The document provides an overview of strategies for becoming a profitable gambler. It discusses the importance of understanding risk, reward, and probabilities involved in games. It describes advantage play, which involves using statistical techniques and understanding probabilities to gain an edge legally, such as counting cards in blackjack. It also warns about illegal advantage techniques like loaded dice. Finally, it defines expected value as the average gains or losses that can be expected from a game based on probabilities and payoffs.

1.
Gambling
Awareness
101
In
order
to
become
a
profitable
gambler
it
is
important
to
be
aware
of
risk,
reward
and
probabilities
involved
in
the
game.
There
are
statistical
techniques
that
can
help
you
make
a
decision
when
gambling.
The
people
who
risk
their
money
in
order
to
make
a
substantial
profit
need
to
be
three
things:
logical,
strategic
and
unemotional.
They
need
to
understand
the
inherent
risk
involved
in
any
game.
Advantage
Play
Advantage
play
is
ubiquitous
in
the
lives
of
successful
gamblers.
It
is
essentially
the
legal
way
to
gain
a
mathematical
edge
within
a
game.
This
is
commonly
seen
in
the
game
of
black
jack
or
poker.
For
example,
let’s
imagine
that
you
are
playing
a
game
of
black
jack
against
five
people
including
the
dealer.
Each
player
is
dealt
two
cards
with
one
card
facing
up
and
another
facing
down.
If
you
see
that
you
are
dealt
a
two
face
up
and
a
jack
face
down,
and
that
there
are
five
cards
showing
a
value
of
ten,
then
you
know
that
there
are
roughly
fourteen
cards
that
can
make
you
go
over
21
out
of
the
remaining
forty
cards
or
35%
you
lose.
You
do
not
know
what
the
values
of
the
face
down
cards
are.
This
is
why
it
is
just
an
approximation.
Then,
suppose
everybody
calls
for
a
third
card—they
come
out
to
be
a
queen,
king,
king,
ten,
and
a
jack.
The
card
you
receive
is
a
two.
You
would
then
have
roughly
26%
chance
that
you
will
go
over
on
your
next
card.
As
you
can
see,
the
more
cards
that
come
out…
you
can
learn
how
its
affects
your
future
chances.
If
you
are
aware
of
these
probability
enhancers,
then
you
can
make
smarter
gambling

2. decisions
on
the
floor.
Most
gamblers
have
tried
to
count
cards,
especially
in
black
jack.
They
are
essentially
using
a
similar
idea
to
make
educated
guesses
on
their
next
cards.
Thus,
this
would
give
them
an
edge
over
the
house
and
come
out
on
top
with
profits.
Nowadays,
however,
it
is
not
as
simple
as
this.
Most
casinos
use
roughly
four
to
six
decks
a
game.
This
makes
it
much
more
difficult
to
count
since
you
are
now
dealing
with
many
more
cards.
Nevertheless,
there
are
also
many
illegal
ways
of
gaining
an
unfair
advantage.
There
are
scenarios
in
craps
when
gamblers
can
attempt
to
throw
the
die
a
certain
way.
Still,
given
the
cameras,
heightened
security
and
strict
rules
when
throwing
the
die,
it
is
much
harder
to
achieve
this
feat.
Be
mindful
of
the
loaded
dice
scam.
A
“loaded”,
or
weighted
die
is
one
that
has
been
fixed
to
land
with
a
specific
side
facing
up
more
often
than
it
normally
would.
A
type
of
loaded
die
is
hollow
with
a
small
weight
and
a
semi-­‐solid
substance
inside
whose
melting
point
is
just
lower
than
the
temperature
of
the
human
body,
allowing
the
cheater
to
change
the
loading
of
the
die
by
applying
body
heat,
causing
the
semi-­‐solid
to
melt
and
the
weight
to
drift
down,
making
the
chosen
opposite
face
more
likely
to
land
up.
A
less
common
type
of
loaded
die
can
be
made
by
inserting
a
magnet
into
the
die
and
then
embed
a
coil
of
wire
in
the
game
table
which
in
turn
would
create
an
electro-­‐magnet.
After
running
current
through
the
coil,
it
increases
the
likelihood
of
a
certain
side
landing
on
the
bottom.
These
are
obviously
the
illegal
way
of
gaining
an
edge
when
gambling.

