Bryce Carlson on card clumping (long...)

[Brycarlson]

I have resisted getting involved in the newsgroup's card-clumping
controversy because so much of what is written seems to be flash and
flame, and so little appears to be a real search for truth. However,
there are a lot of players out there who really do want to know the truth
of the matter--and have no idea what or whom to believe. So, in an effort
to shed some light on the matter I have conducted a series of computer
studies, consisting of several billion hands of simulated Blackjack, that
I believe go a long way toward clarifying the issues involved.

These simulations were run using the Omega II Blackjack Casino v1.2 for
MS-DOS and Windows. This program has the ability to perform real-world
shuffles (picks, riffles, strips, cuts, etc.) as they are done in a
casino, as well as perform random card selections using a pseudo-random
number generator (P-RNG).

Before we get into the results of the simulations, however, let's take a
look at the
psychodynamics that I believe are driving the card-clumping "industry."

First off, accurate card counting is difficult; consequently, the vast
majority of would-be card counters are, and always will be, losers. It's
that simple. Becoming a winning counter takes a lot of hard work, and a
lot of good judgment. Not surprisingly, therefore, many players yearn for
an easier way. A shortcut that will allow them to target games they can
beat using simple methods they can master in a few short hours. This
hunger for a free lunch is not unique to Blackjack, but as I say in
Blackjack for Blood, "...in the game of Blackjack, as in the game of life,
winning is tough. It requires determination, preparation, and plenty of
perspiration." But, unfortunately, "...this is not what most people (are)
looking for." What they want, instead, is "...a simple rule for riches
they (can) memorize on the taxi ride to the casino."

So, from the players' perspective, card-clumping systems are very
seductive--they promise an easy alternative method for winning play.

Now, let's take a look at it from the perspective of the entrepreneurs
who sell books, systems, programs and tapes hawking card-clumping
"technology." What's in it for them? Answer: $$$. Big $$$.

Players WANT to believe in a simple "winning" concept such as
card-clumping--and where there's a want, sooner or later someone will
market a way.

Of course, authors of card-counting works also sell books, systems and
programs to wanna-be winners. So, what's the difference? The answer is
both simple and straightforward: Bryce Carlson, Stanford Wong, Arnold
Synder, Kenny Uston, Peter Griffin, etc., have all based their works on
accepted scientific principles, with a minimum of speculation, estimation,
or guesswork.
Publishers of card-clumping systems, on the other hand, have based their
works almost entirely on plausible-sounding theories backed up by
anecdotal testimonials. Science versus "religion." Fact versus faith. A
modern paradigm for an age-old conundrum.

Now having said all this, you are likely expecting me to state
categorically that there is nothing to the card-clumping concept. That it
just doesn't happen. Well, surprise, I'm not prepared to do that. Based
on the computer studies that follow, it does appear that under certain
(unusual) circumstances, some non-random "clumping" effects are produced
in some (unrealistically incomplete) multiple-deck shuffles. As we shall
see, these effects are generally small, probably not exploitable, rarely
(if ever) encountered--and such biases seem to favor the player as often
as they favor the house. But, they are there.

Ready for more? OK, here are the studies, and the results.

Let's begin by discussing the Omega II Blackjack Casino's ability to
perform real-world shuffles, as well as simple random card selections
based on a P-RNG (pseudo-random number generator).

The card-clumping system sellers and their faithful followers discount the
fact that computer simulations have not backed up their claims of bias by
stating that these effects only occur in games where the decks are
actually shuffled as they would be in a casino, not in computer-simulated
games where the cards are selected by a P-RNG. They have a point. Almost
all Blackjack simulation programs do select cards with a P-RNG. Note,
however, that the operative
word is "almost." The Omega II Blackjack Casino v1.2 DOES do real-world
shuffles as they are done in a casino. The card-shuffling routines in the
Omega II Blackjack Casino have been thoroughly analyzed and tested. You
can trust these results. And, just in case you don't trust what you can't
see, the Blackjack Casino allows you to step through the various shuffle
routines--all the while visually displaying the cards in their current
sequence and order. John Imming's
highly-regarded Universal Blackjack Engine also does such real-world
shuffles, and his program has even more bells and whistles in its
shuffling algorithms than the Blackjack Casino does. So, there are
programs out there capable of performing realistic casino-style shuffles.

