[Alternatively, the
inside scoop on the first shit Kevin Spacey movie I’ve seen]
Today’s thought is a conspiracy theory of sorts. The theory
is that the entire concept of card counting is a marketing ploy by casinos
themselves to draw in the punter.
Long bow to draw I know, but let me explain. Did you know
that the highest risk group of compulsive gamblers are male, university
educated, between the ages of 25 and 35? Second highest, same except for
female, not male.
Firstly, that old analytical philosophy problem –
Three hippie wannabes
arrive just in time for the Woodford Falk Festival and ask for accommodation at
the local backpackers’. Unfortunately,
the only vacancy the place has is a tiny room with only two beds. The manager
offers to get an old folding bed he has lying around to accommodate three
people if they would like. The three are quite put out; however as it is the
only room left in town, decide to take it. The room rate is $30 per night, and
the three each hand over a ten dollar note.
On getting the promised
folding bed, the manager feels quite bad about not having decent accommodation
left for the three guests and as he orders one of his staff to take up the
folding bed to the room, hands the boy five dollar coins and asks him to
distribute this money evenly to the three guests as a discount and apology. The
boy, not being that smart, cannot work out how to distribute $5 between three
people, so pockets $2 and gives each of the guests a one dollar refund, with a
heartfelt apology.
So the three hippie
wannabies have paid nine dollars each for the room (3 x 9 = 27) plus the two
dollars pocketed by the bellhop, gives us $29. Question is – what happened to
the other dollar?
And now back to the main event...
IN Australia, we live in a culture that has a bipolar
approach to the understanding of success, intelligence and destiny. We live in
a country without a head of state, we love the monarchy at times, while at the
same time yearn for the freedom that a republic will apparently bring. We live
in the ‘lucky country’ but in many situations, the reliance on luck at the
expense of knowledge or value appears un-Australian. By the same token, the
smart, savvy know-it-all is the villain in many Australian cultural stories.
It is the Aussie larrikin who still relies on advice and
gumption that we admire, but only to a certain level of success. We admire this
person not because they are successful, but because they have learnt to tap
into a secret code of success. This is why they are successful, and by the same
token, this is why we may be successful too, if only we knew the language. We
admire stories that give pay dirt to this; the Da Vinci Code; Waltzing Matilda;
the Packer Dynasty; the ANZACs and so on. All these stories are stories of luck
and courage mixed with reliance on a certain form of intelligence.
To take a specific case in point: counting cards in the game
of Blackjack. This is seen as tapping into a secret code; a Da Vinci style
understanding; a shibboleth of mathematics over reality. This code will make
you successful if you both understand it, and have the courage and luck to take
it further. It is the perfect contradiction of luck and knowledge. Courage is
relevant too, but not to break the law or transgress social norms. It is more
to take on the ‘big guys’ and dare to beat them.
Technically, in most jurisdictions, counting cards is not
illegal. The point at which an action breaches the law is when it interferes in
some way with the natural order of a game. By this understanding, card counting
falls into a grey area in some states, in other states it is not an offence as
it does not in any way interfere with the play of the game in the way that
marking cards or shuffling them inappropriately would. In many works of fiction,
novels, cinema and television dramas, we may learn that card counting is not
illegal, but ‘robs’ the casino of profits, and indirectly the general public
lose out by the casino not having as much money.[1]
The act of card counting itself is not very mathematically
complicated. The game of Blackjack is a simple game; two cards are dealt to
each player, the player closest, yet still under a 21 score wins. Face cards
are worth ten, aces are worth either one or eleven (whichever is more
favourable to the player) and the other cards are worth their numeric value.
Players may ask for more cards, up to three (at which point the player wins
automatically), but if the value of the cards in front of them is higher than
21, they automatically lose.
Card counting works on maintaining knowledge of what cards
have been dealt out of the shoe as a basic average value, and thus the average
value of the cards left in the shoe. As most casino croupiers are instructed
not to deal themselves higher than 17, the higher the average value of the
cards that remain in the shoe, the higher the chance that the player may beat
that 17.
