I am a slow learner I suppose.

[ZenMaster_Flash]

Today I received an email from an aspiring A.P. re: True Count Denominator

"I see a few people using 2 deck true counting I have been using 1 deck true count is this correct?

Also what would the bet ramp look like for 10,000 bank roll , Im not ready for casino play yet was just
curious what it will look like and what true count would max bet be."

Here is my response, including an implied question:

The bet ramp does not really change because you are computing differently.

Think of it this way -- With a Level 2 Count your T.C. is represented by BIG numbers because you are counting mostly by twos (2's) - not ones (1's), thus you reach (numerically) bigger T.C.'s with a Level 2 count. So … accordingly with Hi-Lo each digit of the moving True Count adds or subtracts about 0.5%, while with Hi-Opt II or ZEN each is worth ½ of that 0.25%.

It remains proportional and approximate; very close to the mean percentage.

I do believe that the change in expectation as T.C. increases is less at big T.C. numbers than at more modest numbers.

Tangentially, I will mention that there is a point of diminishing returns.

Maximum advantage is reached with a ten density of 71%, (according to the renowned immortal Peter Griffin, Ph.D.), and declines beyond that as the probability of a 20-20 'push' will be vastly increased from the "off the top" probability of approximately 9%.

The advantage / disadvantage "moves" MOST when you are at common points of reference e.g. T. C. between approximately +/- 1 and +/- 6, or so I believe.

The noteworthy champion of the two (2) deck True Count Computation is the author of Blackjack Blue Book, wherein the Mentor Count is presented, Fred Renzey.

I have never understood greater "granularity"; which means more [not less] "data points".

I took a couple of stat' courses in graduate school, but admittedly did not ACE them [no pun intended].

I have been waiting years to fathom how moving from 1 deck to 2 decks is a move in the right direction. Will a kind soul present that clarification for me. A refutation will be welcome as well.

Intuitively, moving to ½ deck as some (e.g. Kenny Uston) have promulgated, is moving in the right direction.

Science in general, and mathematics in particular, supersede our primitive non-empirical "intuition".

Computer sim's can use the precise number of cards remaining; viz. a T.C. determined via 1/52nd of a deck << or 1/416th in an 8 deck shoe.>> L.O.L.

In DD games I Side-Count Aces and 7's via ¼ decks, but I use ½ deck T.C. determination.

In shoe games, Aces are easily side-counted via 1/4 decks, while my regular T.C. uses a 1 deck denominator.

RE: Mentor style True Count computing see: http://www.blackjackinfo.com/bb/showthread.php?t=9709

On TWO related topics of genuine importance - NOT recognized often enough:

1. "Truncating" your True Counts is good. "Flooring" them is best. "Rounding" is poor.

2. If you make an index play (violating Basic Strategy) without having clearly met the requisite T.C. you are ACTUALLY better off playing Basic Strategy.

The latter is counter-intuitive [no pun intended], but is to be found via a thorough reading of The Theory of Blackjack, 6th ed. I am purposely not citing the page number because

I fantasize that my fellow BJ aficionados will read and re-read this magnum opus, ad infinitum; by ignoring the complex mathematics, (that I do not comprehend)

[shadroch]

If this was sent to you as a PM, you really shouldn't be making it public.

[bebe]

I sure who ever sent it knows its a honor for ZMF to work with them and does not care
he posted it. Atleast thats the the way I see it.

[NaLaAa]

This at least is some information i've located http://www.blackjackinfo.com/bb/showthread.php?p=59562

[alexost]

It is essential to understand there is a difference between how the indices were calculated for the true count (2 deck (Mentor), 1 deck (Wong Hi Lo), half deck (Revere Point Count, Hi Lo Lite), and the resolution that you are calculating your true count to (whole deck, half deck, quarter deck, exact deck).
The indices are defined during the author/developers system calculation whereas the resolution you can choose according to how precise you want or believe you need to be when calculating the true count.

For example, using Wong's Professional Blackjack Hi-Lo, the indices are calculated using whole decks. So you have to divide the running count by the number of whole decks remaining. But how precise you want the resolution is up to you.

Here is a chart I made to help understand and calculate the true count for Wong's Hi-Lo. I chose whole deck resolution for 6, 5, 4, 3 decks remaining, and quarter deck resolution for 2 or fewer decks remaining. I am a recreational counter and when I play I usually try to play good 1 or 2 deck games.

Decks RC	6	5	4	3	2	1.75	1.5	1.25	1.00	0.75	0.5
C.F.	/6	/5	/4	/3	*.5	*.6	*.7	*.8	*1	*1.3	*2
1	0	0	0	0	0	0	0	0	1	1	2
2	0	0	0	0	1	1	1	1	2	2	4
3	0	0	0	1	1	1	2	2	3	3	6
4	0	0	1	1	2	2	2	3	4	5	8
5	0	1	1	1	2	3	3	4	5	6	10
6	1	1	1	2	3	3	4	4	6	7	12
7	1	1	1	2	3	4	4	5	7	9	14
8	1	1	2	2	4	4	5	6	8	10
9	1	1	2	3	4	5	6	7	9
10	1	2	2	3	5	6	7	8	10
11	1	2	2	3	5	6	7	8
12	2	2	3	4	6	7	8
13	2	2	3	4	6	7
14	2	2	3	4	7
15	2	3	3	5	7
16	2	3	4	5
18	3	3	4	6
19	3	3	4	6
20	3	4	4	6

