That was a horrible explanation of it, (with errors!) although it laid out the concept of it. It's in fact +7 and not +4 there, an error (forgot to factor in the four extra Aces). I tried to talk about it in terms of percentages to give the idea of what is going on in this relationship of the three primary groupings to one another and how I look at things a bit differently.
Those are percentages I came up with to try and convey a concept on splitting things into three groups instead of two, taken from old notes. Those percentages were something I used to come up with one of my charts and mean little or nothing when it comes to determining indices. It gets you thinking in terms of the deck as having three groups with 1/3 of the deck each and Aces as a special little group all to themselves off to the side is all.Originally Posted by OGBasher
Last edited by Tarzan; 09-05-2014 at 04:09 PM.
Determination of TC for betting purposes
To arrive at TC for betting purposes we balance out the {2-5} to {T}, factor in the effect of surplus or deficit {6-9}, factor in (A) and then divide by the number of decks remaining to arrive at TC. Let's start with the basic breakdown of the count itself and the applicable tag values as follows:
{2-5} {6-9} {T} (A)
+1 +.3 -1 -1.2
We think of "3-0-0"per deck as TC3 and think of "0-0-3"per deck as TC-3. We value a {6-9} as 1/3 the value of a {2-5} at +.3 so how does this factor in? We count three {6-9} as equal to the value of one {2-5}, so a count of "6-0-0"=RC+6 and "6-1-0"=RC+6.3. Aces are side counted to the 1/4 deck level. That is to say that if you have seen two Aces played and there is 3/4 of a deck in the discard rack, you have an extra (A) and you would add 1.2 to your RC. If you see there is 3/4 of a deck in the discard rack and four (A) have been played, you are short of the mark by one (A) and deduct 1.2 from your RC. If there's 3 full decks in the discard rack and twelve (A) have been played then there is no change to RC. Let's look at further examples as follows:
4-3-0-5r @1 TC+6.2
"4-0-0" = +4
"0-3-0" = +1
+1(A) = +1.2
3-2-0-3r @1 TC+2.4
"3-0-0" = +3
"0-2-0" = +.6
-1(A) = -1.2
2-7-0-4r @1 TC+4.3
"2-0-0" =+2
"0-7-0" =+2.3
On this last example what do you notice? The Aces are evened out with four available and one deck remaining. Let's move on to a different scenario, which is surplus or deficit {6-9}. Since the effect of {6-9} is +.3 then "0-9-0" = RC+3. Let's jockey this around in a different way though with a count of "9-0-9"... Think of this as "evil other universe" of the positive {6-9} because "9-0-9" = RC-3. To factor this into the mix we compare {2-5} to {6-9} and then adjust for the {6-9} accordingly, some examples of this as follows:
6-0-4-4r @1 TC+.7
6-4 = +2
2-1.3 = +.7
There are two more {2-5} than {T} putting us at +2 but subtract the value of four
{6-9} and deduct -1.3 from that. When there is a zero in the {6-9} column, you deduct the quantity of {6-9} up to the first of the other two numbers you hit. If the count was
7-0-4, you would still only deduct -1.3 in other words.
3-0-6-6r @1 TC-1.6
3-6 = -3
-3-1 = -4
+2(A) = +2.4
Here we have a negative deck composition in which there are three more {T} than
{2-5}, putting us at -3 and deduct the deficit of the three {6-9} to get -4 but there are two extra (A) that send you 2.4 back in the other direction.
5-0-7-3r @1 TC-4.8
5-7 = -2
-2-1.6 = -3.6
-1(A) = -1.2
We have to stop a minute and think about something pertaining to this last example, (5-0-7-3r @1) and why it's irrelevant. You don't need to calculate that down to the exact negative number and only need to verify that you in fact have a negative number warranting a minimum bet. Your playing decision is based on the hand versus the deck composition and not TC. The only reason to calculate this roughly is to make a determination on wonging out of the table but it does not alter betting, which is at a minimum and does not necessarily have that much to do with playing decision depending upon the hand in question because specific deck compositions are what playing decisions are based on.