There are many practical problems with this simple
understanding though. The main and more obvious two are: firstly the greater
the chance of a 10 value card coming out of the shoe is always equal across all
players at the table, including the dealer, not just the players counting
cards. Secondly, casinos were built by conmen and gangsters for conmen and
gangsters, and as such are very good at detecting when the law of large numbers
is not being adhered to; when someone is cheating, or using a successful system
of any kind.
Many stories of strange dyes, chemical compounds or X-ray
glasses that enable a player to know the value of a card before it is dealt are
recorded throughout history. One may guess that many more stories of how to
cheat have been lost to history; most likely the more successful ones. Whether
they are true or not, whether the gamblers were exposed as cheats is horses for
courses really. It is not the way casinos deal with it.
For example, if a gambler starts winning a large amount of
money, someone pushes a button. If a gambler continues winning a large amount
of money, many more buttons get pushed, or signals are raised in whatever way.
Casinos don’t need to know how and why someone is winning a large amount of money
to exclude a player. They don’t need to be fair; they don’t have to be open to
everyone who wants to enter. They do not have to prove that a player was
cheating, or explain themselves to an independent arbiter (such as a court of
law) ‘beyond reasonable doubt’ as the
state does; at least in theory.
The most wonderful story of card counting is the urban myth
of the uber-smart students from MIT that apparently took Vegas ‘to the
cleaners’. This has been the focus of speculation and romantic notions of brain
over brawn the world over. It has been moulded into a very widely selling
“non-fiction” book ‘Bringing Down the
House’ and an ultra-Hollywood movie ’21’.
The hook of this story is that in gambling (as in life?), there is some way
that people may beat the house. In a pure game of chance, there is some
knowledge, some secret, some Da Vinci Code, secret order, or perhaps some not
so secret order to things that if one can tap into, one will win and be kissed
on the arse by fairies forever.
In reality, the deconstruction of the situation provides that
the only people that this kind of story favours are the casinos. When people
gamble too much, whether it is out of a non-specific impulse control disorder
or just a slight, once off miscalculation; almost all the time can be
simplified to an explanation of the patron thinking that they knew something;
had some sort of control over the randomness of the situation. In the very
least, the money lost by the casino for every one person that is actually able
to control themselves enough to successfully count cards, would be made up for
a hundred times over by a thousand gamblers whom only thought they could.
It is hard to trace the story of the MIT students who were
involved as there are so many incantations of the story across time and circumstance.
One of the simplest versions of the stories revolves around an MIT first year
student named Andre Martinez, although other variations of this story refer to
‘real life’ inspirations of the MIT team
being John Chang, J.P. Massar, Jeff Ma and Bill Kaplan. Interestingly, the
movie and book both white wash these names; anglocising them; Kevin
Lewis and Ben Campbell are the
central characters.
Andre Martinez was apparently “an absolute genius”, so smart
that on his third day as a first year undergraduate, he was “fast-tracked ...
to graduate-level seminars”[2]
by the never named maths professors at MIT.
Yeah, right... MIT just decided to forgo the hundreds of
thousands of dollars in tuition fees.
Every once in a while, this story is retold with reference to
Professor Edward Thorpe, also at MIT, and a real genius from the era of Bletchley
Park fame; but a generation and a half earlier. When this happens, the role of
Martinez is that of a student of Thorpe’s controversial 1962 book; Beat the Dealer: A Winning Strategy for the
Game of Twenty-One but one who was able to understand something that
Professor Thorpe missed. The key ingredient in the being kissed on the arse by
fairies spell that it would seem, no one else has understood.
The explanation as to exactly what the 1990s MIT team came up
with is never given. The notion that they played in a team, with spotters,
gorillas and Big Players to avoid detection has been floated around.
Apparently, according to the myth, the Las Vegas Casinos have never thought
that people may signal to each other in teams on the gaming floor, and were
unprepared for this outcome. There is also usually a further story about
players being able to cut the deck to a specific number of cards down to bring
out an ace. That an ace is of very little value on its own, without a ten value
card is never really discussed.
