In my first book I created E-Z Count which was easy, but not as accurate as a true counting system. It tells one enough to know when you have the advantage, and, to bet more aggressively. If you bet a progression, and you get the advantage, you can simply double your unit and bet the same progression or change to a more aggressive betting sequence. If you don’t bet a progression, you could simply double your bet as long as you kept the advantage.
I continued to think about designing a better ten count. I had an idea that counting the ten value cards or the Aces and ten value cards and comparing the number to the expected value would be the basis of an easy but more accurate counting system. While I was working on this, I bought a copy of Blackjack Bluebook II, and there was a short section on what I had been working on. I knew it could work and was a viable, yet easy, system. Although disappointed to learn someone had discovered it two years before me, I was glad someone of Mr. Renzey’s caliber had felt it had merit.
I thought about some of the problems with card counting. One of the problems with plus- minus systems was the minus part. You are constantly adding and subtracting. I felt if you only added, going in one direction, you could have a more user friendly system. Another idea came to mind regarding what we were counting. Most plus-minus systems count small cards as +1 and the large cards as -1. What is this telling you? It gives you a relationship between the two groups. It tells you there are more in one group than another. A count of plus two means there are two more tens and Aces than small cards, but does it tell you there is an excess of tens and Aces? Not necessarily.
A couple of examples might serve well here, but let’s look at deck composition first.
Cards per deck: 52 Cards per six deck shoe: 312 Number of ten value cards per deck: 16 Number of Aces per deck: 4 Number of ten value cards per six deck shoe: 96 Number of Aces per six deck shoe: 24
Example #1: Two decks have been played from a six deck shoe. We should have seen 32 ten value cards and eight Aces for a total of 40 Aces and tens combined. If we have seen 30 Aces and ten value cards, then there is an excess of ten Aces and ten value cards in the remaining four decks. Plus ten divided by four yields a true count of two and a half. This is the number of excess tens and Aces per deck based on the Ace-Ten Count.
Now let’s look at a hypothetical situation using the same number of Aces and ten value cards. You have seen 30 Aces and ten value cards and 30 small cards for a plus-minus count of zero. 104 cards have been played, including 44 neutral cards. As this example shows, there can be an excess of ten value cards and Aces remaining yet your plus/minus counting system indicates the count is zero.
Example #2: The plus-minus running count is plus eight, with four decks remaining. Therefore, the true count is plus two. This is a favorable situation, so I’m going to double my bet. However, the cards that have been dealt are 40 ten value cards and Aces, 48 two through six cards, and 16 neutral cards. So even though the remaining decks are Ace-Ten neutral, the plus-minus count is two.
There are many scenarios when the Ace-Ten count is different from the plus-minus count. The discrepancy is caused by variation in the number of neutral cards seen. The greater the number of decks being used, the greater the discrepancy can be. This may be one of many contributors for the lower performance of counting systems in shoe games. If you have counted cards before, you might recall times when the count was negative, yet you won several hands in a row. You may have been in situations when there was a very positive count, yet you lost every hand. It is possible you were in a period where the Ace- ten concentration differed from the plus-minus count.
What is really important when you count cards? Is knowledge of the concentration of small cards remaining to be played important to you? Is knowledge of the concentration of Aces, tens, or even nines important to you? Is the knowledge of the ratio of small to large cards most important to you? I just showed you that the latter may mislead you. I want to take a moment to review the benefits of knowing the composition of the remaining cards to be played.
Knowledge of Ten and Ace Concentration
1) An Excess of Ten Cards A) It is half of a Blackjack B) Card of value when doubling down with 11, 10, 9, and even 8. C) Card of value with some soft doubling. D) Two tens make a great hand, and 10-9 isn’t bad. E) Under extreme situations, 10-10 may be split. F) Tens are great when one splits Aces, nines, and eights. Even sevens though you could do better. G) Makes taking insurance a profitable wager.
