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Las Vegas Gambling Tips: The Mathematics Of Poker and Gambling |
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On The Town With Vegas Vic
By: Victor H. Royer
Welcome to Las Vegas! My name is Victor H. Royer, but everyone just calls me Vegas Vic. I was named after that famous neon sign in Downtown Las Vegas, that cowboy with the hat on top of the Pioneer Club, always waving his hand and beckoning to his long love, Sassy Sally, on the other side of the street. I will be writing a few articles for AccessVegas.com, so I hope you enjoy them.
The Mathematics Of Poker and Gambling
There are quite a few people in the gaming business, particularly
writers and gaming experts, who are often prone to overusing
mathematical percentages, frequencies of occurrence, probabilities
and so. Basically, overusing the importance of mathematics in
gambling. Even I have been, on occasion, guilty of doing so. It is
easy to understand why. Mathematics is such a useful tool in trying
to explain certain things. It is also an undeniable fact. Without
mathematics, gambling would not be possible, at least not the way we
understand it now in the current world of casinos and casino games.
Indeed, just about everything in gambling relies on mathematics in
one way or another. For example, if we have a starting hand of
two-aces and a suited 10 in seven card stud, we may know that the
mathematics indicates that we will make a straight flush about 0.02%
of the time, or that we will make three of a kind about 9.75% of the
time, or that we will make two pair about 41% of the time. Simple
math, right?
Well, not entirely. Although such a sequence of cards will,
inevitable, prove to be so in the long run of infinite statistical
probability (all universe being equal), it doesn’t mean that it
will do so for you while you are actually playing. Further, computer
programs which are written for tests such as these which produce the
overall statistics for poker hands, based on the randomness of
expected probability, aren’t perfect. Perfection, as a concept,
is all but impractical in the real world, and not just in gambling.
Your home computer isn’t perfect, and neither is mathematics as
a science. In mathematics, there are no absolutes. The truisms
expressed in mathematical terms are in themselves based on certain
assumptions, many of which are totally unsupported by any
empirically-derived circumstances. In fact truisms are largely
vacuous in concept. They may have absolute inherent values within
their own designated parameters, but are for all intensive purposes
useless. An algebraic truism such as (a = a) may be absolute, but
useless for anything but itself. And mathematical equations such as 1
+ 1 = 2 may be useful in determining values, but they are based on
assumptions of perceived reality of whole numbers, and what their
meaning is within specified circumstances. So what does all this mean
for poker players? Or gamblers in general?
It means that the expected probability of making a hand, or of a win
or loss, is an assumption, one which is based in large part on a
further set of assumptions which went into the creation of the
mathematical profile of that hand’s statistical probability
ranking and odds. In addition, such series of mathematical
assumptions are further compromised, versus the real-world of
in-casino play, by the fact of the testing and research which goes
into the validation of such hand’s ranking and percentage of
event calculations. These tests involve a whole series of probability
tests, vested in the principles of probability calculus and
event-actuality. Such tests are conducted under laboratory
conditions, and consists of millions of simulations done with
computers. These computer tests themselves run on other computer
programs, and in the end provide an analysis of the relative
frequencies of occurrences which are then computed to equate to the
expected percentages. This then becomes the basis for the probability
ranking of such hands under the designated starting and ending
circumstances. What is missing in all of this is the reality of the
short-term play by players in the actual casino. No poker player will
play the game for the same number of consecutive events which were
part of the tests for that sequence of hands. This is simply
impossible by any human, and therefore machines are used to perform
these tests and calculations. Consequently, what is missing in all
such mathematically-derived recommendations for profitable play,
whether for poker hands or any other gambling game, are the facts of
the limited exposure by the player to that sequence of hands, or
game.
Of course it is better to play hands whose starting percentage value
is statistically higher than another. That is simple common sense.
However, reliance on such numbers alone isn’t. If you
continually chose to play hands simply and only based on the expected
mathematical probability of event occurrences, then you will lose
more often than not. Yes, the statistics indicate that if you played
the hands for all their test-events, in the end you’d be that
percentage favorite to win the pot (overall, based on the percentage
value and raking of such hands in such events). But that isn’t
what you will do as a player in the casino, playing poker for a few
hours, or even several days, weeks, or even months at a time. In your
actual in-casino play, you will play any given hand at far less than
the overall mathematically-derived probabilities of event occurrence.
This means that no matter what starting hand you select, even the
better-odds higher rank hands, your individual event-occurrence
expectation will not be anything close to the overall mathematics of
that hand’s overall percentages. You will either win the pot at
a rate far higher than the mathematical probabilities indicate, or
far less. You will either win a lot more than the mathematics
indicate should be your event experience, or not nearly as much.
Therefore, the reality is that choosing any poker hand solely
based on the averages of expected event probability of occurrence
won’t do. It is for this reason that I have come to believe
that over-reliance on mathematics as a guide for gambling success is
inherently flawed.
Your choices of hands to play need be far more “variable”.
And “variables” are the death-knell for mathematicians.
