Odds
Versus Probability.
What's The Difference?
If
you are interested in learning how to win at gambling, you need
to become familiar with the concepts of "odds" and
"probabilities."
These
terms can be expressed as ratios, percentages or fractions and
each has a slightly different meaning.
Just in case you slept though your course Statistics 101,
or even managed to escape the experience altogether, I am going
to attempt to clear things up.
Probability
A
general definition of probability is "the likelihood that a
given event will occur." When we apply this concept to
gambling, we usually end up with a specific expression like 1
out of 2 or 1:2.
When
probability is expressed as two numbers, the first number
represents the expected frequency of a specific event occurring.
The second number is the total number of possible
events or outcomes, including the specific event and all other
events that can occur.
Let's
take a look at the concept of probability applied to coin flips.
Consider this question  "What is the probability of
a head showing on the next coin flip?"
Since
there are two possible outcomes (heads or tails) and we are
looking for only one event (heads), this probability can be
expressed as 1 out of 2, 1 to 2 or 1:2 or even 1/2.
This
two number expression can also be converted to a percentage by
dividing the first number by the second number, which, in this
case, will give us: 1 divided by 2 equals 0.50, which can also
be expressed as 50%.
Therefore,
the probability of getting heads on the next coin flip is 1 to 2
or 50%.
Let's
apply this concept to the game of roulette.
The American version of the game has the numbers 1 to 36,
plus a zero and a doublezero, for a total of 38 numbers.
This gives us 38 possible outcomes on any spin of the
wheel. If your
favorite number is 17, and you wanted to know how likely this
was to show on the next spin of the wheel, you could express
this as 1 out of 38, 1 to 38, 1:38 or 1/38.
To
determine this probability as a percentage means  1 divided by
38 equals 0.026, which is 2.6% as a percentage.
Interpretation?
There is a 2.6% probability or chance of your wager on
the number 17 winning on the next spin of the roulette wheel.
Odds
The
definition of odds is the "likelihood (or probability) of a
given event occurring, compared to the likelihood of that same
event not occurring."
Odds,
like probabilities, can be expressed as two numbers in the form
of a ratio. The first number represents the expected frequency
of a specific outcome occurring, which is the same as with
probabilities. However,
unlike probabilities, the second number states only the number
of all the "other possible outcomes."
This
figure excludes the specific event  that is, the first amount.
Going
back to our coin toss, we can ask "What are the odds of a
head showing on the next coin flip?"
If
we decide to pick "heads" as our bet selection, we
know that on a twosided coin heads can only show one way.
The only other option is a tails.
We can show the odds of a heads showing on the next
coin flip as 1 to 1, 1:1 or 1/1.
Unlike
probabilities, which can also be expressed as percentages, odds
are always shown as ratios.
Now,
let's calculate the odds of number 17 showing up on an American
roulette wheel, with 38 numbers. Our number 17 represents just
one number. The
remaining numbers, excluding the number we chose, are 37, making
the second figure in the ratio thirtyseven.
The odds of a 17 showing on the next spin, or any other
single number showing on the next spin of the wheel, is
expressed as 1 to 37, 1:37 or 1/37.
If
we reverse this ratio, we will show odds against a 17 showing.
The odds against a 17 showing on the next spin of the
roulette wheel are 37 to 1 or 37:1.
The
House Edge in Roulette
The
house gains its edge over the player because of the appearance
of a zero and a doublezero on American roulette wheels.
European wheels have only one zero, giving the
player a better chance of winning.
Let's
calculate how the casino's edge affects the payoff of a wager on
our favorite number, seventeen.
We
have already calculated the probability of the number showing,
which is 1 out of 38 or 1 to 38.
If
the house did not have an edge over the player, the correct
payout for winning the wager would be the real odds against
winning the bet, which is 37 to 1.
However, the house gains an edge by shortchanging the
player on the payoff of a winning bet and only pays the wager at
35 to 1.
The
house keeps 2 out of the 38 numbers for itself.
These numbers are the zero and doublezero.
The
house edge over our bet on the number 17 can be calculated as
follows:
Wheel
with zero and doublezero  2/38 = 0.0526 or 5.26%
Wheel
with onezero  1/37 = 0.027 or 2.70%
Some
casinos use a special rule for roulette's outside bets which
allows the wager to stay up for an additional spin after a zero
appears. In this
case the bet is said to be imprisoned.
This rule lowers the house edge even more.
The
Gambler's Fallacy
Many
gamblers place wagers based on a poor grasp of the law of
averages. They
believe that because an event has not occurred for a while that
it is due.
In
one incident, when I first started playing roulette, I came up
to a table and starting watching before I began wagering.
One man was wagering on red, which showed three times in
a row while I was watching.
I exchanged my cash for
chips and starting betting black since I knew that long streaks
of a single repeating number are fairly rare.
I wagered $5 on black, feeling somewhat superior to the
man who keep wagering on red.
Red showed again. Next
spin I wagered $10 on black, feeling more confident that black
was "due" to show.
The ball landed on red again.
I
continued to double my wagers until I had lost six bets in a
row. At this point
I backed off and watched as red showed on eleven consecutive
spins.
If
I had not backed off wagering I would have run into the house
betting limit before I eventually won a bet.
There
are a couple of lessons to be learned here.
First, no number or event is ever due in a game of
chance. This
includes all wagers in the games of roulette, craps and
baccarat. However,
in general, bucking the trend is not a good idea.
The trend is your friend in roulette just like it is when
playing the stock market.
The
second lesson is that it often pays to be flexible in selecting
your wagers in roulette. Gambling
probability is defined as the "likelihood" of an event
occurring. It does not mean "definite" and it certainly
doesn't mean that the event will happen on the next spin or even
the next two or three spins.
A
Breakthrough New Roulette Strategy
Just
recently I finished working on a yearlong project that resulted
in developing a amazing new roulette strategy that one of the
testers even called "infallible."
Let
me tell you a little more about this system.
Subjected to the most rigorous testing, it has been
proven to 
Incredibly,
this strategy performs so well, that it really develops an edge
over the game of roulette even against the higher house edge
doublezero games. Recognizing
its superior winning strengths, it was aptly named the
"Maximum Advantage Roulette Strategy."
This
system only requires making one bet at a time and wins a
documented 97.75% of the games played.
And,
because of the low level of wagers used, you can get started
with this strategy as a $5 better (recommended) with a measly
$100 investment (I suggest that you use $150 because I am very
conservative).
I
highly recommend that you "risk" five minutes of your
time and read more about this proven performer here.
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