It is at this point that the already shaky story falls apart a
little more than somewhat. This is the part of the story where maths geeks from
MIT went to Vegas and were able to instantly transform into any random
character that they thought may be a laugh; from a rich dot-com kid, to an
Eurotrash brat to a woman, the theatrical abilities of these mathamagicians are
capable of fooling Vegas casino floor managers. Everyone seems to forget, when
hearing stories such as this, that if a maths geek is good at pretending to be
someone that they are not, there is only one persona that they would wish to
take on; that of someone capable of having sex.
Remember that old joke; ‘How do you tell if a mathematician
is an extrovert or an introvert...if he’s an extrovert, when he speaks to you
he’ll look at your shoes rather than
his own”.
The idea that a Las Vegas Casino floor manager, who are
required to pick a cheat, liar, drunk, thug or fraud out as part of their job
would be fooled by something as silly as this is all but beyond belief. But the
story also loses its grasp of maths at the same time as it loses its grasp of
the realities of the abilities of maths geeks. For example, the actual state of
play, as told by Nigel Goldman, in his recent book ‘Great Gambling Scams’ telling the story of the initiation of a new
recruit into the MIT team,
“...Then, quite suddenly, with only half a dozen or so hands
left to go until the end of the shoe, Martinez suddenly bet $1,000. Kevin upped
his ante to $500. The dealer dealt them both queens, and herself a five.
Kevin’s next card was the ace of hearts, winning him $750, while Martinez’s was
another queen. Martinez, against all casino etiquette, split the queens,
receiving a face card on each, and then the dealer drew a nine, followed by a
ten to bust. They had just won $4,750 on that one hand alone. ... The cards
were coming out: Fisher got a ten, and Martinez a queen. The dealer received a
five, and Fisher matched his ten with a nine, while Martinez received another
queen. He had $1,400 in the box, and he chose to split the queens, normally a
dreadful decision, but in these circumstances a fabulous play with the odds
massively in his favour. ..... out came the cards, an ace and a ten. Bingo! The
dealer dealt himself a nine followed by a jack to bust.”[3]
The mechanics, the maths of this
story are way off. The idea that Martinez in both instances receives two queens
is highly improbable to the point of ridiculous. This is matched by the idea
that both players in both situations received a ten value card and one nine,
while the dealer received a five on both occasions. On both occasions, the
reason that the players won was that the dealer bust. It had nothing to do with
counting cards.
A better example of this is in the
movie ‘21’. We see our now very European looking ultra-genius surrounded by
seedy characters in an Asian casino, downtown.
He is signalled by his Asian team member; giving off a slight inferiority
issue; by an incredibly awkward arm gesture, then using the word ‘magazine’ in
a sentence to indicate +17[4]
from a pre-determined code. This is done in a way so awkward that everyone in
the room would have known it was a code.
Our Anglo-hero Ben narrates that the
count is +18 after he gets a blackjack and the dealer received a 7, then 8. No it’s not Ben, you ultra genius. Here
is the point where another of the severe failings of card counting in practice
can be seen: while a pack may get to the improbable, yet possible mathematical
understanding that it is +15, +16 or higher, to indicate the severe uneven
distribution of cards dealt that have added an advantage to the player, every
single card that is dealt after this point will diminish this count back to zero;
the count must return to zero at the end of the shoe unless there are cards
missing.
To take the example of Goldman’s
second play above, the table has been dealt two queens, a jack, two tens, two
nines, an ace and a five. By the rules
of card counting, this one hand would remove at least five points from the
value of the deck, more if there are other players at the table. So a ‘magazine’ (+17) would become a +12 (a
gaol bait?) in that one hand. And the main reason the players won is because
the dealer yet again received the five, which is improbable to say the least.
Even in the highly unlikely event that the
shoe is still ‘hot’ after losing this much value, every winning hand will
diminish the count by this sort of figure, so while the maths may work; it will
not work for very long. The truth of card counting is that while it does work,
it doesn’t give the player a very high advantage and it doesn’t work very
quickly, you need to do it for a very long time to win any kind of advantage.