3. Expected
Value
Expected
value
is
the
average
gains
or
losses
to
be
“expected”
from
a
game.
For
example,
suppose
you
play
a
game
in
which
you
pay
five
dollars
to
roll
a
dice.
If
you
get
an
even
number,
you
are
rewarded
the
corresponding
number.
If
you
get
on
odd
number
you
are
rewarded
nothing.
Your
expected
value
per
game
would
be
$-­‐0.5.
You
obtain
this
by
multiplying
probabilities
of
each
outcome
by
their
corresponding
gain
or
loss
and
summing
them
together.
This
is
shown
mathematically
as:
E=1/6
x
2
+
1/6
x
4
+
1/6
x
6
-­‐
3/6
x
5
=-­‐0.5
Essentially
this
means
when
you
risk
five
dollars
to
potentially
make
two,
four
or
six
dollars
your
average
over
time
would
be
negative.
You
can
expect
to
lose
roughly
fifty
cents
per
game.
If
you
play
this
100
times,
you
can
expect
to
lose
fifty
dollars.
Casinos
use
this
idea
in
order
to
stack
the
probabilities
in
their
favor
in
order
to
be
constantly
profitable.
This
edge
is
why
and
how
the
house
always
wins
on
average.
This
is
called
Advantage
Play.
Another
simple
example
is
shown
through
a
game
of
roulette.
On
a
European
roulette
table,
a
croupier
spins
the
wheel
and
releases
a
ball
to
fall
into
one
of
37
slots.
There
are
18
red
and
18
black
slots
and
one
green
0
slot.
If
you
were
to
constantly
bet
$1
on
black,
since
the
payout
is
1
to
1,
the
expected
value
per
game
would
come
out
to
$-­‐0.027
per
game.
This
is
shown
mathematically
as:
18/37
x
$1
–
19/37
x
$1
=
-­‐$0.027
That
extra
green
slot
is
enough
to
stack
the
probability
in
favor
of
the
house.
For
an
American
Roulette
table,
your
expected
loss
would
be
roughly
$-­‐0.0526
per
game
on
account
of
the
two
green
slots
for
0
and
00.
It
is
a
small
edge
the
house
gets,
and
it

4. quickly
adds
up
over
the
hundreds
of
thousands
of
game
that
are
played.
This
edge
holds
true
for
any
way
you
choose
to
bet
and
no
matter
what
the
payout
odds
are
for
each
type
of
bet.
You
could
have
bet
on
6
numbers
on
an
American
Roulette
table.
The
pay
out
would
be
6
to
1.
This
is
shown
mathematically
as:
6/38
x
$5
–
$1
x
32/38
=
-­‐$0.0526
If
you
played
the
American
roulette
game
1,000
times
the
house
would
be
expected
to
gain
$52.60
from
you
alone.
It
would
be
wise
to
consider
playing
on
the
European
table
as
opposed
to
the
American.
It
is
interesting
when
you
think
about
the
influence
that
adding
just
one
or
two
more
slots
has
on
a
game,
its
outcome
and
profit
potential.
It
is
enough
for
the
casino
to
almost
always
come
out
on
top
on
average.
For
every
winner
there
will
be
more
losers.
It
makes
you
wonder
why
playing
at
all
makes
any
sense?
Most
people
don’t
understand
this
simple
concept.
Casinos
are
a
business,
and
like
any
other
business,
it
is
there
to
make
money.
It
is
important
to
understand
that
more
than
half
of
the
gamblers
walking
around
any
casino
floor
are
losers.
Variance
Variance
is
an
important
concept
to
understand
when
gambling.
It
is
the
measure
of
how
far
the
numbers
lie
from
the
mean.
Although
there
are
various
formulas
used
to
describe
the
variance
of
a
certain
data
set,
the
concept
remains
the
same.
The
simplest
mathematical
version
of
variance
is
basically
the
probability
of
the
outcome
times
the
square
of
the
difference
between
the
shown
value
and
the