[Renzey]

The noteworthy champion of the two (2) deck True Count Computation is the author of Blackjack Blue Book, wherein the Mentor Count is presented by Fred Renzey.
I have never understood greater "granularity"; which means more [not less] "data points". I have been waiting years to fathom how moving from 1 deck to 2 decks is a move in the right direction. Will a kind soul present that clarification for me. A refutation will be welcome as well.
RE: Mentor style True Count computing see: http://www.blackjackinfo.com/bb/showthread.php?t=9709

The "count-per-remaining-double-decks" gives you larger whole numbers with which to gauge the richness/leanness of the remaining supply of cards. Since you're working with larger whole numbers, they are divisable into smaller whole numbers without going into fractional numbers.
As an example, suppose you're playing a shoe game with the Zen Count and true up your RC to the traditional "count-per-deck" method (1dTC). Computing this quickly, it looks like Insurance would be warranted at just about a +5.5 TC. Had you been using a 2dTC, Insurance would be warranted at +11.0 TC. You'd have the benefit using whole TC integers for many indices that fall on fractional numbers, but were moved to the next higher TC integer for practical purposes.
That's what's meant by "finer granularity".

But for shoe games, finer granularity is just one of two conveniences afforded by the 2dTC method of truing up your RC. The other is that as the shoe winds down to critical territory (around 2 decks left), there's little or no truing up to be done. Right at that point, the TC is the RC. Just play by the RC. If there's a little less than 4 decks in the discard tray, use about 90% of the RC for your TC. If there's a little more, use 110%.
If and when you get 4.5 decks deep, then you do need to add a third to your RC to get the TC.

Several balanced count users tell me they're quick and comfortable with the 1dTC method, and that's fine. But for those who use a level 1 count like Hi/Lo, many index plays such as 8 vs 5, 12 vs 2 and 9 vs 7 don't fall right on whole numbers. They could get closer to "on-the-money" by using 2dTC.

In the end, this debate could fall into that same basket with "angels dancing on the head of a pin". I'm merely saying that if you're just starting out, I think the 2dTC method is technically superior, and probably easier.

[Mr. White]

Mr. Renzey,

Out of curiosity, and realizing there are a lot of factors that could go into this, do you have any general estimate on the performance difference between a system using 1dtc vs 2dtc? (For example, a level one system with a full set of whole-number indices, shoe games.)

[Renzey]

Mr. Renzey,

Out of curiosity, and realizing there are a lot of factors that could go into this, do you have any general estimate on the performance difference between a system using 1dtc vs 2dtc? (For example, a level one system with a full set of whole-number indices, shoe games.)

Off hand, I honestly don't know, but am confident it would be quite small. I can however, run two long sims, comparing 1dTC vs. 2dTC. I'll have to get to that soon.

[Renzey]

I can however, run two long sims, comparing 1dTC vs. 2dTC. I'll have to get to that soon.

Mr. White,
Ran the two sims -- 750 million hands each. Rules were Hi/Lo Count, 6 deck, H17, das, 4.25 decks dealt. Played one hand at a two-handed table on a 100 max bet bankroll.
Ran them on Wong's BJCA, hence, no SCORE.
Betting ramps were:

1dTC
...-2.......0.......+2.......+3........+4 (playing all whole number indices from -2 to +5)
...0u.....1u.......4u........8u.......12u

2dTC:
...-4.....-3......-2......0.....+3.....+4....+5.....+6......+7......+ 8 (whole nmbr. indices -4 to +10)
...0u....0.5u....1u....1u.....3u.....4u.....6u.....8u.....10u .....12u

Results:
.............Unit.......Avg Bet......Hourly SD......EV%..........Hourly Win.........Lifetime ROR
1dTC.......1u.........1.99u.........41.64u......+0.812.......1.616u +/-.015u.........10.7%
2dTC.......1u.........2.03u.........41.71u......+0.820.......1.668u +/-.015u.........10.0%

Initially, a 3% gain for 2dTC. But BJRM says you could increase your betting stakes by 2.9% with 2dTC to achieve the same 10.7% ROR as 1dTC -- thereby winning 1.717 original sized units per hour using 2dTC. Looks like a 6% overall performance gain???
Would love to see an official SCORE comparison.

[Mr. White]

Mr. Renzey - thanks for the response!

I had screwed around with sims a bit and also saw similar increases in performance, but thought I had an error because it just seemed like such a large gain.

So, would you say its safe to say that a level 2 count with 2DTC will probably NOT see a simmed performance gain of quite the same magnitude seen in the level 1 2DTC sim (due to the fact that the level 2 already has finer betting ramps and more precision in the indices)?

[ZenMaster_Flash]

Now, at long last, I fully understand.
Part of my bewilderment rested upon
my failure to realize that this issue is
moot for Level 2 Counts and above.

By the way, Shadrach, scroll back to
my original post. It was not a PM, it
was email from a player that I know.

[Renzey]

Mr. Renzey - I had screwed around with sims a bit and also saw similar increases in performance. Would you say a level 2 count with 2DTC will probably NOT see a simmed performance gain of quite the same magnitude?

I will guess that a level 2 count with 2dTC would perform much closer to that of 1dTC because of the already finer calibrations of the level 2 count.