The role of the character of Cole Williams plays a strange part in the saga. Cole is, in the initial stories, a
clever security chief who catches the MIT card counters in the most bizarre
way.
Sensing that there is a team at work
counting cards, he makes an assumption that this team would be made up of
college students and orders a copy of every single college year-book in the
country and studies them all. As the story goes, the MIT team used their
college year-book photos on a fake California ID cards used in the casino. The
likelihood of this story being true is all but zero. The number of colleges
there are in America, all of whom have tens of thousands of students, not to
mention staff (who would represent a considerably stronger assumption on Cole’s
behalf) coupled with the sheer volume of visitors to a Las Vegas casino would
make the odds of someone correlating black and white photos in the tens, if not
hundreds of millions to one. As previously stated, Vegas was built by mobsters
and conmen, for mobsters and conmen; the way they identify cheating is the
signal when someone wins large amounts of money, regardless of the
circumstance. Then they beat them up, or spike their drink.
But the role of Vincent Cole gives
validation to the story. He is the one guy whose determination and gumption
undoes the skill and smarts of our all American, all-anglo geniuses. Cole gives
the story the understanding that it is easy to get away with counting cards, by
juxtaposing the amount of effort and determination required to catch someone at
it.
In the movie, Cole’s character takes
on so much more. ‘His’ casino was ‘taken’ for a seven figure win by Professor
Rosa when he was absent from work. He was at his father’s funeral no less. As a
result of this event, Cole was fired.
Also of note is Cole’s character in the movie is played
by the very talented, yet very non-European actor; Lawrence Fishbone.
In the movie, an exaggeration from
the book, Cole is depicted as the end of the old ways of things. He and his
company and knowledge are being replaced by technology; “Biometric Facial
Recognition Software” which will apparently make his role redundant. We hear
him talking about whether card counting beats the system, only to see him
pointing to his brass knuckles clad fist and stating “this is the system”.
The book, Brining Down
the House has faced some criticism and scrutiny since its publication in
2002 regarding the truth of what happened, by whom and when. John Chang, one of
the real life inspirations behind the character of Mickey Rosa, stated that “I don’t even know if you want to call the
things in there [the book] exaggerations, because they’re so exaggerated
they’re basically untrue.”[5]
Ben Mezrich, the book’s author, claimed that “Every word on
the page isn’t supposed to be fact-checkable ... I took literary license to
make it readable ... The idea that the story is true is more important than
being able to prove that it’s true.”
This last statement: that something may be true in contrast, or at the
expense of being able to be proven true is so vague that it bears little need
for analysis. It is important to note, however, that the entire book is
presented as a work of non-fiction; from the subtitle ‘The Inside Story of Six M.I.T. Students Who Took Vegas for Millions’
to the prose and chronological structure of the book itself; it is very much
written, and intended to be read, as a work of fact.
21
The movie ‘21’
brings Hollywood to Vegas. There is a love story; betrayals of friends and
students; back room punch ups and Sir Isaac Newton being labelled a plagiarist.
The opening sequence is of a poor kid, quite drably dressed, riding an old
pushbike surrounded by cars zooming past. The boy, as we later find out, was
raised by his mother, widowed and working class. He is poorly dressed, even
though he works in an upmarket clothing store and is seeking only to attend
Harvard Med School on a scholarship. To get this scholarship, he needs ‘life
experience’ to ‘dazzle’.
The movie
introduces a love interest and a vengeful and vindictive professor character.
The love interest, Jill Taylor, is older, smarter, considerably better looking
and more popular, yet she spends the entire movie shy and subservient to Ben
Campbell. She is comes from a gambling family. Her father and uncle lost a
fortune on blackjack, and used to play blackjack every night with her as a
child. The love story can be seen as the joining of the natural, yet innocent
talent of Campbell with the experienced and pure talent of Taylor.
