With a running count of +19, and 2 decks remaining, the true edge is 19/8, or almost a 2 1/2% raise from the starting advantage. If you have any trouble with fractions like these-for instance, if you do not know fairly quickly that 19/8 is about 2 1/2-then you should not use the Zen Count. I would suggest that you stick with the simple Red Seven, and play according to running count. In my opinion, the true edge method is the easiest way to adjust a running count to estimate your advantage precisely, but not all players are comfortable with the math.

In the first half of the shoe, you can just as accurately estimate the remaining decks to the nearest whole deck by always rounding up. For example, if your running count is +10, and 5 1/2 decks remain to be dealt, round up to 6 decks, and then make the fraction 11/24, which is easy and accurate enough for bet-sizing. It is clear that your advantage has risen slightly less than 1/2%. Technically, with 5 1/2 decks remaining, it would be more accurate to use the denominator 22, halfway between 5 and 6 decks remaining. The true edge is more precisely 11/22, or exactly a 1/2% raise. The real difference between 11/24 and 11/22, however, is so small that it is unlikely to have any effect on the bet size.

Deeper in the shoe, however, as the denominators get smaller, the effect of rounding the remaining decks up to the nearest full deck will have more of an effect. In the previous example, with a running count of +19 and 2 decks remaining, we came up with the fraction 19/8, or just under 2 1/2. If there was actually only one deck remaining (which we rounded up to 2), our actual fraction should have been 19/6, which is slightly better than 3%.

Again, this is more important when there are fewer than 4 decks remaining. By rounding up from 1 1/2 to 2 decks, you should tend to bet more conservatively, which is better than rounding down and overbetting. Some players may want to make a chart of denominators in half-deck increments, but I doubt that it’s necessary. If you know that your 4-deck denominator is 16, and your 3-deck denominator is 12, it would probably not take more than an instant for you to come up with a denominator of 14 if you estimated that 3 1/2 decks remain in the shoe.

In single-deck games (or in any multiple-deck game that’s played down into the last deck), the most accurate method of true edge adjustment is to break the deck into four distinct quarters. In the first quarter, your true edge is your running count divided by 4; in the second quarter, it’s divided by 3; in the third quarter, divided by 2. And in the bottom quarter, your true edge is simply your running count, as a running count of +6 with a quarter deck or less remaining to be dealt would indicate a 6% raise in your advantage.

I think it is very practical to know your advantage quickly while you play, and the Zen true edge method is simply a count-per-quarter-deck adjustment, which will always provide you with your true edge when you use the make-a-fraction technique. You might also note that the Zen true edge playing strategy chart is much simpler than the old count-per-deck chart. In fact, it is very similar to the Hi-Lo Lite chart.

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The Zen Count is a balanced card-counting strategy for counters with above average skill. If you can use the Zen Count accurately, it will add about 0.1% to your advantage in shoe games, and about 0.2% in single-deck games, compared to what you would expect with the Hi-Lo Lite.

The recommended drills for learning how to count cards are the same for the Zen Count as for the Red Seven Count or the Hi-Lo Lite, so these exercises will not be repeated here.
The Zen Count Point Values
The point values of the Zen Count are:

A -1
X -2
9 0
8 0
7 +1
6 +2
5 +2
4 +2
3 +1
2 +1

As the cards are played, keep a running count of all cards seen. After a shuffle, the count starts again at 0. Like the Hi-Lo Lite, this is a balanced counting system, so if you count down a complete deck, starting at 0, your final count will also be 0. Because the point values are balanced, you also have to adjust your running count to the true edge. All Zen Count betting and playing strategy decisions must be made according to the true edge, not the running count.

Because the Zen Count has more complex point values than the Hi-Lo Lite, it is more accurate. With the Zen Count, you must estimate the true edge by dividing your running count by the number of remaining decks, multiplied by 4 (instead of 2). Otherwise, you use the same make-a-fraction method, in which the running count is the numerator, and the denominator is the number of remaining decks multiplied by 4. In order to do this quickly at the tables, you must memorize the following chart:

Decks Remaining Denominator

8 32
7 28
6 24
5 20
4 16
3 12
2 8
1 4
1/2 2

I think most players who remember their multiplication tables from third grade could reproduce this chart with no memory work whatsoever. It is important that you are able to immediately insert this denominator into your fraction so that your true edge does not require you to make calculations at the table. If your running count is +7 with 3 decks remaining to be dealt, you should immediately know that your true edge has risen by 7/12, or slightly more than 1/2%.