Although the Blackjack Casino is capable of performing a large number of
different shuffle-related routines, the studies done here used only the
following procedures: A wash of "new" decks (W); a two-block zone riffle
of the entire pack (R); a strip of the entire pack (S); a random cut (C),
and the introduction of a fresh pack into the game in new-deck order (F).

These procedures are performed by the Omega II Blackjack Casino in the
following manner:

(W) Wash: The pack is randomly broken into packets of from 1 to 8 cards.
The program then randomly puts these packets back together. The cards
within a packet maintain their initial order, only the packets themselves
are randomly reordered.

(R) Two-block zone riffle: The pack is divided into two approximately
equal blocks. Then half-deck "picks" from each block are riffled
(randomly interleaved) together to form a new stack. This procedure is
repeated until all the cards are in this new stack.

(S) Strip: The program randomly strips small packets of from 1 to 4 cards
off the top of the pack
and places them in another stack. This procedure tends to reverse the
order of the pack.

(C) Cut: The program performs a random cut. All possible cuts are
equally likely.

(F) Fresh pack: A fresh pack is brought into the game in new-deck order.

The simulations were all performed assuming a 6-deck game with Las Vegas
Strip rules, including double after splits, and resplitting of all pairs
including Aces. Penetration varied slightly, but was always to a fixed
number of rounds that generally totaled about 245 cards. The game was
dealt face-up and blackjacks and busted hands were immediately "placed" in
the discard tray (buffer). A fresh pack of 6 decks in new-deck order was
brought in periodically, just as it would be in a real casino. From other
computer studies, as well as from well-documented
direct probability studies, we know that the theoretical expectation for
this game, assuming flat bets and Basic Strategy play is -.34% (of the
original bet) for the players. In other words, the house enjoys a slight
edge in this game (of +.34%), assuming Basic Strategy play.

Each computer study consisted of 100,000,000 (one hundred million) rounds.
The Omega II Blackjack Casino in fast, so such extensive studies were
feasible. The percent standard deviation for each player's expectation in
each study was about +/- .011%.

Each shuffle study consisted of seven individual simulations. Each
simulation was similar except for the number of players (from 1 to 7
players).

Study #1 did not use real-world casino-style shuffles, but instead
performed random card selections using a pseudo-random number generator
(P-RNG). The results were virtually the same for all seven simulations (1
player, 2 players, 3 players, etc.). Since the results did not differ
regardless of the number of players at the "table," only the results for
the 7-player simulation are shown (below):

PLAYER 1 RESULT -.35% DELTA -.01%
PLAYER 2 RESULT -.33% DELTA +.01%
PLAYER 3 RESULT -.34% DELTA +.00%
PLAYER 4 RESULT -.35% DELTA -.01% } MEAN DELTA +.00%
PLAYER 5 RESULT -.35% DELTA -.01%
PLAYER 6 RESULT -.34% DELTA +.00%
PLAYER 7 RESULT -.34% DELTA +.00%

As expected, no biases or other unusual results were obtained. The
results are almost exactly as predicted by theory (-.34%).

Study #2 did use real-world casino-style shuffles. The shuffle was
typical of that performed in many casinos and consisted of the following
shuffle sequences: For fresh packs brought into the game in new-deck
order, the shuffle sequence was FWRRSRC (fresh pack, wash, zone-riffle,
zone-riffle, strip, zone-riffle, cut). For reshuffles of the pack in play
the shuffle sequence was RRSRC (zone-riffle, zone-riffle, strip,
zone-riffle, cut). As with Study #1, the results were
virtually the same for all seven simulations (1 player, 2 players, 3
players, etc.). Since the results did not differ regardless of the number
of players at the "table," only the results for the 7-player simulation
are shown (below):

PLAYER 1 RESULT -.32% DELTA +.02%
PLAYER 2 RESULT -.35% DELTA -.01%
PLAYER 3 RESULT -.31% DELTA +.03%
PLAYER 4 RESULT -.33% DELTA +.01% } MEAN DELTA +.01%
PLAYER 5 RESULT -.35% DELTA -.01%
PLAYER 6 RESULT -.32% DELTA +.02%
PLAYER 7 RESULT -.34% DELTA +.00%

In this 7-player simulation, a fresh 6-deck pack was introduced every 440
rounds. As can be seen, little if any bias is evident. Given the large
number of rounds (100,000,000), the player results do vary slightly more
than would be expected on statistical grounds, and this minor increased
variance probably is due to non-random effects. But these effects, if
they exist, are very, very small, seem to favor neither the players as a
group nor the house, and are of no practical significance, whatever.

