Pick a Card, Any Card: The
Irrelevance of Personal Statistics
Christopher Grapes
Intermediate Expository
Composition 201
Leslie Jewkes
12/14/2012
Abstract
Personal statistics are around us
constantly. Whether something as basic as buying a lottery ticket, or as
potentially life altering as results from a doctor's examination. But do most
of them really matter? Can we even understand them in any meaningful way? Do we
even trust them to begin with? The answer to these questions is a firm
"no". Personal statistics and probabilities are mostly an irrelevance
that the human mind cannot realistically fathom or understand, due to the need
for the brain to seek out patterns, even when none exist. What does a 50/50 chance
of a coin toss actually mean? What does it mean if it lands on heads two,
three, four times in a row? The answer? "Nothing".
"The laws of probability, so true in general, so fallacious in particular." - Edward Gibbon
The human mind is hardwired for
pattern recognition. This is, in part, why uncertainty is inherently fearful
for most people. And yet, in spite of this, oftentimes patterns and
probabilities are ignored or even outright denied, replaced instead with a
preference for superstition or "gut feeling". The probability of
being involved in a fatal plane crash on any given flight is approximately one
in fifteen million. The probability of being involved in a fatal car accident
on any given drive is approximately one in twenty thousand. Yet millions of
people are terrified of flying, whereas hardly anyone is afraid of driving. It
presents us with a conundrum - if knowing a probability doesn't alleviate
irrationality, what use is probability to an individual anyway? The answer is
simple - personal statistics and probabilities are irrelevant and ultimately
meaningless.
It is challenging to narrow down
what is meant by personal statistics. Broadly speaking it means any sort of
probability that would have an effect on the individual themselves. While this
isn't necessarily irrelevant over the whole spectrum (after all, a 70% chance
of rain isn't an irrelevance if someone was planning to go outside), it is the
apparition of order that the mind places upon it that is ultimately irrelevant.
A 70% chance of rain does not equate to "it will rain", nor does it
mean that it will rain exactly seven times out of ten. It is a summation of a
random event - an attempt to create order from chaos that the human mind
latches onto and imposes its own rigid pattern upon.
Several games of random chance use
the pattern recognition of the mind for various purposes. The game show Deal or
No Deal, for example, is, on paper, completely free of drama and excitement -
twenty two boxes, with random amounts of prize money ranging from 1 cent to
$500,000. A contestant chooses a box and then has to choose other boxes to
eliminate. The odds of holding the winning box are, without exception, one out
of however many boxes are still left. It is entirely random chance and
impossible to predict or interpret. Yet contestants ignore logic when in the
thick of the game. The most often used tactic is to choose boxes based on the
results of previous games, reasoning that whichever box held the $500,000 last
game cannot possibly contain it this game. This same phenomena of
conditionality is present at casino games like roulette, where a display board
will show the results of the previous ten spins. Looking at it with a rational,
logical perspective suggests that this is completely pointless - a spin landing
on 3 will not change the probability of it landing on 3 the next spin. The odds
are equal that it will land on 3 five times in a row as it will land on 3, 6,
13, 24, 22 or any other random sequence of numbers. What does this show? That
our predilection for pattern recognition is conditional - true randomness is
something our brains simply cannot understand, and thus a non-existent pattern
is created in order to cope.
Deal or No Deal uses this
predilection not just for drama, but also to influence choice. After each round
of box eliminations, an unseen banker (who knows exactly what each box holds)
calls the host and offers a set monetary figure to the contestant that they can
then accept, immediately ending the game, or reject, continuing to eliminate
boxes. Players here have been known to continue playing, looking for patterns
within the banker's figures in an attempt to fathom what box they hold. The
logic goes that, should the banker offer them large sums, the odds are good
that they hold the winning box. Yet, often when a contestant ends up with a
final choice between 1c and $500,000 (or similar extreme figures), the banker
will offer a much lower figure than expected, maybe just a couple of thousand
dollars. This is, again, a illusion intended to promote false drama. The
banker's figures do not follow mathematical patterns, but psychological ones.
