Risk and Reward - The Science of Casino Blackjack by N Richard Werthamer (2009).pdf

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Risk and Reward
N. Richard Werthamer
Risk and Reward
The Science of Casino Blackjack
123
Dr. N. Richard Werthamer
43 West 16th Street
New York NY 10011
USA
rwerthamer@nyc.rr.com
ISBN 978-1-4419-0252-8
e-ISBN 978-1-4419-0253-5
DOI 10.1007/978-1-4419-0253-5
Library of Congress Control Number: 2009926050
Mathematics Subject Classification (2000): (Primary) 91A60 (Secondary) 60J60, 60-02
c 2009 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in
connection with any form of information storage and retrieval, electronic adaptation, computer software,
or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are
not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject
to proprietary rights.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
Preface
How did a physicist like me get involved with blackjack? I skied in. As a young
doctoral candidate at the University of California, Berkeley, I would occasionally
join my friends on ski trips to the Lake Tahoe area. Always on a student’s tight
budget, we found that we could stay inexpensively in Reno motels and that the
cheapest meals were at the coffee shops astutely placed at the back of the town’s
casinos. I found it hard to pass all the gambling frenzy without joining it. Fortunately
for that budget and my financial peace of mind, I was usually lucky in winning a
few dollars. Once, I paid for my entire trip with an unlikely hit at roulette.
When I learned that an optimized method for playing blackjack (what is now
called Basic Strategy) had been published in a scholarly statistics journal, I quickly
looked it up in the university library. Blackjack became my game of choice for sub-
sequent Tahoe excursions and, in later years after skiing and I had parted company,
for trips to other destinations with casinos. But my real recreation of choice became
blackjack analysis!
My original motive for exploring its mathematics was to see if the articles and
books I had chanced upon were correct, or if I could find a better way to win.
Visions of big money danced in my head! Later, as I came to appreciate the realities
involved, my interest shifted to the mathematics for its own sake, complex enough
to be a challenge even for a professional scientist yet easy enough to yield to a
sustained effort on almost every issue. Also, I wanted to verify (or, as sometimes
happened, falsify) claims about the best way to play, asserted in the literature with
little or no proof.
When I had finally addressed all the questions that occurred to me, my first
instinct as a scientist was to write up the results and publish them in a suitable schol-
arly journal: an archival record for other practitioners of applied math. Yet I came
to realize that the results were sufficiently insightful about playing actual blackjack
in the real world that they would be even more valuable to the wider casino-going
public. To reconcile my internal debate between these two readerships, I decided to
serve both at once. The outcome is this single two-part book, which first describes
all its conclusions in completely non-mathematical terms for the many that enjoy
gambling, and then also provides detailed derivations of those conclusions so that
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