Study #3. The card-clumping "gurus" generally blame the wash (W) for
producing most of the biases they claim exist in multiple-deck games. To
test for this, the above study was run, again, except that this time when
a new 6-deck pack was introduced into the game, NO wash was performed.
The fresh pack shuffle, therefore, consisted of FRRSRC. Reshuffles of
the pack in play did not change (RRSRC).

This time non-random effects, though small, were evident. Furthermore,
these effects varied based, primarily, on the number of players at the
table. Therefore, all seven simulations are presented below:

Simulation #1. One (1) player. Fresh pack every 1120 rounds.
Penetration to 43 rounds per "shoe."

PLAYER 1 RESULT -.44% DELTA -.10% } MEAN DELTA -.10%

Simulation #2. Two (2) players. Fresh pack every 960 rounds.
Penetration to 29 rounds per "shoe."

PLAYER 1 RESULT -.43% DELTA -.09%
PLAYER 2 RESULT -.38% DELTA -.04% } MEAN DELTA -.07%

Simulation #3. Three (3) players. Fresh pack every 800 rounds.
Penetration to 22 rounds per "shoe."

PLAYER 1 RESULT -.35% DELTA -.01%
PLAYER 2 RESULT -.33% DELTA +.01% } MEAN DELTA -.01%
PLAYER 3 RESULT -.37% DELTA -.03%

Simulation #4. Four (4) players. Fresh pack every 640 rounds.
Penetration to 18 rounds per "shoe."

PLAYER 1 RESULT -.31% DELTA +.03%
PLAYER 2 RESULT -.34% DELTA +.00%
PLAYER 3 RESULT -.32% DELTA +.02% } MEAN DELTA +.02%
PLAYER 4 RESULT -.31% DELTA +.03%

Simulation #5. Five (5) players. Fresh pack every 560 rounds.
Penetration to 15 rounds per "shoe."

PLAYER 1 RESULT -.25% DELTA +.09%
PLAYER 2 RESULT -.22% DELTA +.12%
PLAYER 3 RESULT -.27% DELTA +.07% } MEAN DELTA +.10%
PLAYER 4 RESULT -.25% DELTA +.09%
PLAYER 5 RESULT -.23% DELTA +.11%

Simulation #6. Six (6) players. Fresh pack every 480 rounds.
Penetration to 13 rounds per "shoe."

PLAYER 1 RESULT -.19% DELTA +.15%
PLAYER 2 RESULT -.16% DELTA +.18%
PLAYER 3 RESULT -.22% DELTA +.12%
PLAYER 4 RESULT -.17% DELTA +.17% } MEAN DELTA +.16%
PLAYER 5 RESULT -.20% DELTA +.14%
PLAYER 6 RESULT -.16% DELTA +.18%

Simulation #7. Seven (7) players. Fresh pack every 440 rounds.
Penetration to 11 rounds per "shoe."

PLAYER 1 RESULT -.11% DELTA +.23%
PLAYER 2 RESULT -.13% DELTA +.21%
PLAYER 3 RESULT -.16% DELTA +.18%
PLAYER 4 RESULT -.12% DELTA +.22% } MEAN DELTA +.21%
PLAYER 5 RESULT -.13% DELTA +.21%
PLAYER 6 RESULT -.15% DELTA +.19%
PLAYER 7 RESULT -.14% DELTA +.20%

Clearly, there is some (small) bias present in this study. In addition,
it appears that the more players at the table, the better off the players
are. With one or two players, there appears to be a small bias of about
.1% against the players. With three or four players, any biases, if
present, appear to cancel out, resulting in no net effect (except, for the
peculiar increased variance of results noted in the P-RNG study, above).
With five, six, or seven players at the table, there
appears to be a small (.1% to .2%) net bias working for the players.

This number-of-players-dependent bias pattern was not expected (not by me,
anyway). To see whether or not it was repeatable, and whether small
changes could alter it, I ran the entire 7-simulation study, again, this
time varying the penetration and frequency of fresh-pack introductions,
somewhat. The results, though varying slightly from the previous study,
showed the same pattern of increasing bias favoring the players as the
number of players at the "table"
increased, with the break-even point at three or four players. This
effect, though small, seems to be both real and persistent (at least, when
all players use Basic Strategy). It is interesting to note that a
player's position at the table does not seem to be a factor correlating
with expectation.

