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. ðŸ™‚

Hello Ken,

Of how much would the minimum you advise my bankroll should be and at what point would I start winning? Also, at what point would I convert my running count to true count on a 6 deck shoe? After the first deck played, after half of the first deck, 2nd deck. What difference does it make?

Your minimum bankroll will likely be affected by the quality of the games near you. If you have good two-deck games nearby, you can probably make money with a bankroll of $3000 or so. I recommend that your biggest bets be no more than 1% of your bankroll, so a $3000 bankroll would mean limiting your top bet to just $30. At that rate, your hourly expected win will definitely be less than minimum wage. But it’s a start. If you are forced to play 6-deck games instead, you really need $5000 at a minimum. You can always take a shot with a smaller bank, with the understanding that you may go broke and have to wait to raise another starting stake.

You should convert your running count to a true count each time you need to decide how much to bet. (And if you are using strategy variations, you may also want to do so in the middle of a hand.) Having a good idea of where the true count stands gets much easier with experience, so it doesn’t feel like you are constantly struggling to convert from the running count.

so is this the way you should bet when you are counting cards?

Yes, this lesson shows a good way of calculating an appropriate bet spread for counting.

how can you calculate DD BJ T/C positive or negative count is only few cards to deal.thanks

Just like in any number of decks. You divide the running count by the number of unseen decks.

Let’s say you are playing a deeply dealt double deck game, and 1.5 decks have been used already.

If your running count is +3, you divide that by the number of unseen decks, which is 0.5.

+3 / 0.5 = +6.

Your true count is +6.

any advise for a bankroll of 500$ ?

With a $500 bankroll, you will be overbetting your bank regardless of how good a game you can find.

The only realistic approach with that bankroll would be to take a shot, and if you lose your bank, you’ll have to go back to work to gather another bankroll.

If you try this approach, it is extremely important to play the very best games that you can. In fact, if you cannot play a decent 1 or 2 deck game, I wouldn’t bother.

The six-deck games really can’t be tackled without a much larger bankroll.

thanks for the reply,

i’ve another questions if don’t mind ,

if i split the cards and i win just one hand and the bet was 5$ , how much im gonna take for that ?

Each hand plays independently, with its own bet. If you win one hand for $5, and lose the other, your net result is zero. If you win one hand and push one hand, you would win $5.

and can you show me what’s the different between this chart http://www.blackjackapprenticeship.com/resources/blackjack-strategy-charts/ and yours

thanks

Their chart looks like a 6-deck H17 strategy, although it doesn’t state that anywhere. I didn’t check every decision, but at a quick glance it appears accurate. If in doubt, pull up the matching rules at the Strategy Engine here. The Engine’s charts are accurate.

anyone have an idea of the morocco’s blackjack rules ?

Hi Ken,

have a question. if i play only with positive counts (TC>=2), my bankroll could be smaller than 50 top bets adviced in this lesson?

Hmm, I haven’t thought about this particular question before, and I am not certain how much reduction of bankroll risk would result from playing only in positive counts. But, off the top of my head, I suspect it doesn’t help all that much. Because most of the variance in counting already comes in positive counts (because you are betting quite a bit more in plus counts), eliminating the minimum bet hands in negative counts isn’t going to make much difference. Sorry!

I have a question. What is better: bet $100 in one place or $50 in two places at the same table, considering a positive count?

I believe that at the same table there is a high correlation among the hands. On the other hand, the risk of playing two places at the same hand is fewer.

Betting two spots of $50 is better than one spot of $100. The expected win is the same, but the risk will be quite a bit lower despite high correlation between the hands. In fact, you have roughly the same risk betting two spots of $75 each as one spot of $100. And in that case, the total $150 bet over two spots will of course have a higher expected win in positive counts than the $100 single bet.

Hi Ken,

Say for example I was at a $15 minimum table, would you recommend using the same spread like the one listed. So $5 would be $15, $10 would be $30 etc etc?

Also, say for example I had a bankroll where I could afford to bet $20 – $240. If I was at a $5 table should I just bet $5 when the count is 1 or less and then jump to $40 when it get to 2. Other than maybe raising casino interest in your play, would this be a good strategy

Yes, you can think of spreads in terms of bet multiples no matter what the table minimum is. Of course, your bankroll needs to be proportionally larger too.

For your second question, a bigger spread will create a bigger return. In short, the less you can bet into bad counts and the more you can bet into good counts directly translate into better return. Larger spreads also create larger swings, in many cases much larger. So make sure you understand the bankroll required.