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The most common method of determining true count is to divide the running count by the number of remaining decks (or half-decks). The chief difficulty of this method is that it often involves dividing by fractions. The true edge methods I propose solve this problem, and other methods may be used as well.

The "True Index" Method
For strategy variations, instead of adjusting your running count, you may find it easier to adjust your index number to the true index at which you would alter your basic strategy. This method works well for players who are not comfortable working with fractions.

With the Hi-Lo Lite you simply multiply the index number of the decision in question by the number of remaining half-decks, then compare this number to the running count. For instance, let's say you're trying to decide whether or not to take insurance in a 6-deck game with a running count of +9. Four decks have been played, so 2 remain. Since your Hi-Lo insurance index number is +2, you compute your true index by multiplying +2 by the 4 remaining half-decks, ending up with +8. And you would take insurance here because your running count of +9 is higher than the true index.

This method may be used for all strategy decisions, but to do it quickly, you must instantly know the number of half-decks remaining.

The "True Shoe" Method
To use this method of true count adjustment, you simply divide your running count (which is always a whole number) by the index number of the decision you are considering (also always a whole number), and the answer is the number of half-decks or fewer that must be remaining for you to make the play. For example, your Hi-Lo running count is +10 and you want to know whether you should stand on your hard total of 12 against the dealer's 2.

Your standing index number for this decision is +2. Simply divide the running count of+10 by 2, which of course equals 5, and if less than 5 half-decks (2 1/2 decks) remain, you would stand. In order to justify this strategy deviation, with this running count, your true shoe size must be 2 1/2 decks or fewer. Otherwise, follow basic strategy and hit.
The easiest way to use the true shoe method, with any counting system, would be to first convert all strategy indices to count per deck. This way your running count divided by your index always results in the true number of decks remaining, instead of half or quarter-decks, where the decision changes.

NOTE:
If your running count is negative and your index number is positive, or vice versa, don't bother to make any true count adjustment using any method. Follow basic strategy.

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True count is an adjusted running count that indicates the ratio of high cards to low cards. True count is, in fact, not "true" as a precise indicator of your advantage, but it does reflect the balance of the cards so that you may approximate both your advantage and your playing strategy.

Most level-one systems, like the Hi-Lo, recommend that true count be estimated as count per deck. The true edge with the Hi-Lo Lite is simply the count per half-deck. Some authors who have developed higher level counting systems, most notably Ken Uston and Lawrence Revere, have advised count-per-half-deck adjustments.

Take a full 52-card deck. Count the point value of all the tens and aces using the Hi-Lo Lite. With 16 tens and 4 aces counted as -1 each, the points add up to -20. If you now count all of the points of the low cards, 2's, 3's, 4's, 5's, and 6's, at +1 each, you'll find that these add up to +20. The deck is perfectly balanced between plus-valued cards and minus-valued cards.

Now, let's remove 8 tens and 2 aces from the deck. Adding up the point values of the high cards remaining in the deck, we now get -10. Our balance looks like this:
= .50 = 50%

A
The deck is heavy in low cards and light in high cards. There are, in fact, exactly half as many high card points as low card points in the remaining deck.

If this situation occurred at a blackjack table, that is, if 8 tens and 2 aces had been played in the first round of hands, and no low cards came out of the deck, the running count would be -10.

But consider what the balance would look like if this situation occurred while playing a 6-deck shoe game. To start with, six full decks contain 96 tens and 24 aces, or 120 total high cards, and there are also 120 total low cards. The high card points balanced against the low card points look like this:

= 1.0= 100%
Now, if we remove 8 tens and 2 aces, our balance looks like this:
= .92 = 92%

The balance is only slightly tipped because there were so many more points to start with. Although the same cards as in our single-deck example have been removed, we still have nearly as many high card points as low card points in the shoe (92%, to be precise).