Encouraged (though not necessary happy) with these results, I next ran a
series of studies degrading the shuffle more and more in an attempt to get
biased results large enough to be potentially meaningful and exploitable.

From the perspective of the card-clumping cult, the results of these
subsequent studies were disappointing. As the shuffle got more and more
primitive, only a slight increase in the bias effect was noted. As
before, with one or two players, it hurt the players, with three or four
players, it seemed to virtually disappear, and with five, six, or seven
players, the players were somewhat favored.

Finally, it an attempt to get a bias effect large enough to mean anything,
I ran a study using a VERY primitive shuffle. For fresh packs the shuffle
sequence was FRC (fresh pack, zone-riffle, cut). For reshuffles of packs
in play the sequence was simply RC (zone-riffle, cut). Note, the lack of
a wash (W) with fresh packs. There is no casino in the world, that I am
know of, that uses a shuffle this primitive and incomplete. Furthermore,
even with this unrealistically incomplete
shuffle, if a wash (W) were introduced into the fresh-pack shuffle
sequence, any bias virtually disappeared.

Here are the results of this final study.

Simulation #1. One (1) player. Fresh pack every 1120 rounds.
Penetration to 43 rounds per "shoe."

PLAYER 1 RESULT -1.10% DELTA -.76% } MEAN DELTA -.76%

Simulation #2. Two (2) players. Fresh pack every 960 rounds.
Penetration to 29 rounds per "shoe."

PLAYER 1 RESULT -.80% DELTA -.46%
PLAYER 2 RESULT -.68% DELTA -.34% } MEAN DELTA -.40%

Simulation #3. Three (3) players. Fresh pack every 800 rounds.
Penetration to 22 rounds per "shoe."

PLAYER 1 RESULT -.44% DELTA -.10%
PLAYER 2 RESULT -.43% DELTA -.09% } MEAN DELTA -.09%
PLAYER 3 RESULT -.41% DELTA -.07%

Simulation #4. Four (4) players. Fresh pack every 640 rounds.
Penetration to 18 rounds per "shoe."

PLAYER 1 RESULT -.29% DELTA +.05%
PLAYER 2 RESULT -.36% DELTA -.02%
PLAYER 3 RESULT -.31% DELTA +.03% } MEAN DELTA +.02%
PLAYER 4 RESULT -.34% DELTA +.00%

Simulation #5. Five (5) players. Fresh pack every 560 rounds.
Penetration to 15 rounds per "shoe."

PLAYER 1 RESULT -.18% DELTA +.16%
PLAYER 2 RESULT -.15% DELTA +.19%
PLAYER 3 RESULT -.13% DELTA +.21% } MEAN DELTA +.16%
PLAYER 4 RESULT -.24% DELTA +.10%
PLAYER 5 RESULT -.18% DELTA +.16%

Simulation #6. Six (6) players. Fresh pack every 480 rounds.
Penetration to 13 rounds per "shoe."

PLAYER 1 RESULT -.17% DELTA +.17%
PLAYER 2 RESULT -.19% DELTA +.15%
PLAYER 3 RESULT -.23% DELTA +.11%
PLAYER 4 RESULT -.14% DELTA +.20% } MEAN DELTA +.19%
PLAYER 5 RESULT -.10% DELTA +.24%
PLAYER 6 RESULT -.09% DELTA +.25%

Simulation #7. Seven (7) players. Fresh pack every 440 rounds.
Penetration to 11 rounds per "shoe."

PLAYER 1 RESULT +.19% DELTA +.53%
PLAYER 2 RESULT +.11% DELTA +.45%
PLAYER 3 RESULT +.10% DELTA +.44%
PLAYER 4 RESULT +.15% DELTA +.49% } MEAN DELTA +.47%
PLAYER 5 RESULT +.16% DELTA +.50%
PLAYER 6 RESULT +.12% DELTA +.46%
PLAYER 7 RESULT +.09% DELTA +.43%

As with the previous study, I was suspicious of the trend toward a
player-favored bias as the number of players at the "table" increased.
So, as before, I ran the entire 7-simulation study, again, varying the
penetration and frequency of fresh-pack introductions, somewhat. As
before, the results, though varying slightly, continued to show the same
pattern of increasing bias favoring the players as the number of players
at the "table" increased, with the break-even point at three or four
players. Also, as before, a player's position at the table does not seem
to be a factor correlating with expectation.