Would you accept a guaranteed figure against an unknown? When polled, the
average guaranteed figure needed before they'd accept would be $40,000. Yet, on
the show itself, the vast majority of contestants accept the guaranteed figure,
regardless of what it is, by the final round (Fig. 1). The banker's offer
always falls in between the minimum and maximum boxes still on the table, thus
the 50/50 choice of winning more than the offer is always present come the
final round. This shows the psychological element at play - any pre-determined
thoughts and plans are immediately removed for a sudden gut feeling.
One place where this gut instinct
overriding logic is most apparent is on music players - specifically portable
mp3 players that feature shuffle modes. When the shuffled music is truly
random, people often pick out specific patterns in the randomness. In a survey of
40 people, 65% of respondents believed their music player favored particular
individual songs, artists or genres over others. Apple, in an effort to silence
critics of this perceived flaw, even introduced user variations in their
shuffle playback, allowing users to fine-tune the feature to either ignore or
concentrate on specific songs, genres or artists, using conditional probability
to better balance the playlist. Yet, even with these added features, some still
believe the iPod is choosing patterns. Some even believe that the iPod is
exhibiting knowledge of the outside world, choosing songs to match their moods.
A student interviewed for the New York Times claimed that his iPod "knows
somehow when I am reaching the end of my reserves, when my motivation is
flagging. [...] It hits me up with 'In Da Club,' and then all of a sudden I am
in da club" (Dodes).
Curiously, this detection of
nonexistent patterns within otherwise completely random sequences is
demonstrably higher in those with a gambling addiction. One study found that
"probable pathological gamblers may be more apt to impose order on random
and non-random stimuli and find patterns that suggest predictability whether
there is any predictability or not" (Turner et al, 69). The study also
suggests that gambling addicts may have difficulty in recognizing patterns that
do actually exist. This may be a large reason why roulette wheels display
previous numbers, despite it being logically meaningless - a gambler may wish
to play roulette when they spot what they perceive to be a pattern emerging in
the chaos. To the gambler, if the last few numbers have all been red, then
black has to logically be next. This psychological
phenomenon is known as the "law of small numbers", defined as "the
erroneous belief that the balance of random outcomes that occurs in very large
samples will also occur in small samples" (Roney, Trick 198). Effectively,
flipping a coin a million times should see a rough 50/50 balance of heads/tails
results. Flipping a coin ten times could result in heads every single time.
Thus the casino owners deliberately exploit this psychological belief in order
to increase active players (and therefore profits).
The infamous "Monty Hall
Problem" is a strange inverse of this pattern recognition issue. The
problem presents a game show where the contestant is given three doors to
choose from - behind one is a brand new car, behind the other two, nothing. The
contestant selects one, then the host, knowing what is behind each door, removes
one with nothing behind it. The host then gives the contestant the chance to
stick with the door they have, or switch to the last one left. Though most
perceive this as a 50/50 choice and ultimately go with "gut feeling",
conditional probability applies (unlike Deal or No Deal or roulette, the odds
do change based on previous actions) - statistically, switching would win 66%
of the time, compared to winning 33% of the time when sticking. Yet, even when
confronted with this specific mathematical probability, many will reject it,
still sticking to gut instinct. Even with the problem explained and the raw
statistical probability laid bare in front of them, 45% of people surveyed
decided to stick with the door they initially chose. One particularly
interesting find in a study of the Monty Hall problem is that pigeons seem to
possess superior pattern recognition and adaption than humans. This has
ultimately been put down to psychological reasoning, and that humans, when
consistently presented with the problem, "show either indifference or a
bias to stay with their original selection despite the fact that neither of
those strategies is optimal"(Beran et al, 5). In other words, gut instinct
and superstition overrides our in-built pattern recognition that pigeons rely
on for survival.