2) An Excess of Aces A) It is the other half of a Blackjack. B) It combines well with Split 10s, 9s, 8s and even 7s. C) A-A makes a great splitting hand . D) Aces go great with double downs on 10, 9, 8, and even soft doubles such as A-6, A-7, or A-8.
3) Dealer effects of Aces and Tens A) Combine with 2-6 (Tens), and Ace-5 (Aces), to make dealer stiff hands. B) Tens bust all dealer stiff hands. C) Aces make a dealer stiff 12-15 worse. D) Aces make a dealer 11 into a stiff hand, just as it does yours.
Effects of an excess of small cards
1) You catch more stiff hands. 2) The dealer catches more stiff hands. Unlike you, the dealer hits all of them, and with an excess of small cards, will make a lot of them into pat hands. 3) When you hit your stiff hands, you will make more of them pat as well. 4) Soft doubling may be more productive with a negative count (A-3 through A-6). 5) You actually have more double down opportunities when there is an excess of small cards. Unfortunately, your bet is often the minimum
As you can see, most of the player advantage is derived from an excess of tens and Aces and not from an excess of small cards. One can infer from the excess of tens and Aces there is a small card deficit. Perhaps these facts were very apparent to Dr. Thorp when he developed his Ten-Count. Dr. Thorp stated the Ten-Count was as powerful as his complete point count, which was a refinement of the simple point count.
The problem with the ten count is the level of difficulty. The difficulty lies in calculating the ratio precisely in your head rapidly prior to placing ones bet. Dr. Thorp recognized this and suggested that calculating the ratio to the nearest 1/10th would be adequate. That was the problem then. The problem now is instead of beginning at 36 non-tens and 16 tens, the count for a six deck shoe begins at 216 non-tens and 96 tens. The multiple deck shoe games made a difficult task next to impossible. This fact, however, does not diminish the effectiveness of a ten count. It can still be a powerful count if we could find a way to accurately count tens alone, or Aces and tens in the high numbers.
In the previous section I introduced the Renzey Ace-Ten Front Count. Mr. Renzey’s evaluation of it shows an almost 1% gain. Using basic strategy for a six deck game, the player is at about a 0.6% disadvantage, depending on the rules. Mr. Renzey stated with just checking the count at one spot, after two decks had been played, you would have a 1/3 % advantage. If you check the count at half deck intervals from one to four decks, the performance would be improved above the 1/3% mark. Having seen the performance of the best plus-minus counting systems used in six deck play, this is in excess of their performance. The high performance Complete Zen Count created by Arnold Snyder, only yields 0.275% player advantage in a six deck game with 75% penetration. According to Renzey, the Ace-Ten count is in the same range.
Counting Aces and Tens Only
Starting with a fresh shoe, the count begins with 0 and you count forward only. You will find it takes just a few seconds to count all of the Aces and tens on the table, no matter how many players are playing. As you scan the table, the Aces and tens seem to pop out at you because they are such unique cards. The most difficult part of the Ace-Ten Count is deck estimation. After one deck has been played, per the discard tray, you should have seen 16 ten-value cards and 4 Aces, for a total of 20. The mix may be different from 16 and 4, but the combined total is your concern. If you have counted fewer than 20 at the point of one deck played, you have a positive deck. If more than 20, you have a negative deck.
For example, you count 15 Aces and tens for the first deck. The running count is +5 (20- 15= +5). Now, just as with any balanced count, you have to convert to a true count. With this example it is easy. Divide the count by the number of decks remaining: +5 divided by 5 decks = a +1 count per deck. The following table shows the expected, or neutral, count for one to four decks:
Decks Played Neutral Count Remaining Decks 1 20 5 1 ½ 30 4 ½ 2 40 4 2 ½ 50 3 ½ 3 60 3 3 ½ 70 2 ½ 4 80 2
The beauty of counting Aces and tens is the expected count is always a multiple of ten.
