http://www.saliu.com/bbs/messages/274.html
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Posted by Ion Saliu on August 19, 2000 at 11:29:05:
In Reply to: BEING THERE posted by Mr. T on August 15, 2000 at
09:21:42:
• My emphasis has been MATHEMATICS IN GAMBLING. If there is a gambling
system, I analyze it mathematically, first and foremost. It includes
COUNTING CARDS, the most talked about gambling system. Many gamblers
fall in love with one or more systems. Sometimes they go beyond that
and worship their system. Card counting has become a religion for at
least two decades.
Mathematically, the card counting system has a minor influence today,
if any. I showed in a previous post the only impact counting can have
in a single deck game, Player against Dealer. A +2 count, generously
translated into a 2% Player's advantage results in a 0.01% better
chance to get a blackjack (a "natural"). Such a chance increases, at
best, from 4.77% to 4.78%.
The main mathematical aspect is the SEQUENCE of the remaining cards.
Card counting does not even attempt to "predict" the card sequence. In
reality it is impossible to "detect" the sequence of the remaining
cards. The number of sequences is staggering. They are calculated by
the FACTORIAL operator (N!). Let's exemplify briefly in an ideal
situation. Before Edward E. Thorp's "Beat the Dealer" book (an
important work, indeed) the Dealer dealt all the cards in a single
deck. Therefore, the penetration was 100%. A card counter would wait
up until the last quarter of the deck or so. Let's say the counter
estimated that around 13 cards were remaining in the 52-card deck. The
legend has it that many struck it big at the blackjack tables simply
by betting huge amounts towards the end of the deck. Mathematics,
however, does not confirm such claim. To calculate the number of
possible sequences of 13 cards, we use 13! = 1x2x3x…x12x13. The result
is: 6,227,020,800 (over 6 trillion sequences). Let's be fair. There
would be only 10 unique cards among 13, since 10=J=Q=K. In this case,
10! = 3,628,800 (over 6 million possible sequences)! Imagine an even
better situation for Player, that the count is +3 and that there are
no "neutral" cards remaining (e.g. 7 , 8). We can use software to
generate 13-card sequences. The composition would be 8 high cards (H)
and 5 low cards (L). I used my software for the task (SHUF-5.EXE or
SHUF-6.EXE). The program generated thousands of sequences, from card 1
to card 13. I considered 1-5 as L and 6-13 as H. Here are the three
final sequences of the run:
L, H, L, H, H, H, L, H, L, H, H, L, L
H, L, H, H, H, L, L, H, H, H, H, L, L
H, H, L, L, L, H, H, H, L, H, L, H, H
Let's play the first sequence now, between one Player and the Dealer.
Player gets L, Dealer gets H. Player gets H, Dealer gets H. Player
stands, Dealer stands. Dealer wins one hand. Player gets H, Dealer
gets H. Player gets L and stands, Dealer gets H and wins the 2nd hand.
Player gets L, Dealer gets H, Player gets H, Dealer gets L and draws
L; more probably, Dealer wins the hand.
In the 2nd sequence, Player gets H, Dealer gets L, Player gets H and
stands, Dealer draws L, and must draw to LH, gets an H and busts.
Player wins the 1st hand. Player gets L, Dealer gets L, Player gets H
and stands, Dealer gets H and draws another H (bust). Player wins the
2nd hand.