With this last study, we, at last, seem to have an effect worthy of the
name "bias." As to whether or not it is exploitable is another story. As
noted, to get significant non-random effects resulting in a noticeable
bias it was necessary to limit the shuffle to an unrealistically
incomplete zone-riffle, cut (RC) sequence that is not found anywhere in
the world that I know of. Also, as noted, even with this primitive
shuffle, the introduction of a simple wash (W) in fresh-pack introductions
virtually eliminated the bias, completely.

The card-clumping "gurus" have claimed that orthodox researchers have
failed to detect biases in the deal because their studies have been
distorted by unrealistic conditions (such as the use of P-RNG's in
simulations). It appears, however, that it is the card-clumping wonks,
themselves, who are trading in unrealistic conditions. You could search
the world over and never find a casino so careless as to use the
simplistic shuffles necessary to produce a meaningful bias.

We're not quite through yet.

The argument could be made, however, that just because the AVERAGE bias
produced by realistic casino shuffles is too small to matter, it does not
necessarily follow that meaningful--exploitable--opportunities do not
arise for clump trackers, any more than the fact that Basic Strategy
expectation is on AVERAGE close to zero means that
meaningful--exploitable--opportunities do not arise for card counters.

That's a plausible-sounding argument. But there are problems with it. To
begin with, to the extent that card-clumping concepts are valid,
card-counting concepts are not. They are essentially opposites. In
card-counting theory, the best predictor of the next card being "big" is
that the last several cards have been "small" (a "plus" count). In
card-clumping theory, the best predictor of the next card being "big" is
that the last seveal cards have also been "big" (a "big"-card clump).
Consequently, if card-clumping theory were valid, multiple-deck team play
would not work. A "Big Player" being called into a "plus" shoe would
generally walk into a catastrophe of dealer three- and four-card 20s and
21s. But that's not what happens. Team play does work. Kenny Uston's
teams made a fortune with it. I have done very well with it; and teams,
led by players you've never heard of, are out, tonight, making money with
team play. This fact, alone,
argues strongly against the card-clumping concept.

Here's another important point: If the pack were often strongly
"polarized" with biased clumps not conforming to a normal distribution,
Basic Strategy would be very ineffectual--especially in small-card clumps.
Consequently, the very fact that any kind of reasonable shuffle produces
(as the above studies have shown) at best (worst?) a nominally detectable
average bias against Basic Strategy play is strong evidence that no such
biased clumping or polarization of the pack
occurs.

I know that none of this is going to have the slightest impact on the
Jerry Patterson's, or the Boris's, or any of the other financially- or
emotionally-invested faithful in the card-clumping cult.

They will argue that these studies are far from comprehensive. That I
didn't look hard enough, or long enough, or in the right places. And
that, in any case, I DID find the elusive biases the orthodox cognoscenti
say don't exist. Perhaps; and I do look forward to further research and
results. But it's not up to us to prove that real-world biases can't
exist--it's up to them to prove that they can, and that they do. And that
is something they have never done. And probably never will.

Caveat emptor. Let the buyer beware.

Bryce Carlson <bryca...@aol.com>

[Chuck Stull]

In article <40t80t$k...@newsbf02.news.aol.com>, jhi...@aol.com says...
>
>
> From John Imming:
>
> I would like to thank Bryce for taking the time to run these
>simulations and present his thoughts on card clumping. In general,
>I agree totally with his logic.

I have also been one to sit back and stay out of this fiasco, partly because
I didn't have the ability to rebut or add to the discussion. I was also
embarrassed that so many knowlegable people had just come on at
a time when the group was full of flaming and nonsense. What a relief that
you gentlemen have been willing to take your time to give us all a
dispassionate understanding of the facts involved.

Thanks you greatly -- I do hope that the responses add to our understanding,
not just a rehashing of the same old argument.

BJ

[Brycarlson]

Bryce Carlson continues....

To clarify; the sentence, below, should have read, "Each computer
simulation consisted of 100,000,000 (one hundred million) rounds."

