This free course on blackjack and card counting was created by the GameMaster, publisher of the GameMaster Online website. It is reproduced here in its entirety with permission of the author. His 24-lesson course is an excellent introduction to winning blackjack.
To start at the beginning, visit the Welcome page.
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.
|Time||Expected Win||68.3% of the time||95% of the time|
|3 hours||$22.50||+$191 to -$147||+$360 to -$316|
|12 hours||$90.00||+$428 to -$248||+$766 to -$586|
|48 hours||$360.00||+$1,036 to -$316||+$1,710 to -$992|
|90 hours||$675.00||+$1,600 to -$250||+$2,525 to -$1,175|
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 $191 and a loss of $147. Most of the other sessions could see you winning as much as $360 or losing as much as $316 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 $2500, but some of you could be down by $1175 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.
Have a look around the blackjack knowledge base at this site. With over 200,000 posts about blackjack, that should keep you busy.