It is very, very complicated. We are dealing with over three and a
half million sequences. The matters are a lot more complicated when we
consider the neutral cards and multiple players. The impact of card
counting appears to be near negligible. I count cards sometimes up to
the latest card. I call it the "real running count". At the end of a
round the count is positive, for example. When it is my turn to make a
decision after my first two cards, the count turns out to be very
negative. A card counter would have bet bigger at the beginning of the
round. When it was his/her turn to make a decision, the count would be
clearly negative. The player might expect a low card. Quite often,
Player gets the opposite, a busting high card. I noticed frequently
such sequences. They seem to be totally random. If you are a faithful
card counter, you should expect to lose serious money for a
significant number of rounds (hands). Sometimes, but rarely, card
counting might help in hitting or double-down decisions. Once, I
shocked the audience when I doubled-down on 12 against dealer's 6. The
dealer announced his pitboss my play. Curiously, I won! The count was
very negative. I did it more for showmanship…
•• The personal side of my previous posts on Thorp and Uston relied on
books I have read. I have never claimed I experienced first hand
Thorp's or Uston's casino playing. First of all, I praise the two
computer programmers who took on a very difficult challenge. Trying to
discover rules in random events such as gambling represents an
enormous task. Yes, the casinos did change the rules after Thorp
published his book. The simple fact that the casinos added
"penetration" to the deck diminished the effect of counting to
fractions of a percentage point. One problem I have with the two
authors is the fact that they reached a point of worshipping card
counting. I am sure they did a large number of computer simulations. I
am sure they noticed the negligible effect of the system. Yet they
continued to influence a large number of players that card counting
was the road to the riches. I would like to present a few more
excerpts on Thorp and Uston. Carl Sifakis writes in his 1990
"Encyclopedia of Gambling" (pg. 36-37). "Dr. Thorp is still in
computerized mathematical research, but he is now concerned with
looking for values in stocks… The late Ken Uston, author of numerous
books on counting, was at the end of his life involved in computer
work in the Middle East, helping Kuwait track billions of dollars in
investments. He was not playing blackjack in Atlantic City, although
he had won a court case that barred casinos in New Jersey from
refusing to let counters play. In fact, Uston, upon winning that case,
didn't hit the blackjack tables in Atlantic City but signed up to do
TV commercials for Resorts International, the very target of his suit…
One long time gambler, Murray Friedkin, says of Thorp in ‘Big Julie of
Vegas' by Edward Linn: ‘Thorp is the smartest man in the world; if you
don't believe me, ask him…Whatever Thorp may say, I can tell you that
if he has made any money on blackjack he made it by writing a book.'
The late gambling expert John Scarne derided the counters and
challenged Thorp to a $100,000 match at blackjack. He later extended
the challenge to other leading counting advocates. There were some
nos, then yeses, then considerably more backing and filling; the
blackjack contest never came off."
Edward O. Thorp is associated with another gambling "system": the "Big
Toe Method" of beating the "Wheel of Fortune" ("Big Six"). Says Carl
Sifakis in the same book I quoted above: "Is the Thorp Big Toe Method
still in use? The bottom line is that the money wheels of all kinds
are still in place in the casinos, something that would not be the
case if there was a way they were being beaten considerably." (pg.
31).
Why this aura of legend surrounding card counting at blackjack? Even
more mystique is added when considering that Las Vegas is still
barring card counters from playing blackjack. Says Carl Sifakis: "And
what of the casinos today? Blackjack is a much bigger game today than
it was before ‘Beat the Dealer' appeared. More people than ever
patronize the tables and casinos today make more money from the game
than ever before. That's a significant bottom line." Roger Gros,
senior editor of "Casino Player" magazine writes in his 1996 "Casino
Gambling the Ultimate Play-To-Win Guide": "After all, casinos make
most of the money they make at the table games via blackjack. It's
great advertising when someone reports a big win at the blackjack
tables. Players have been encouraged for many years to believe that
blackjack can be beaten, and the casinos don't want to do anything to
disrupt that message." (pg.30).
I think the legend of card counting plays as the most successful means
of advertising for the casinos. It certainly attracts a large number
of players who believe counting at blackjack is a road to riches.
There are also other ways that the card counting legend favors the
casinos. Read any book on card counting and virtually all of them
contain the same cliché. "If you are a card counter, make some
bonehead plays so that the pitboss won't ban you!" I think many card
counters take the advice seriously. They do make bonehead, stupid
plays from time to time just to hide their card-counting skills. What
a stupid strategy for the player! What a profitable play for the
casino! It is admitted that counting cards offers no more than a 2%
advantage for the player. That's a slim margin by all standards.
Making bonehead plays can easily wipe out the slim, potential 2%
advantage. The casinos owe big time to all authors of card-counting
books. Then, in places where it is legal to ban skilled players from
the blackjack action, the casinos commit downright robbery. From what
I have read, the casinos show a strong bias towards barring a player
when he/she is at a serious LOSS! I read once that a known card
counter was losing some $14,000. Exactly at that point, the pitboss
approached the counter and asked him to leave the blackjack game! Get
it? The $14,000 went immediately to the casino bottom line. Meanwhile,
the player was deprived of a reasonable chance to recuperate his loss.