Going further, look at the point where 3 decks have been played. We know a neutral Ace- ten count is 60. Since there are 3 decks remaining, a plus one count would be 60-3 or 57. A +2 count would be 60-6, or 54, and a +3 count would be 60-9 or 51. On the negative side, a -1 count would be 63, -2 would be 66, and -3 would be 69.
There aren’t any tables to have to remember, just plug in the numbers to the simple formula below, and you have your true count. Expected Count minus Ace-Ten Count divided by decks remaining equals true count.
So, now we have a count. What can we do with it? How do you bet it? Let’s look at what Dr. Thorp did with his Ten Count. Dr. Thorp kept a ratio of non-tens to tens. The neutral ratio was 2.25:1 or just 2.25. When the ratio dropped to 2.0, he bet 2 units. When it dropped to 1.75, he bet 4 units. When it dropped to 1.65, he bet 5 units. We can calculate a ratio equivalent in a plus/minus form, but to do so we must separate the tens from Aces, then add them back.
When one deck has been played, 16 tens have been played. 5 decks remain with 260 cards. To have a 2;1 ratio, 87 tens must remain. Only 9 of the 16 tens should have shown. Now add in the 4 Aces, and you have a count of 13. The expected 20 Aces and tens minus 13 equals 7, and 7 divided by the remaining 5 decks equals a count of +1.4. Therefore, a count of +2 is slightly below a 2:1 ratio of non-tens to tens, and would merit a two unit bet.
Doing the same for the other ratios, a table is derived for betting the Ace-Ten count in the same way.
Thorp Ratio Ace-Ten Count Bet Above 2.0 +1 or less 1 unit 2.0 to 1.75 +2 2 units 1.75 to 1.65 +3 4 units Below 1.65 +4 5 units
Betting Correlation of the Ace-Ten Count
Betting correlation can be defined as the ratio of the profitability of a system compared to the ideal or total gain possible. To calculate the betting correlation we first must know the effects of removal of cards from a full deck. Dr. Thorp did this in developing his many counting systems. The numbers used here come from The Theory of Blackjack by Peter Griffin.
This is the same table used to develop the plus/minus count earlier. What the numbers indicate are the effect in per cent advantage that removal would have on the player, positive or negative. As you can see, removal of the smaller cards has a positive effect and removal of Aces, tens and nines has a negative effect on the player’s advantage. Look at the five card. Its removal has a +.69 effect which is the highest positive effect of all of the cards. (Remember the Thorp 5 count.) Now look at the effect of removal of a ten value card. The number is a negative number because its removal has a negative effect on the player. This helps the player to understand why the small cards have a positive number when counted and the large cards have a negative number.
With the above numbers and a formula we can calculate the betting correlation for any counting system if we know the count values assigned to the cards. The formula we use is the sum of the products (of the count values times the effects of removal) divided by the square root of the sum of the squares of values times the sum of the squares of the effects of removal. Let me calculate the betting correlation for the plus/minus count we are most familiar with.
Now the denominator: The sum of the squares is 5 x 1 squared plus 5 x -1 squared which equals 10. The sum of the squares of the effects of removal as calculated by Dr. Griffin is 2.84. Now we multiply 10 x 2.84, take the square root, and the denominator becomes 5.33. Now divide 5.17 by 5.33, and we find the betting correlation to be 97%.
To evaluate the Ace-Ten count, we do the same process using the values of +1 for 2-9 and -1.6 for tens and Aces. When calculated, it has a betting correlation of 0.89 or 89% for the Ace-ten count, which is not bad for a count so easy to do. For comparison, the Thorp Ten count has a betting correlation of 0.72 or 72%.
Similar systems could be used, such as counting Ten value cards only, or counting the Aces, Tens, and nines. These would use different count numbers since there are 16 tens per deck, and 24 Aces, tens and nines per deck. I prefer the Ace-Ten count because your count is a multiple of ten, making the math easier, and it counts the cards which matter most for betting purposes.
