Although this author--Victor Royer--hangs out with Jean Scott and the
rest of the guru-clique, he wrote a very refreshing article this week
on the truth about mathematics, from someone who makes little dicky's
involvement in math and programming look like Michael Moore's take on
America.
As I've said so often, the New Era of Video Poker will soon take over
that which is so desperately clung onto by only a handfew of vocal
dinosauers. I can imagine the P-A-I-N as the Queen reads on.....
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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.