The role of
the vengeful and vindictive professor, played by Kevin Spacey, brings
completely new dimensions to the story. Professor Mickey Rosa, a maths
professor at MIT gives the all-American Hollywood lecture. It appears to last
for three or four minutes as opposed to the traditional two hours; it does
nothing more than pompously ask a question about Newton being a plagiarist;
then provides an insanely brief account of a maths paradox the ‘game show host
problem’ [sic] which gives surprise to everyone, including the professor, when
our hero can answer it. This is made especially more surprising given that Ben
is able to explain it, while omitting the main element that makes the equation
work and seemingly misses the point completely. But the key understanding, that
secret code, the Shibboleth; that private language is mentioned ‘variable
change’ by our hero, and Professor Rosa is taken back by not knowing this
student who had been in his class, sitting in the front row all year, yet had
escaped Professor Rosa’s attention until now.
Campbell
makes that wonderful understanding when asked if his choice is being lead by a
game show host, trying to use reverse psychology to trick him into losing. “I
wouldn’t really care [if the game show host is trying to trick him] my answer
is based on statistics, based on variable change.”
Ben Campbell stated that he would change his gamble based not
on the actions of the game show host, but on statistics and variable change. He
explains it as “when I was originally asked to choose a door I had a 33.3%
chance of choosing right. But after he opens one of the doors and reoffers me
the choice it’s now 66.7% if I choose to switch.”
In reality,
the ‘game show host paradox’ – generally referred to as the Paradox of
Betrand’s Boxes proves the direct opposite point of view, that mathematics is a
human invention, a language set up to explain the world that has massive
failings in some circumstances. Bertrand’s Boxes sets up three possible boxes
and asks one to make a choice about which one has the marble in it. A choice is
given, then one box is removed by the host, leaving two choices, one of which
being the original choice and one more. The language and rules of mathematics
tells us in this situation that the probability of one’s original choice being
right is 33.34%. This remains the case when one box is removed. So sticking to
that choice, maths tells us, gives us a 33.34% of being right. If we were to
change our choice to the other box mathematics tells us that we would have a
66.67% chance of choosing the box with the marble in it.
The point of
the paradox is that this simply is not what happens in the real world. In the
real world the chance of winning is only increased where the game show host
knows which one is the winning one. Remove this point and you’ll remove the
paradox.
There can be
a wedge drawn between mathematical theory, reality and outcome. These can be
viewed as only two issues; firstly the inability of western thought to deal
with the two concepts (or perhaps one concept) of zero and infinity. Secondly
is the divide between addition and multiplication (or subtraction and division)
that are falsely taken to be equivalent. There is perhaps another explanation
in the notion that maths is purely analytical truth; that two plus two does not
equal four, it merely is four by virtue of the definition of what four is.[6]
But this veers too much into British philosophy for a story about gambling.
Three hippie wannabes
arrive just in time for the Woodford Falk Festival and ask for accommodation at
the local backpackers’. Unfortunately,
the only vacancy the place has is a tiny room with only two beds. The manager
offers to get an old folding bed he has lying around to accommodate three
people if they would like. The three are quite put out; however as it is the
only room left in town, decide to take it. The room rate is $30 per night, and
the three each hand over a ten dollar note. On getting the promised folding
bed, the manager feels quite bad about not having decent accommodation left for
the three guests and as he orders one of his staff to take up the folding bed
to the room, hands the boy five dollar coins and asks him to distribute this
money evenly to the three guests as a discount and apology. The boy, not being
that smart, cannot work out how to distribute $5 between three people, so
pockets $2 and gives each of the guests a one dollar refund, with a heartfelt
apology. So the three hippie wannabies have paid nine dollars each for the room
(3 x 9 = 27) plus the two dollars pocketed by the bellhop, gives us $29.
Question is – what happened to the other dollar?
The end of
the movie sees a typical Hollywood wrap up; the same old American ‘Mighty
Ducks’ meets ‘Police Academy’ with a little sprinkle of ‘Ocean’s Eleven’. The
protagonist loses his edge by losing his sense of identity then alienates his
friends and contemporaries. He has a chi
moment, asks for the trust and confidence of his friends both old and new,
which they give to him (evidently they have not read Derrida). He then earns
their trust back by pitting the bad guys against each other so that talent and
honour win out over common sense and reality.