What this means to card counters is that although the running count may be -10 in both situations, the advantage, and playing strategy, would differ. The running count must be adjusted to reflect the true balance of high cards to low cards.

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I ran 100 million hands, and tallied the results with both a flat bet and a 1 to 4 spread at 75% penetration. This time, in the "lite" version of the Hi-Lo, I widened the border again, converting all of Wong's indices to plus or minus 1, 5, or 10. The results:

Strategy Flat Bet Ito 4
Wong -0.06% + 1.32%
Hi-Lo Lite -0.05% + 1.33%

The fact that the Lite system outperformed Wong's by one-hundredth of one percent was, again, insignificant in a test of 100-million hands. What is important is that from the practical dollars-and-cents perspective, it doesn't matter which of these systems you use. The simulation results indicate that you may use a vastly simplified Hi-Lo strategy, and maintain full power, even in a one-deck game.

So, in 1991, I published a series of three articles in Casino Player magazine about this astonishing discovery. I developed the Hi-Lo Lite counting system to be a feature of the revised Blackbelt in Blackjack, but then, in October of 1991, the Oakland Firestorm destroyed the manuscript, so I published the Hi-Lo Lite without much fanfare in the December 1991 issue of Blackjack Forum. Since that time, I have been personally advising players to simplify their strategy charts with this modified approach.

John Imming later discovered the reason why the lite approach to indices works so well. In attempting to determine why his Universal Blackjack Engine software sometimes spat out different indices for the same counting system via simulations of hundreds of millions of hands, Imming discovered that the actual indices were not precise, but constantly wavered according to the level of penetration and other factors. Some indices went up and down by a few numbers until finally settling.

In 1997, Ken Fuchs, co-author of Knock-Out Blackjack, presented a paper at the 10th International Gambling Conference in which his simulation results of a slightly different lite counting system supported my findings. Then, George C. privately devised a lite version of the Zen Count, which John Auston tested against the regular Zen indices using the Statistical Blackjack Analyzer software. It took Auston a billion hands of each system to determine that the lite indices underperformed against the regular indices by about two-hundredths of one percent.

It was George C, incidentally, who discovered that all of the +1 and -1 lite indices could be adjusted to 0, with no notable loss of power. So, the version of Hi-Lo Lite published here has been further simplified. If you want to test the Hi-Lo Lite via computer simulations of your own, note that the true edge methodology is not the same as true-count-per-deck. If your blackjack simulation program does not allow you to enter indices as true-count-per-half-deck, then you must double the Hi-Lo Lite indices.

For the most important strategy decisions, all indices are either 0 or +4. To fully adjust the complete chart, make all +2s into +4s, -4s into -8s, and so on, in order to test the system with a count-per-deck simulator.

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Stand only when your true edge is equal to or greater than the number in the table. Double down only when your true edge is equal to or greater than the number in the table. Note that no soft doubling indices are provided here—there is very little value to varying from basic strategy in these situations. If you want to use these indices, you will find them in the Appendix.

Split all pairs according to basic strategy. A few of the ten splits have some dollar value, but there is very little value in varying from basic strategy on other pair-split decisions. You will find extensive pair-split indices, which may be useful camouflage, in the Appendix. Learn these if you want, but they are worth very little in dollars and cents.

Surrender only when your true edge is equal to or greater than the number in the table. Note that these are the late surrender indices. Should you discover an early surrender game, which is rare, you will find the proper indices in the Appendix.

Take insurance only when your true edge is equal to or greater than
+ 2.

The easiest way to learn the Hi-Lo Lite strategy indices is to start with the bold indices and learn them in blocks. Unless you play in games with surrender, you may ignore the bold indices for surrender.

The 0 Block is most important, and after that, learn the +2 Block. Shoe game players need never learn any indices other than these. If you play in hand-held games, these indices are still the most important. Learn the others in blocks, if you want to add an extra few tenths of a percent to your advantage, starting with the positive indices. The negative indices are least important.

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