After all, blackjack is almost an even-odds game for a player using
the basic strategy. It is fair to expect swings in the winning and
losing columns of the player. Of course, the banned player is allowed
to play blackjack again. The pitbosses pretend to have forgotten
him/her, until another significant loss for the player. The player is
thrown out again! If the known counter is winning, the rationale is
that a swing in the fortune will follow. Sooner or later, the player
will encounter a severe loss. That's when you ask a counter to get
out! What casino would be happy if a winner takes the money and run?
In conclusion, mathematics must offer the main perspective when
gambling is concerned.
Ion Saliu
==============================
However, although the author correctly points out one of the
casinos major advantages against card counting, which is the
casino has a right to quit when it is ahead (baring the counter
when he is losing, or otherwise stopping him from spreading bets
is analogous to the casino "quitting when it is ahead") a few
interesting points are missing:
Card counters, as a whole, lose a lot more than they win.
Yet a *team* of well disciplined card counters can still win
today. Why? Because casinos cannot afford to shuffle every
table in the casino, or bar hundreds of patrons. A large team of
card counters can force a casino to either shut down its games,
or allow card counters to play unabridged.
Card counters are not breaking any laws, and if two or three
hundred of them enter a casino, everyday for a week, I wonder if
the casino will blow out all of its customers by dealing a
terrible game, or allow a few card counters to remain and play
unabridged? That was a key question that my team board of
directors asked about 12 years past.
A large team of well disciplined and efficient card counters with
almost an unlimited bankroll is the casinos' worst nightmare.
It would be interesting to see such a team play again, with the
press in tow to record all of the illegal tactics the casinos
will use to try and stop them.
Hell, this sounds like a great movie! But, for those that really
know me and my teams, they also know it is true.
The casinos have an advantage over those card counters that "duck
and run" or try to hide. They can cheat them, kick them out,
force them to quit when they are losing, and a myriad of other
tactics that renders card counting a worthless system.
However, when the casinos confront a large team of efficient card
counters, they panic. They know none of the card counters are
breaking any laws, yet there are so many of them the casino would
need to shut down its entire blackjack game to get rid of them.
In all cases save one, the casinos made a deal to allow a few
card counters to remain and play undisturbed if the majority of
the card counters "went away." The one exception was when a
certain casino decided to change all of its games to an
unbeatable game. About a month later, that casino went bankrupt.
Ahhh, the good ol days. Will I ever make them return? You never
know.
Doug Grant (Tm)
"Sonia" <Sonia...@aol.com> wrote in message
news:dd3d785b.0108...@posting.google.com...
> The text has been taken from Ion Saliu's website.
> Go to his Webside and read for yourself or read bellow the
text.
> Is an excelent math text about card counting
> Here is the link:
>
> http://www.saliu.com/bbs/messages/274.html
>
> =============================================
>
>
> Posted by Ion Saliu on August 19, 2000 at 11:29:05:
>
> In Reply to: BEING THERE posted by Mr. T on August 15, 2000 at
> 09:21:42:
>
>
> . My emphasis has been MATHEMATICS IN GAMBLING. If there is a
> possible sequences of 13 cards, we use 13! = 1x2x3x.x12x13. The
> very negative. I did it more for showmanship.
>
> .. The personal side of my previous posts on Thorp and Uston
> looking for values in stocks. The late Ken Uston, author of
numerous
> books on counting, was at the end of his life involved in
computer
> work in the Middle East, helping Kuwait track billions of
dollars in
> investments. He was not playing blackjack in Atlantic City,
although
> he had won a court case that barred casinos in New Jersey from
> refusing to let counters play. In fact, Uston, upon winning
that case,
> didn't hit the blackjack tables in Atlantic City but signed up
to do
> TV commercials for Resorts International, the very target of
his suit.
> One long time gambler, Murray Friedkin, says of Thorp in 'Big
Julie of
> Vegas' by Edward Linn: 'Thorp is the smartest man in the world;
if you
> don't believe me, ask him.Whatever Thorp may say, I can tell