5. expected
value
and
taking
their
sum.
For
example,
if
you
were
to
roll
a
dice,
then
the
variance
would
be
roughly
2.92.
This
is
shown
mathematically
as:
1/6x(1-­‐3.5)
2+
1/6
x(2-­‐3.5)
2
+
1/6
x(3-­‐3.5)
2
+
1/6
x(4-­‐3.5)
2
+
1/6
x
(5-­‐3.5)
2
+
1/6
x
(6-­‐3.5)
2
=
2.92.
Statistical
variance
gives
a
measure
of
how
the
data
distributes
itself
about
the
mean
or
expected
value.
Unlike
range
that
only
looks
at
the
extremes,
the
variance
looks
at
all
the
data
points
and
then
determines
their
distribution.
If
there
were
a
relatively
high
variance,
you
should
expect
a
wide
spread
of
values,
and
it
would
be
wise
to
reconsider
your
bet
on
a
given
outcome.
It
is
a
good
indication
of
what
kind
of
challenge
you
will
be
facing
when
placing
a
bet.
From
the
variance
you
can
always
obtain
the
standard
deviation,
by
taking
its
square
root.
The
standard
deviation
typically
corresponds
to
the
deviation
from
the
expected
value.
In
the
case
shown
above,
the
standard
deviation
would
be
the
square
root
of
2.92,
which
would
be
roughly
1.71.
Knowing
these
values
you
can
make
more
educated
guesses
about
where
the
bet
is
going
and
how
likely
you
are
to
succeed.
These
ideas
can,
perhaps,
save
you
a
lot
of
money
down
the
line.
If
you
are
aware
of
these
concepts
and
their
applications,
you
can
make
more
thoughtful
decisions
throughout
your
gambling
career.
Bankroll
Management
Bankroll
management
is
just
as
important
as
the
gambling
strategy
itself.
A
successful
gambler
needs
to
be
aware
of
his
capital
and
his
ability
to
absorb
losses.
It
is
very
important
to
understand
that
it
takes
money
to
make
money
in
the
long

6. run.
Many
people
see
the
stock
market
as
gambling
because
there
is
a
chance
the
stock
price
can
go
up
or
down
and
there
is
a
50%
chance
of
each.
However,
there
are
probability
enhancers
that
indicate
which
way
a
price
is
likely
to
go.
Traders
and
financial
advisors
undertake
this
endeavor
everyday.
The
big
hedge
funds
and
investment
banks
such
as
J.P.
Morgan
and
Goldman
Sachs
are
able
to
make
loads
of
money
on
small
price
movements
because
of
their
huge
bank
account.
They
can
also
absorb
losses
if
the
market
goes
against
them
if
they
are
wrong.
This
is
because
they
manage
their
bankroll
in
such
as
way
as
to
only
risk
roughly
2%
of
their
financial
assets
on
any
one
trade.
However,
a
typical
retail
trader’s
2%
will
be
much
less
than
J.P.
Morgan’s
and
Goldman
Sachs’.
Thus,
most
retail
traders
will
risk
much
more
than
2%
of
what
they’re
willing
to
spend
on
gambling
for
the
night.
This
goes
the
same
for
gamblers
in
a
casino.
A
good
example
is
found
in
professional
bull
riding.
It
takes
a
very
strong
guy
to
be
able
to
handle
all
the
highs,
lows,
twists
and
thrusts
in
any
event.
A
weaker
person
would
not
be
able
to
hang
on
as
long.
This
is
because
the
stronger
guy
was
able
to
absorb
the
shocks
from
the
bull
without
getting
knocked
out
of
the
game.
With
knowledge
of
the
expected
value
of
any
game,
odds
and
your
bankroll
account
you
can
absorb
losses
that
will
be
inevitable
given
the
presence
of
variance.
It
allows
you
to
stay
in
the
same
longer,
and
hopefully,
when
you
win,
it
is
much
greater
than
your
accumulated
losses.
When
I
say
losses
I
mean
long
run
losses
given
since
you
started.
Winning
$1,000
one
day
after
losing
$15,000
since
you
started
a
month
ago
does
not
make
you
a
winner.

