The quicksand known as Gambler’s Fallacy
October 2,
2009
Dear Mark: I know
you don’t believe in the doubling up theory
after a loss in blackjack, but after I have
seven or eight losses in a row, wouldn’t betting
more be warranted, if not just for the due
factor? Jim K.
Your compass is off, Jim, if it reliably shows
your viewpoint regarding sequences in gambling.
You believe that after so many losses, a win is
more likely to occur to self-correct a losing
streak. From your point of view, your
statistical justification of seven or eight
losses leads you to the faulty conclusion that,
based on the past evidence of so many losses, a
win is way overdue, and hence to the casino’s
favorite hunch: so why not bet more.
What you’re describing, Jim, is called Gambler’s
Fallacy, and you, and far too many of your
brother and sister players for that matter,
erroneously believe that a sequence of events in
a random process—separate hands of
blackjack—will display the essential
characteristics of long-term play even when the
sequence is short.
As your query ponders, if you lost seven times
in a row, should you wager heavily on the next
hand because it’s way overdue? But just because
you have a deviation in one direction (Loss, L,
L, L, L, L, L), that doesn’t mean an aberration
in the opposite direction will occur over the
short run to restore balance. Deviations are not
‘corrected’ as time goes on, just diluted. The
same holds true with consecutive wins, that
streaks may well continue after a series of
winning hands. Yes, Jim, the deck might be ‘hot’
while your hind end is sitting there, but the
probability of subsequent wins doesn’t
necessarily increase the likelihood of a win.
The solution to Gambler’s Fallacy is to treat
each hand as an independent event. Cards, Jim,
have no memory of any past actions.
Oh, and Jim, that logic of betting more after a
loss is called the Martingale System, an
historic name for doubling up after every loss.
In essence, you the gambler double your previous
bet (after a loss) to recoup that loss and also
win back your initial wager. Above I discussed
why this form of betting isn’t foolproof,
because you don’t necessarily win even after an
extended losing streak. But also, you don’t have
an inexhaustible bankroll, and the casino limits
the maximum size of your wager. Let’s say your
initial bet is $10 and you lose, followed by $20
to recoup your losses. Then $40, $80, $160,
$320, $640. You invested $1,240 just to get your
measly 10 bucks back.
Then there is the possibility that you were
playing on a table with limits of $10-$1,000. A
string of seven defeats and the casino
automatically protects itself by its table limit
of $1,000, and you, Jim, in all probability, are
wiped out by then, all in less than three
minutes.
Dear Mark: Great column last week on
multi-line/multi-coin video slots machines. So
if I am to get you right, you are just
recommending one coin per line, correct? Mary S.
That’s right, Mary. On multi-line/multi-coin
slots, I by and large recommend playing one coin
per line, because more than likely, you are
playing on a Straight Multiplier or “equal
distribution” machine. The payouts on additional
coins per line are just straight multiples of
the one-coin payout on most of these machines,
so there's no advantage to playing more than one
coin per line.
Gambling Wisdom of the Week: “A
belief which leaves no place for doubt is not a
belief; it is a superstition.” -Jose Bergamin,
author
|