Moving on to another opposite effect scenario let's try a spike in the {6-9} with a negative situation between {2-5} and {T} with some examples as follows:
0-6-2-5r @1 TC+1.2
0-2 = -2
0-6-0 = +2
+1(A) = +1.2
0-9-2-5r @1 TC+2.2
0-2 = -2
0-9-0 = +3
+1(A) = +1.2
0-4-2-6r @1 TC+1.7
0-2 = -2
0-4-0 = +1.3
+2(A) = +2.4
In these examples the deficit {6-9} counteract against the negative balance between the {2-5} and the {6-9}. The difference in all three examples above have the same balance of {2-5} to {T} that amounts to -2 but the variations in quantity of {6-9} and (A) can alter things drastically from as you notice. Using these basic elements, we can take any four digit sequence of numbers and arrive at a very accurate TC for betting purposes. We are thinking in more dimensions than a simple single number line and using this orchestra of various points of information we can calculate an incredibly accurate TC on any crazy set of numbers that comes our way but obviously it's the positive counts that require the pinpoint accuracy because it's not like we have the opportunity to bet less than zero... the best you're going to do is to wager a minimum bet in any negative count anyway, so a broad brush calculation confirming that the deck is negative is sufficient to confirm a minimum bet is warranted before you ever have to calculate too very far. If I have a count of 0-1-3-4r @1 I automatically know I'm throwing a minimum bet out there at a glance without having to come up with the exact calculation. If I have a count of 6-8-0-10r @2 it becomes very important to get an exact TC for betting purposes as the count is positive with two extra (A) and we break this down as follows:
6-8-0-10r @2 TC+5.5
6-0-0 = +6
0-8-0 = +2.6
+2(A) = +2.4
11/2 = 5.5
These positive counts are the ones to pay the close attention to. Don't panic or whether it works out to a .6 or a .7 because it's not like you are going to be worrying about betting 2.7 units instead of 2.6 units out there in the heat of battle. One more example as follows:
9-12-0-5r @2 TC+4.7
9-0-0 = +9
0-12-0 = +4
-3(A) = -3.6
9.4/2 = 4.7
It's about the repetition. After seeing the same count adding up to the same TC enough times you no longer have steam coming out of your ears trying to calculate it. Also the cancellations are easier to pick right out. Let's look at some examples of counts that have elements that cancel each other out as follows:
8-0-6-4r @1 TC0
+2
-2
12-0-9-8r @2 TC0
+3
-3
3-2-0-1r @1 TC0
+3.6
-3.6
0-6-2-8r @2 TC0
-2
+2
You will acclimate to quickly recognizing these cancellations and at a glance if you know that the TC is about neutral, you need not calculate the exact because whether the TC is +.2 or -.3 you are still placing your minimum bet out there! You can avoid a lot of completely unnecessary calculations at the table this way, opening yourself up more time to perform other tasks at the table. All of the above examples have the same TC0 calling for a minimum bet but the deck compositions depicted can mean different playing decisions for individual hands! Even though all the above examples add up to TC0 the deck compositions depicted can mean different playing decisions for specific hands. Keep in mind that TC determination is strictly for betting purposes and you can have a multitude of differing deck compositions that arrive at the same TC for betting purposes. This means you can have the same TC for betting purposes but have a playing decision altered based on differing ratios of keycards to other cards within the three basic groupings and surplus or deficit (A). All of the above four examples are TC0 but due to the deck compositions and not TC playing strategies can vary on a given hand. An A,5vs4, for example, in which you would hit in the first two examples and double in the second two examples even though the TC is the same in all four examples.
Quirks, shortcuts and ease of calculation
Ease of calculation at the tables is important. These values are based on EOR and whether you count an even distribution of {6-9} as .3 or .33 it makes little difference. For the greatest ease and speed at the tables you count a {6-9} as .3 but you would count three {6-9} as 1 and simply think of three {6-9} as equaling the value of one {2-5}. You will see why and understand using this speed math for ease of calculation later. You think of the {6-9} as sets of three making +1 or -1 and anything besides a full set of three puts you at either .3 or .6, not worrying about the extra .03-.06 in other words.
Legend for count
0 - 0 - 0 - 0 @1
{2-5} {6-9} {T} (A) no. of decks remaining
-The burn card is a (2), so the count is now 1-0-0-0. You are dealt two {T} and the dealer is showing a (4), so now the count has become 2-0-2, etc.