>Each computer study consisted of 100,000,000 (one hundred million)
rounds.
>The Omega II Blackjack Casino in fast, so such extensive studies were

>feasible...

Each computer study consisted of a set of several simulations--each such
simulation consisting of 100,000,000 rounds.

Bryce <bryca...@aol.com>

[JHIRWC]

Form John Imming: I would like to thank Bryce for taking the time to run these simulations and present his thoughts on card clumping. In general, I agree totally with his logic. The Omega II Blackjack Casino is a licenced variation of the UBE, version 4.3. This version was the last of my text based software. I agreed to modify and licence it to Bryce because I respect his work greatly and because he was willing to "keep alive" a very solid text based program that I had 4 years of my time and effort invested in. The shuffling algorithems in the program had 4 years of testing, and they are VERY solid. The current UBE is event driven, graphics oriented, and has many more features. However, the Omega II is more reasonably priced. Within the next 24 hours, I plan to do a much more detailed post using the Randomness sieve in the latest UBE version 7.5. It will come to the same bottom line conclusion that Bryce does. About 4 years ago Arnold Snyder noticed some peculiar patterns that occur with UNREALISTICALLY SLOPPY shuffles. We both looked at it in hopes of getting an article out of the phenomenon for Blackjack Forum. However, after much thought we both decided that there was nothing here that could be PRACTICALLY EXPLOITED by the average player. When I originally wrote the UBE almost 8 years ago, the ability to analyze real world shuffles was a major goal. In fact, that is why I call my small company Real World Casino. I originally wrote the program as private stock for myself and an old time professional team player who convinced me to write the program in the first place. Edie Holliday, the person who talked me into doing it, was very interested in the idea that some shuffles had an inherent affect on the game. After much simulation, I came to the conclusion that with a realistic shuffle, this was simply not the case. Fortunately, Edie was also interested in card counting (deck subset logic), so I built that into the program also. Edie was also an old time dealer who was interested in various hi-hi-lo-lo stacks that a cheating dealer could perform. The UBE can handle these, but with a realistic shuffle even these degenerate into randomness very quickly. To be effective, they have to be combined with phony shuffles. Because I have found them to be of academic interest only, I have downplayed this aspect of the software for many years. However, because of the flap-doodle on this group that has revolved around this theory, I have looked at and refined the shuffling algorithems even more. They will be available in version 7.5, which will be shipping as soon as I get the manuals back from the printer. One final note. Any software that claims to analyze shuffles should allow the user to view the deck before the shuffle, execute the shuffle, and then show the user the order of the deck AFTER the shuffle. I have always had this feature in my software, so I am sure it is in the Omega II . In the UBE 7.5, it is even more extensive. One MORE final note. I have run extensive analysis on the shuffles generated by the shuffle master IV and for all practical purposes, they may as well be coming out of a random number generator. Sorry about that. If I could prove otherwise, I am sure that I could sell more software, but the truth is the truth. Another FINAL thought. For years, I have tried to avoid getting into verbal food fights with people with sincere but ill concieved ideas on this subject. However, if I am to stay on this group, I guess that I cannot avoid it any longer. John Imming jhirwc@aol,com

[Lee Jones]

In article <40se59$e...@newsbf02.news.aol.com>,
Brycarlson <bryca...@aol.com> wrote:

>So, in an effort
>to shed some light on the matter I have conducted a series of computer
>studies, consisting of several billion hands of simulated Blackjack, that
>I believe go a long way toward clarifying the issues involved.

Just when I thought I was going to THROW UP if I saw the term "card-clumping"
again, Bryce writes a *massively* long post, and I find myself riveted
throughout.

His post has raised the S/N ratio of this newsgroup by several decibels.

Regards, Lee
"And he's right - it won't change the Patterson/Boris babble."
--
Lee Jones | "Shiny happy people holding hands"
le...@sgi.com | -R.E.M.
415-390-3356 |

[Edziu Iskra]

Thank you very much, Bryce. You renew my faith not in the concpet of a
professional, but the concept of responsible authority. It would have
been almost too easy to just stay out of the fracas and let people banter
about unsubstantiated claims, and let the foolish be fooled. You and Mr.
Imming do the concept of "authority" a credit by responding to the time
and need in an appropriate fasion.

I salute you.
--
-- Edziu