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.
Good Online Casinos
Homework
Go to this site,
Blackjack
Math (http://www.bjmath.com/main.htm) and poke around a
bit. It'll be worth your time.
