The GameMaster's Blackjack School
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 |
$675.00 |
+$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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