7. Bankroll
management
is
what
will
allow
you
to
hopefully
make
more
educated
guesses
and
allow
you
to
come
out
on
top
with
a
profit.
Most
people
when
gambling,
after
losing
a
significant
amount
on
any
given
bet,
will
feel
hopeless
and
let
their
emotions
take
over.
They
will
then
make
a
rash
decision
and
decide
to
go
all
in.
This
is
not
proper
bankroll
management,
and
it
is
what
also
gives
the
casino
another
edge.
In
Vegas,
where
the
casinos
are
open
24
hours
a
day
serving
alcohol,
it
greatly
enhances
the
probability
that
the
gambler
will
make
a
rash
decision
and
lose
money.
From
either
mental
fatigue
or
inebriation,
this
will
work
against
them.
Casinos
are
a
lucrative
business,
which
uses
logic
to
stack
the
odds
in
their
favor
even
before
any
gambler
chooses
to
bet
in
any
given
game.
Risk
of
Ruin
The
formal
definition
of
‘Risk
of
Ruin’
(ROR)
is
the
amount
of
money
that
you
are
willing
to
risk
before
you
stop
gambling.
The
formula
that
determines
this
probability
calculates
the
percentage
of
your
bank
account
you
are
playing
with.
Mathematically
this
can
be
shown
to
be:
ROR=((1-­‐edge)/(1+edge))
Number
of
games
This
edge
is
essentially
the
probability
that
you
think
you
can
win
minus
the
probability
you
think
you
will
lose.
It
is
a
critical
statistical
concept
that
many
gamblers
do
not
take
into
consideration
because
they
most
likely
believe
it
will
not
happen
to
them.
For
example,
lets
say
Gambler
A
is
willing
to
risk
a
maximum
drawdown
of
40%
of
his
$60,000
account
on
poker
games
before
he
stops
playing
which
is
a
point
of
ruin
at
$24,000.
Let’s
imagine
that
this
poker
player
has
won
6
out
of
his
last
10
games.
This
would
give
him
a
win
percentage
of
60%
and
a
loss

8. percentage
of
40%.
His
edge
would
be
equal
to
20%.
Let’s
say
the
buy
in
for
his
poker
games
are
$500
each.
This
would
give
him
access
to
48
games.
The
ROR
in
this
particular
case
for
Gambler
A
would
be
.00000000353
or
.000000353%.
I
encourage
you
to
carry
out
the
calculation
on
your
own.
This
is
a
very
low
probability.
Now,
let’s
imagine
that
Gambler
B
enters
into
the
same
poker
tournament
with
$12,000
in
his
account
and
is
willing
to
risk
the
same
percentage
of
his
bank
account
as
Gambler
A
at
40%.
The
ROR
at
this
point
would
be
$4,800.
Let’s
say
Gambler
B
also
has
a
60%
win
percentage.
Gambler
B
would
have
access
to
about
11
poker
games
for
this
tournament.
The
ROR
of
Gambler
B
would
come
out
to
.026
or
2.6%.
This
is
interesting
because
as
you
see
here,
the
risk
of
ruin
is
much
higher
even
though
they
have
the
same
win
percentage
and
same
max
drawdown
percentage.
The
only
difference
is
the
amount
of
capital.
Please
note,
however,
this
only
holds
true
if
the
gamblers
maintain
the
60%
win
rate.
Once
you
start
losing
more
than
you
win—
the
ROR
quickly
rises
and
you
will
have
a
greater
chance
of
reaching
your
limit.