Let's make a list of various counts showing TC for betting purposes that will demonstrate the relationship of the {6-9} to {2-5} and {T} as follows:
0-1-0-4r@1=TC+.3
1-0-1-4r@1=TC-.3
0-2-0-4r@1=TC+.6
2-0-2-4r@1=TC-.6
0-3-0-4r@1=TC+1
3-0-3-4r@1=TC-1
0-4-0-4r@1=TC+1.3
4-0-4-4r@1=TC-1.3
0-5-0-4r@1=TC+1.6
5-0-5-4r@1=TC-1.6
0-6-0-4r@1=TC+2
6-0-6-4r@1=TC-2
As you can see surplus {6-9} lower TC and deficit {6-9} raise TC. Now let's go back to 10-0-4 and examine this. 10-0-4 means there are six more {2-5} removed than {T}, putting us at RC+6 but alas! We have a serious surplus of {6-9} so this has an effect on our TC+6, lowering this value.
To make this calculation you go from the column with the zero to the lowest number, which in this case is 4. The difference is calculated as -1.3, so +6-1.3=4.6 (4.7 but we leave it in terms of .3 or .6 for ease of calculation in real time at the tables). Let's do a few more! With study of the pattern recognition and through repetition, this process of TC calculation becomes almost automatic and a simple task. It's much like memorizing your multiplication tables back when you were a kid, drilling it into memory so it's very automatic and you don't really even think about it much. Let's have a quick look at the basics of how RC is calculated.
1-0-0 RC+1
0-0-1 RC-1
0-1-0 RC+.3
1-0-1 RC-.3
1-1-0 RC+1.3
0-1-1 RC-.6
2-0-0 RC+2
0-0-2 RC-2
0-2-0 RC+.6
2-0-2 RC-.6
2-2-0 RC+2.6
0-2-2 RC-1.3
3-0-0 RC+3
0-0-3 RC-3
0-3-0 RC+1
3-0-3 RC-1
3-3-0 RC+4
0-3-3 RC-2
Once again for ease of rapid calculation everything is a whole number, a .3 or a .6. Now let's get back to this ease of calculations thing and talk about something critical to your shortcuts and that is immediate recognition of whether you have a positive or negative count. Why is that? Because we are determining our TC for betting purposes if it's a negative number you can't bet less than zero! As mentioned previously the only reason to get an accurate gauge on a negative count is to determine any predetermined wonging out point and nothing else until you see a hand in front of you since you are betting the minimum in any negative count situation. Once you see cards in front of you it's more to do with deck composition than RC/TC but if the count is somewhere between -.5 and -1.5 and your wonging out point on a NMSE 6D game is TC-4 or 5, then you needn't calculate that the TC is exactly -1.6 instead of -1.3 because the information is irrelevant, either way you have a minimum bet out there.
Let's mix it up a bit with this idea of surplus or deficit {6-9} and their impact with this table as follows:
1-0-1 RC-.3 1-0-2 RC-1.3 1-0-3 RC-2.3 1-0-4 RC-3.3 1-0-5 RC-4.3
2-0-1 RC+.6 2-0-2 RC-.6 2-0-3 RC-1.6 2-0-4 RC-2.6 2-0-5 RC-3.6
3-0-1 RC+1.6 3-0-2 RC+.3 3-0-3 RC-1 3-0-4 RC-2 3-0-5 RC-3
4-0-1 RC+2.6 4-0-2 RC+1.3 4-0-3 RC0 4-0-4 RC-1.3 4-0-5 RC-2.3
5-0-1 RC+3.6 5-0-2 RC+2.3 5-0-3 RC+1 5-0-4 RC-.3 5-0-5 RC-1.6
What are we doing on this calculation? First we are looking at {2-5} compared to {T}, what is the difference? In the case of 5-0-3 for example, the table gives a RC of +1. There are 2 more {2-5} in the discard rack than {T} putting the count at +2.
5-0-3 5-3=2
From there we take the zero column up to the lower of the other two numbers to show three surplus {6-9}.
5-0-3 Three surplus {6-9} = -1
2-1=1
Factoring in Aces
When it comes to our three primary groupings we think in terms of 1/3’s and as three {6-9} equaling one {2-5} or cancelling out one {T} but when it comes to Aces we are thinking in terms of 1/4’s. The (A) are considered a side count completely separate from your three primary groupings.
If you are playing a 6D shoe game, there are 3 decks in the discard rack, you have 3 decks remaining and there are twelve (A) remaining the effect upon the three primary groupings is zero. We would note this in our count as 0-0-0-12r @3. The value of an (A) with one deck remaining is 1.2, so we use this as a point of reference for any level of penetration.
½ deck remaining=2.4
1 deck remaining=1.2
1 ½ decks remaining=.9
2 decks remaining=.6
3 decks remaining=.4
4 decks remaining=.3
5 decks remaining=.2
From there you simply see that if you have 2 decks remaining and ten (A) remaining then you have two surplus Aces, if you have 1 ¾ decks remaining and six (A) remaining then you have one deficit Ace, if you have 1 ¼ decks remaining and seven (A) remaining then you have two surplus Aces, etc.