Mathematics does not like “variables”, because by their
very nature they are mathematically indefinable. What this means is
that anything which cannot be expressed in whole number absolutes,
even allowing for fractions, is untenable. And indefinable. As a
direct result, your success in gambling, and in poker, is not wholly
dependant on such numerical factors alone. The “variables”
in your choices of hands are factors such as:
• Play observation
• Action given to that table
• Your play time and bankroll
• Your betting strategy
• Your psychological predisposition to attractiveness of certain
kinds (such as “liking” certain hands, draws, opponents,
pot odds and so on)
• Your aptitude
• Your skills
• Your ability to notice and adapt
• Your resiliency
• Your dedication to abstinence from depressants such as alcohol
while gambling
And dozens more reasons and situations of this kind. These are all
mathematically indefinable variables, all of which contribute to your
overall gambling success at that game, and in your selection of such
a game and starting hands.
There have been numerous examples where gaming experts have taken far
too much stock in overemphasizing mathematics as the end-all holy
grail of gambling success (and I include myself in this group in some
of my earlier writings). We have all done this at one time or
another, and it is easy to see why. Numbers and percentages are
easily seen, viewed, understood and explained. They are the ideal
“tool” by which to try to impart certain aspects of
knowledge to readers. But what has been by and large missing from
many such writings is the fact that mathematics, and explanations
vested in mathematical derivatives such as percentages and
probabilities, are a tool for explanations, and not
the sum-total of all successes in gambling.
This is not a problem confined to gambling. As a society, we have
become increasingly reliant on the perceived “purity” of
numerical information. It fits nicely in all that we consider, and
perceive, to be constant. We are human creatures in a desperate
search for order. And as such we expect order wherever we look, and
if we don’t find it, we find way of creating it. It helps us
understand. As such, a useful tool. In the reality of your life, and
play, you need to make two basic decisions:
1 Are you playing for entertainment?, or,
2 Are you playing for profit?
If your answer is entertainment, then your reliance on
mathematically-derived assistance is a waste of your time. You should
instead rely on assistance derived from the “variables”,
as described above.
If your answer is profit, then you need to combine the realistic
differential between cold mathematics and the real-world of your
exposure to that set of circumstances, combined further with your
particular selection of “variables”. These then will
constitute your individual success rate.
The mathematics of gambling as I have chosen to apply it and describe
it here, applies equally to your choices of any gambling game. While
much has been touted and written about regarding “odds”
and “percentages” inherent in gambling games (and table
games in particular, myself included as an author of such earlier
works), the fact is that the limited exposure which any gambler will
have to these games all but eliminates any odds-advantages in such
mathermatiacally perfect play, versus the inherent disadvantages in
the game’s rules, thus completely dissallowing and forgetting
even one of the most important game factors such as the game’s
volatility index. In fact, the sad reality is that some players will
win even when playing extremely badly and making all the kids of
decisions on which gaming purists will frown, including playing
decisions which are horrendously wrong -- as based on these
mathematically-derived sets of rules of what to do and when. And this
applies to all gambling games in general.
The point in all this is that your decisions on what to play, and how
to play it, should not be solely vested in principles of mathematics.
Just because a decision in poker, for example, calls for -- let’s
say -- a re-raise, as based on the mathematically-derived sets of
rules for pot-odds and expected probability of a win based on the
hand value, this doesn’t mean that at that precise instant you
should always do so. There may be other variables to factor in this
decision. In the real world where nothing is fixed, your decision in
this case, and other similar cases, may be far more profitable by
ignoring the math and probabilities. Of course, you do need to know
how to play the hand, but then you should also be able to make other
decisions regarding your play, and not only take as your guide the
math, odds and probabilities.
Over-reliance on mathematics, odds information and probability
calculus, can lead one to expect events which simply will not occur
for that slice of the overall reality which you will experience as a
player at that game, and with those hands. Your personal adaptability
to these situations is the key to continued success within the small
slices of the infinite experience. Mathematics and probabilities are
calculated with a mind to infinity, as a resource for estimating the
likelihood of occurrences based on a defined set of parameters and
expectations. All these are assumptions vested in the rules of reason
and theoretical logic. None of them have any semblance of
individual-event-reality as a basis. Consequently, your successes, or
failures, in gambling have far more to do with your abilities to
adapt to the circumstances at hand, and far less to do with what
the odds are, or percentages of expected events, or overall
mathematical statistics. That’s why poker players can make a
living at poker, because they have learned how, and when, to
disregard the mathematics. And the same applies to the few
professional Blackjack players who can affect the overall outcome of
their sessions, as well as to any other player who desires to either
play professionally, or has at least mastered the principles of game
variance.
Adapting is not as hard as it may seem. Yes, you should learn all
that you can about the game, it’s odds, percentages, and
overall mathematics, but then put it away in the back of your mind.
Then play the games based on actual-event-experiences, and be able to
modify your decisions in an instant. Take into account all the
variables of the experience, and the psychological factors, including
your own psyche at the moment, and adapt your decisions accordingly.
And that’s how you will be able to keep yourself ahead, more
than behind, in your gaming success.
Victor H. Royer is the Author of 18 books, more than 50 casino reports, profiles, and manufacturing analyses, and a business consultant. He can be contacted at: vicnvegas@aol.com , or visit his Web site at: http://hometown.aol.com/vicnvegas/myhomepage/newsletter.html
His books can be ordered through this website, by following the link provided.
(c) Copyright 2004 Victor H. Royer. All rights reserved. For syndication purposes, contact MRM Entertainment Inc. at: vicnvegas@aol.com
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