Further examples would be the method
of deciding options by way of a coin toss. A coin toss is widely believed to be
a definitive 50/50 choice - each option has equal possibility of being
selected. Yet, statistically speaking, this is not the case. Not only can the
individual coin bias the results (when testing the results of a Euro coin,
Polish researchers found that " when spun on a surface, [the coin] came up
heads more often than tails" (Clark Westerberg, 308)), but the method used
to flip the coin can also have an effect. In further tests, it was revealed
that by practicing with force and placement of the coin, participants could
affect the bias of the coin by nearly 20%, leading to an odds of 70/30 instead
(307). Yet again we can find an inverse of this problem (a distrust of odds,
rather than an overwhelming faith in them) in shuffling cards. The possible
permutations of a standard 52 card deck is a number with sixty-eight digits -
to put that into perspective, the number of atoms that make up the entire
planet Earth is estimated to be a number with fifty-one digits (Weisenberger).
But even in simple friendly card games with families there is often a strict
protocol and superstition when it comes to shuffling, multiple shuffles with
multiple methods, or cutting the deck in between shuffles. Yet just one
reasonable shuffle is enough to rearrange the deck to a point far outside the
capabilities of a human being to predict the outcome. The odds of even being
able to successfully predict just four cards in a deck are approximately two
and a half million to one, odds on a par with winning second-prize in the state
lottery.
The vast majority of people who play
the lottery will always do so at a loss - their expenditure will far outweigh
their winnings, but they play on, perhaps convinced that their numbers will
eventually come up. A search on Amazon for "how to win the lottery"
will bring up dozens of books, big sellers all, each claiming foolproof
strategies and tips on how to maximize success, each seizing, intentionally or
otherwise, on the aforementioned "law of small numbers" fallacy.
People instinctively avoid picking superstitious numbers, or sequences of
numbers, despite the fact that the sequence 1, 2, 3, 4, 5 is just as likely to
appear as any other random sequence. Superstition and gut instinct overrides
our basic capacity for logic at almost every statistical turn, whether it be
the odds of winning the lottery, fear of boarding an aircraft or even just
pressing "next" on an mp3 player. The human mind is simply not equipped
to process or even truly understand probability, and our attempts to internally
reason the logic behind what is usually an entirely unpredictable outcome
renders the vast majority of personal statistics utterly irrelevant.
Works Cited
Clark,
Matthew P. A., and Brian D. Westerberg. "How Random Is The Toss Of A
Coin?." CMAJ: Canadian Medical
Association Journal 181.12 (2009): E306-E308. Academic Search Complete. Web. 10 Dec. 2012.
Dodes,
Rachel. "Tunes, a Hard Drive and (Just Maybe) a Brain." New York Times. New York Times, 26 Aug.
2004. Web. 12 Dec. 2012.
Grapes,
Christopher. Survey of Statistical
Probability and Choices. Survey. 26 Nov. 2012.
Joseph
Haefner, et al. "Teaching Prospect Theory With The Deal Or No Deal Game
Show." Teaching Statistics 32.3 (2010):
81-87. Education Research Complete.
Web. 13 Dec. 2012.
Michael
J. Beran, et al. "Learning How To 'Make A Deal': Human And Monkey
Performance When Repeatedly Faced With The Monty Hall Dilemma." Journal Of Comparative Psychology
(2012): PsycARTICLES. Web. 29 Nov.
2012.
Nigel
E. Turner, et al. "What Does A Random Line Look Like: An Experimental
Study." International Journal Of
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Roney,
Christopher J. R., and Lana M. Trick. "Sympathetic Magic And Perceptions
Of Randomness." Thinking &
Reasoning 15.2 (2009): 197-210. Academic
Search Complete. Web. 11 Dec. 2012.
Weisenberger,
Drew. "How Many Atoms Are There in the World?" Jefferson Lab, n.d. Web. 12 Dec. 2012.
Bibliography
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