With this procedure and with these simple formulas we can take virtually any deck composition and come up with a TC for betting purposes that matches actual advantage more closely than any other count I know of. Let's look at some more examples factoring in (A).
6-0-4-3r @1 TC-.6 6-4=+2 Four surplus {6-9} = -1.3 One deficit (A) = -1.2 +2 -1.3 -1.2 = TC-.6
6-0-5-5r @1 TC+.6 6-5=+1 Five surplus {6-9} = -1.6 One surplus (A) = +1.2 +1 -1.6 +1.2 = TC+.6
7-0-5-6r @1 TC+2.7 7-5=+2 Five surplus {6-9} = -1.6 Two surplus (A) = +2.4 +2 -1.6 +2.4 = TC+2.7
0-6-2-5r @1 TC+1.2 0-2=-2 Six deficit {6-9} = +2 One surplus (A) = +1.2 -2 +2 +1.2 = TC+1.2
Something you may notice in the above examples and that is at a glance (or at least once you become more familiarized with the system) you can recognize that the first two examples are clearly so close to a neutral count without an exact calculation. You would automatically be placing a minimum bet out there without even having to make the exact determination being so close to TC0.
The third example gets trickier with a lot of surplus {6-9} (EV down), along with surplus (A) (EV up). A Hi-Lo player would gauge this TC at a lot higher than what it really is due to not taking (7-9) into consideration but a positive count is a positive count! You wouldn't believe how often I sat back marking time betting minimums waiting for a solid positive count with a nice clump of Aces that I painstakingly tracked through the last shuffle. To have surplus {6-9} is better than having a seriously negative count with the surplus Aces, that's for sure.
The last example has a cancellation between six {6-9} and two {T} with one surplus (A), so TC is incredibly easy to calculate without much effort.
Where would a Hi-Lo player differ on TC from T system on these four deck compositions? Let's examine this a minute before we move on just for the heck of it. The following assumes an even distribution of (6) within the {6-9} grouping to give a finite point of reference for accurate comparison.
T Hi-Lo
6-0-4-3r @1 TC-.6 TC+1
6-0-5-5r @1 TC+.6 TC0
7-0-5-6r @1 TC+2.7 TC+4
0-6-2-5r @1 TC+1.2 TC0
What do you notice? They are quite close and the greater the surplus or deficit of {6-9} the further apart the TC calculations will be in comparing the two. The following table demonstrates this effect. Once again we are assuming an even distribution of (6) within the {6-9} grouping as a benchmark for accurate comparison.
T Hi-Lo
0-10-0-4r @1 TC+3.3 TC+2
0-9-0-4r @1 TC+3 TC+2
0-8-0-4r @1 TC+2.6 TC+2
0-7-0-4r @1 TC+2.3 TC+2
0-6-0-4r @1 TC+2 TC+1
0-5-0-4r @1 TC+1.6 TC+1
0-4-0-4r @1 TC+1.3 TC+1
0-3-0-4r @1 TC+1 TC0
0-2-0-4r @1 TC+.6 TC0
0-1-0-4r @1 TC+.3 TC0
0-0-0-4r @1 TC0 TC0
1-0-1-4r @1 TC-.3 TC0
2-0-2-4r @1 TC-.6 TC0
3-0-3-4r @1 TC-1 TC0
4-0-4-4r @1 TC-1.3 TC+1
5-0-5-4r @1 TC-1.6 TC+1
6-0-6-4r @1 TC-2 TC+1
7-0-7-4r @1 TC-2.3 TC+2
8-0-8-4r @1 TC-2.6 TC+2
9-0-9-4r @1 TC-3 TC+2
10-0-10-4r @1 TC-3.3 TC+3
The table demonstrates the increased betting correlation when surplus and deficit {6-9} are factored into your TC. Note the huge differences when there is a surplus of {6-9}! Assessment of the count is simple and a matter of procedure once you master it as follows:
-What is the difference between {2-5} and {T}?
-What is the effect of surplus or deficit of {6-9}?
-What is the effect of surplus or deficit (A)?
With these three steps we can decipher any given count to a very precise RC/TC by following a simple procedure and doing simple addition and subtraction.