Campbell
gets his ‘dazzle’ for the scholarship, which he does not get, and the movie
ends with a narrative from Campbell about how he went to Vegas 17 times and won
“hundreds of thousands of dollars” and gained life experience and identity in
some way. The viewer is left with yet another mathematical error: if Campbell
had won his $350,000 in a one fifth share of takings (minus expenses) he would
have to have won multiple millions, not hundreds of thousands.
Gambling success, like most things in life, follows the rule
that the better educated and disciplined you are, the greater your chance of
winning. John Chang, the supposed real life inspiration for Professor Rosa’s
character pegs the yearly income for someone on the MIT Blackjack team to be
$25,000.[7]
Mike Aponte, the real life inspiration behind the Fischer character, claims
that the most the team ever won was $500,000 in one trip. His personal highest
winnings he estimates at $200,000. For some reason he can’t recall his greatest
achievement to the cent, even though all gamblers can always tell you ever
slightest detail about their ‘greatest win’.
More importantly he has stated that the most the team
apparently ever lost in a trip was
$130,000.[8]
These two have also greatly disputed the lack of discipline in Ben Campbell’s
character in the movie, seeing it as a plot development solely to end the
movie. Chang has stated that “Starting from the part where Ben loses control at
the Red Rock and loses 200K, the movie takes off on a tangent that has no
resemblance to reality. Our players were far too disciplined to even think of
doing something like that.”[9]
These two points taken together: that the team were very disciplined; and that
they were able to lose $130,000 in one trip can be taken to understand the MIT
Blackjack team’s operation as purely gambling. While they perhaps used
strategies to make them better than the average, that is not the point. The
point I wish to make is that they were gambling at a game of chance, with
little to no control over the situation. They were using maths to hide this
fact, and their loses, which is a true characteristic of a compulsive gamblers.
There is yet a further observation to make. The real story of
a person from MIT taking on Las Vegas happened more than thirty five years
earlier.
Professor Ed Thorpe, an MIT professor and a mathematician
interested in gambling, but a generation and a bit before, tells the story in a
different way. It’s the same story, but set in the 1950s and doesn’t paint the
Las Vegas casinos as places of fun and tolerant of card counters.
In “Fortune’s Formula” William Poundstone retells stories of
the noble Professor’s drink being spiked, to the point that he could no longer
concentrate after drinking it, of friends being beaten quite randomly and of
the Las Vegas casinos dealing with card counting in the late 1950s and early
1960s. Firstly, by not cutting the deck and playing with a blind eight deck
shoe, and then finally by not playing the last portion of the shoe. This was
the total and complete destruction of someone’s ability to count cards, no
matter how much of a genius they were. The relevant part of a shoe; the last
few hands, were simply not dealt.
Have you thought of my main point yet? Have I made the point?
...
Well, one final observation - while it is a very long bow to
draw to say that this entire concept is a casino run conspiracy, it is true to
say that the main people who benefit from the promotion of this type of story
are the casinos. To seek to convince people that they can go to Las Vegas with
a system that will allow them to win money is not something that will hurt a casino’s
bottom line; it will most likely do the exact opposite. If that isn’t enough to
arise one’s curiosity and cynicism, bear in mind that the movie 21 was financed
by none other than the Metro Golden Mayer Corporation, owners of that iconic
casino, the MGM Grand.
* * * * * * * * * *
[1] For example, see the American
Television drama show “Las Vegas” where this theme is constantly raised.
[2]
Goldman 2007 pp74.
[3] Goldman 2007 pp84, 88
[4] In
the case of +15, this is the
equivalent of saying for every ten value card dealt, fifteen low value cards
have been dealt and thus the average value of the shoe remaining is high.
[5]
Boston Globe FIND REFERENCE
[6] The counter argument states while
that two plus one is three (as opposed to equally three) because it may only be
stated as (1+1)+1; two plus two equals four do to there being two formulations
[(1+1)+(1+1)]; or [(((1+1)+1)+1)]
[7] BlackJackInfo.com
[8] BlackJackInfo.com
[9] www.mickyrosa.com
