Here’s how he arrived at that number:

A “Kelly” bet is Your Bankroll * (Your Edge / Variance).

In blackjack, the variance is around 1.32. 1/1.32 = 76%. So instead of saying you should divide your bet by 1.32, he just multiplies it by .76 or 76% instead. Same effect. He’s taking your advantage and dividing by the variance before figuring the optimal bet.

(As for your other sentence mentioning the 33% stuff, I don’t quite understand what you’re asking.)

I would like to expand on kel’s question a bit.

Correct me if I’m wrong, but this is how I interpreted your response. The 76% KC comes from the fact that blackjack has a higher variance than many other investments. So essentially, due to splits and dd’s, playing 76% KC in blackjack has the same risk/reward as full KC in investments where the initial bet and risk for that bet are known upfront.

If that’s true, then isn’t playing at 76% KC too risky for someone with a $4000/$5000 bankroll since it’s pretty difficult to find a table with less than a $5 min. I get that this question is relative to one’s risk aversity and whether or not that bank is replenishable. So I’ll phrase my question this way: would you recommend playing a smaller fraction of the KC if the bank was non replenishable?

I think kel was referring to making calculations regarding her bank at 33% KC, as to keep her risk of ruin very low. I’ve seen recommendations of anywhere from 25%KC to 80%KC for making betting calculations. I’m sure the latter is just a rounded version of your calculation and the former I read in Snyder’s Blackbelt in BJ. I don’t understand what difference it makes if they both have a theoretical RoR of 0%. My two guesses would be avoiding problems with table minimums and for mental peace of mind as bank fluctuations will be a much smaller percentage of your total bank with a lower percentage KC.

A final follow up question. Assuming your double deck scenario in later lessons, what would you estimate the risk of ruin to be for your betting scheme assuming one starts with the $5000 bank you made the calculations with, but the table minimum is $10. Obviously if my bank starts on a downswing, there isn’t much room for me to recalculate, so I would have to play it out far above my kelly calculations for any bank that dropped under $5000 in order to keep a 1-8 spread.

I hope I worded my questions so that they make sense to everyone. I know I have a tendency to ramble.

Thanks for all your help. I love this site; it’s a very helpful source.

Your understanding of the Kelly bet being reduced because of the variance is accurate, although your use of the abbreviation “KC” in your post is not quite right. The Kelly Criterion already by its definition includes the 76% factor. If you had a different game where bets have a variance of 1.0, the Kelly Criterion would have you bet 100% of your edge as a percentage of the bankroll. Blackjack’s higher variance makes the Kelly Criterion number only 76% of your edge for blackjack bets.

Most people find Kelly too aggressive for their taste, and I agree. I recommend 1/4 Kelly if possible. For small bankrolls, that is really not practical for the very reasons you mention. Table minimums are going to restrict your ability to even stick with full Kelly sometimes.

(I will point out that many players with a supposed bankroll of $5000 are actually willing to lose it and raise another bank to try again. In that case, your real bankroll is effectively a lot more than $5000. That helps a lot!)

I don’t have a quick answer for your specific risk of ruin question on the double deck $10 scenario, and I’m too pressed for time at the moment to delve into the details. Maybe early next week I’ll have a chance to take a look.

That clears things up. I will strive for 1/4 Kelly and probably wait awhile longer until I have a larger bank behind me.

I have used various charts and graphs available to me through blackjackforum and qfit to find that my risk of ruin is slightly over 5%, which makes sense using Uston’s 5% curve as an estimation but I’m unsure on my standard deviation per 100 hands. Any idea how I can calculate/where I can find that number? Also, the dd game available to me deals 65% of the cards and I’m using zen with indexes -4 to 12. This should be a bit better than the game in your scenario, but any help I can get on the calculations would be much appreciated.

Thanks again for all the help

By far the easiest way to get definitive answers for these kinds of questions is to use sim results. Although I understand that it is expensive ($160) when you’re trying to build a bankroll, I think the CVData software from Qfit.com is a wise investment.

Hello and thanks,

after this explanation I understand that the 76% should be taken as a not changing fixed percentage.

Also Thanks for the explanation of the 1/4 with is interesting for me in EU as well.

Hello Ken

One question : If I do not have that large amount of money in my bankroll should not play??

That’s a popular question. If you play with a substantially smaller amount of money, the chances are quite high that you will run into a losing streak that will tap you out. Does that mean you shouldn’t play? Well, it depends on your tolerance for that happening. In truth, your “bankroll” is probably much higher than the actual cash you have on hand today, because you are likely willing to go back to your normal income and build up another starting bankroll if needed. Still, consider carefully how you would handle losing your entire bank. If that would be difficult to accept, you should probably wait until you have more money to begin.

If you choose to play, hopefully you’ll experience some early good luck and build your bank to a reasonable level by chance. If not, back to the drawing board.