4-3-0-3r @1=+4+1-1.2=TC+3.8
1-3-0-4r @1=+1+1+0=TC+2
4-0-3-5r @1=+1-1+1.2=TC+1.2
5-0-3-5r @1=+2-1+1.2=TC+2.2
6-0-3-5r @1=+3-1+1.2=TC+3.2
7-0-4-3r @1=+3-1.3-1.2=TC+.5
All the indices have already been worked out, merely a matter of memorizing them by learning to recognize patterns in deck composition which match up to deck compositions on a chart to give a more accurate/the most accurate playing decision. Maximum usage of the additional information provided by the count.
Thanks Tarzan for the detailed reply. I'm going to be rereading this a few times to help it sink in.
So I can see that you are looking at great opportunities to identify betting situations that normal counts wouldn't identify due to keeping track of the surplus of middle cards (while at the same time, avoiding some close calls.)
I'm going to guess that you use this for a perfect insurance count? Doubling your third column, adding your other 3 columns together, finding the difference between them, and if it's 4x (positive) the number of decks remaining you have your perfect insurance decision.
So you're looking at a BC of probably around .95 and an IC that's basically 1.0. I would have no idea how to find out what the PE would be, but I'm sure it's also very high.
You say that the index plays are just a matter of memorization as they have already been solved. Is the book that is out of print the only location to find these? I hope not, as I find this style of counting to be fascinating and would love to practice for a few months and really see what it's like to have more knowledge at the tables.
Anyway, great information!
DMHE material uses linear approach with side counts. Tarzan uses a non-linear approach to using the same data. It is much more accurate in general. The BC, PE and IC metrics are for linear approaches. Only the IC metric shows the true max at 1.0. Tarzan's BC is probably very close to .98 or maybe higher. His PE is probably in the .90's. The max PE for a linear count with no side counts is .70 but with side counts the PE can get much higher. Using ratios for 3 or more card groups instead of a linear aproach raises the PE ceiling even more. Think of the difference between knowing there are 5 more low cards played than high cards, and knowing there are also this many surplus or deficit of these middle ranks and there are 5 surplus aces with an equal number of T's to lows but not many middle cards and there are a lot more 8,9 than 6,7. When you add the pen you know you have 13 aces and of the remaining 96 cards there are 40% 2-5, 40% T's and 6% 6 or 7 and 14% 8 or 9 even if you can't state the ratios. The count is specific enough that this is the deck composition whether you can state it or not. Know realize you already know the right play for this deck composition for any matchup without doing any math. The linear counter only can say there are 5 more high cards than low cards but other than that the deck composition could be anything.
Thanks for the reply Tthree. I think that actually clears some things up.
You would actually sim indices for each column vs other 3 columns. For most, only one column will be useful for you.
For example, your 16+ vs 7+ would be first column vs other cards.
12-15 vs 12+ would use second column.
Doubles would mainly use 3rd column.
I mean, this is just a rough idea off the top of my head and I haven't actually simmed anything, but I think I'm understanding it better than before.
The hardest to solve would be the soft hands I think.
Look before you leap! I think it takes a certain type of personality to want to take on this type of count or to even go beyond Hi-Lo to HiOpt2 for that matter. Someone that is meticulous with good memorization skills sort of comes to mind. How many hours of blackjack someone plays per year makes a difference also. There's a little bit of difference on the skill level needed to spend 30+ hours a week at the table and the skill level of someone that flies out to Vegas once a year and might spend a few hours at the table. I am going through piles of notes to try and extract the most useful information to come up with the condensed version. I am running across things I scribbled down on a notepad 15 years ago and trying to decipher it into something understandable by someone other than me! Editing and organization.
There are those that question the amount of gain from a count like this and if it's worth bothering with, that whole "getting the most of it" catch phrase. Some are reputable professionals that I respect the opinion of. Think about what you wish to do, how many hours you plan on being at a blackjack table in your lifetime and one more thing! I was showing what I do to a professional poker player recently. This is an intelligent individual, was a 3.8 student in college and clearly someone that could learn this type of count, which I casually mentioned to him. He was a little stunned at the actual card counting demonstration and upon looking at excerpts from the manuscript said, "Aptitude or not, pokers players are inherently lazy!" I don't know if he was joking or not but he was making a calculated judgment and questioning not only his ability to be able to learn it but if he would have the motivation to do it.
Is the essay on determination of TC for betting purposes laid out in an easy to understand manner that reinforces elements of practical application throughout?
Last edited by Tarzan; 09-06-2014 at 08:26 PM.
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