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Lesson
9: Money Management - Part 3
Expectation
and Standard Deviation
If
you flip a coin 100 times, your
expectation is to receive 50
heads and 50 tails. But the reality
may well be different; the measurement
of that reality is called "standard
deviation".
Standard
deviation is a mathematical term
used to predict the outcome of a
situation. In our coin-flipping
exercise, we expect 50 heads and
50 tails to occur, but two-thirds
of the time the actual result will
be somewhere between 45 and 55 either
way. That is, a result of 55 heads
and 45 tails or something in between
is not unusual; it will happen 68.3%
of the time. That measurement is
for 1 standard deviation from the
expectation and if we were to run
hundreds of 'trials' of 100 flips,
we could plot our results on a bell
curve and the vast majority of results
would fall between 55 and 45 either
way. What would be unusual would
be to have a lot of trials where
the result was actually 50-50! Got
that concept in your mind? Good.
You'll need to understand this in
order to survive the mental turmoil
caused by the losses which are inevitable
in this game.
Nothing
has caused counters to give up Blackjack
more than a lack of understanding
about normal, everyday standard
deviation. Counters who have trained
hard unrealistically expect to win
each time they play, so when they
have several losing sessions, they
forget what they've learned. Next
thing you know, they're over betting
their bankroll and fail to play
their hands properly and when they
wake from the daze, their money
is gone.
PATIENCE
AND SKILL WIN -- HUNCHES AND WISHING
WILL NOT WIN. PRAYER DOES NOT WORK
AT BLACKJACK.
So,
what can you expect -- what's the
worst which can happen? Well, you
can lose all your money, but if
you establish a bankroll of at least
50 'top' bets, play proper basic
strategy at all times and don't
over bet, you stand a good chance
of making some $$$ at Blackjack
-- if the game at your local casino
is a game which can be beaten. Did
I ever say this was easy?
The
table below illustrates the possible
results from varying hours of play
at a fairly typical game. Shown
with the expectation are the possible
dollar results as measured by 1
standard deviation (68.3% of the
time) and 2 standard deviations
which covers what will happen 95%
of the time. Three standard deviations
cover what will happen 99.7% of
the time. .
Expected
Win / Standard Deviation
Assumptions: $12 average bet, 50
hands per hour, 1.25% average advantage.
|
|
Results |
|
| Time |
Expected
Win |
68.3%
of the time |
95%
of the
time |
| 3
hours |
$22.50 |
+$240
to -$168 |
+$435
to -$373 |
| 12
hours |
$144.00 |
+$552
to - $264 |
+$961
to -$673 |
| 48
hours |
$360.00 |
+$1393
to -$242 |
+2,212
to -$1,059 |
| 90
hours |
$1,080.00 |
+$2,300
to -$40 |
+$3,320
to -$1,160 |
Let's
talk about this a bit. If you were
to play several hundred 'sessions'
of 3 hours each, the average win
for those sessions would be about
$22.50. (This comes from using a
$5 to $60 betting spread which we
discussed in previous lessons).
But few sessions would result in
a win of exactly $22.50; about two-thirds
would be somewhere between a win
of $240 and a loss of $168. Most
of the other sessions could see
you winning as much as $435 or losing
as much as $373 and a few would
see wins or losses even bigger than
that! Do you see now why it takes
a bankroll of $3000 to support a
$5 to $60 betting spread? In order
to be successful, you must be able
to absorb losses which are many
times that of your 'expectation'.
These fluctuations are real; they
will happen to you at one time or
another and if you're not prepared
for them, you'll either get frustrated
and quit or lose your cool and blow
your bankroll.
Now
look at the results for 90 hours
of play. Most of you will be --
at worst -- about breakeven after
that many hours. A few might be
up by $2300, but some of you could
be down by $1160 or more. Boy, I'd
hate to hear the names you'll be
calling the old GameMaster then!
But it can happen and it won't be
unusual if it does, so ask yourself
right now if you can deal with playing
a disciplined game for 90 hours,
still be at a loss and continue
playing and betting as I've shown
you. It's sad, but most of you won't
be able to deal with that and you'll
be another victim of standard deviation.
That's why I'm not afraid of the
casinos going out of business, even
if every player in the world learns
how to count cards -- few have the
patience to stick it out. I don't
want to be overly-negative, but
that's the reality. However, if
you do stick it out, the percentages
will eventually begin working in
your favor. As I tell all my students,
"the money comes in 'chunks' at
Blackjack". This is not a slow,
consistent way to make money; your
bankroll will, at times, resemble
a roller coaster and it's difficult
to deal with that from an emotional
point of view.
Just
try to understand the concept of
standard deviation and continue
'calibrating' your eyes by doing
deck estimation exercises with six
decks. As I've said before, you
need to be accurate within a half-deck
for computing the true count.
Homework
Go
to this site, Blackjack
Math (http://www.bjmath.com/main.htm)
and poke around a bit. It'll be
worth your time.
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