This is a followup to my previous post - what blackjack is really about.

Blackjack is about hard, cold, unyielding mathematics.  If you want to win at it, there is little room for superstition.  The cards don't care what you want them to be, what you think them to be, or what you do.  The next card in the deck is the same regardless of whether you take the card in front of it or not. 

Just to review the game, the dealer gives each player two cards, which may be up or down, depending on the style of the game.  They might as well be up, because there is no advantage or disadvantage incurred by anyone seeing your cards.   The dealer deals herself one card up and one card down.  You do not play the game against your fellow players, only against the dealer.  Knowing the other's cards only become important if you are counting cards.  You have to make your decision about whether to stand (stay with the cards you have) or hit (take another card) based entirely on what you have and what the dealer has (and what's already been played, if you are counting).  If the dealer is showing a 5 and you have 14, you stand.  If the dealer is showing a 10 and you have that same 14, you hit.  You can also double, split, or at some tables, surrender.  For anyone who doesn't know, doubling is putting twice your original bet on the table, but receiving only one more card.  Splitting is when you have two identical valued cards (two 9's for instance) and split them into two hands, and surrendering is giving up your hand and half your bet to the house.  In some games you can double after a split.

You can buy a playing card-sized chart at any casino gift shop that will tell you exactly what to do for any combination of your cards and the dealer's up card, and most casinos will let you consult it right at the table. They still have the advantage even if you do.  But if you don't play by the chart, you are simply giving your money away.  Play by the chart (or 'by the book' as most people call it) and you reduce the casino's percentage advantage to single digits.

There is only one factor that you can use to gain an advantage over the casino.  You have to count cards.   The success you might gain by counting cards rests on the principle of something called 'conditional probability'.  The simplest type of conditional probability, fortunately the one that comes into play in blackjack, is 'non-replacement probability'.  In a single deck of cards well shuffled, the probability of the first card coming out of the deck being any particular type is almost exactly even.  The 'almost' is because the casino burns the first card in the deck - another small advantage they take for themselves.  But for the sake of simplicity, let's say they don't burn a card.  There are four Kings in the deck and four 2's, and four 8's, etc.  There are 52 card in the deck, so the probability of having the first card in the deck be a Queen is 4 in 52.  You have  a 7.7% ((4/52)*100) chance of the first card drawn being a queen.  Or a 2.  Or a 5, or and Ace, etc.  But let us say that the first card out of the deck is a Queen.  There are now 3 Queens left in the deck, because you don't put the Queen back in the deck after you draw it (non-replacement) and 51 cards left in the deck.  When you draw your second card, the probability of drawing a queen is now 3 in 51, or 5.9%, while the probability of drawing any other card rises slightly to  7.8% ((4/51)*100). 

Now, in a six-deck shoe as is commonly played in casinos, the probability of drawing that queen is now 24 out of 312 card, or the same 7.7%.  But the probability of the next card being a queen is now 23 out of 311, or 7.4%.  So you see, with six decks, the probability of drawing another queen changes not much at all.  This probability is simplified a bit by the fact that the 10, Jack, Queen and King cards all have the same value of 10, and it is only the value that matters in Blackjack.  So there are 96 cards in the six decks that have the value of 10.  That is 96 out of 312 cards with the value of 10, or a 30.77% chance that the first card out of the deck will be a 10-value card.  For the second card, the probability that it is a 10-value card is  95/311, or 30.54.  This is a very small change is the probability.

There is no such thing as taking the dealer's bust card.  In fact, there is no such thing as a bust card.  People commonly think that the dealer showing a 16 is a bust hand for the dealer.  Sorry, it's not.  The dealer is going to make a hand after showing 6 approximately 58% of the time.   In other words, he will bust only 42% of the time when showing an up 6.  There is no hand where the dealer is more likely to bust than to make a hand (i.e. not bust).  The only thing that is true, is that the dealer is more likely to bust when showing a 6 than, say, when showing a 2.  

If the cards are evenly distributed in the 6 decks, the probability of drawing a particular card doesn't change very much.  Say half the cards have been played in the six decks (called a "shoe").  With half the shoe left, there are  156 cards left.  There will be 12 copies of each card.  There will be 48 face cards left in the shoe.  This is the other place where the myth of the 'bust card' comes in.  Superstitious players will swear (both in the sense of 'promise' and in the sense of 'at you') that if you are the last player at the table (third base) and you take a face card, you have ruined everyone else's hand because you took face card that would have made the dealer bust. The probability that the next card was a face card was 30.8% before you took the card, and 30.3% after you took it.  You didn't ruin anyone else's chance of winning their hand by having the dealer bust.

Of course, the cards are randomly distributed through the deck, which is not the same thing as evenly distributed.  There is a chance in a random distribution that the first 20 cards out of the deck will all be face cards.  It's a small probability, but randomness allows for it.  If you flip a coin 10 times, there is a fininte, but small possibility that it will come up heads all ten times.  This is where people become superstitious.  This is also why you need to count cards.  It is to the player's advantage when there are more face cards than small cards in the deck.  You are more likely to make a good hand, and the dealer is more likely to bust.  So, if you want an advantage over the house, you MUST count.  The most sophisticated counting strategies can give you a seven or eight percent advantage over the house, but even easy strategies can gain you a 2% advantage over the house.  I personally can't keep track of the cards well enough to employ a sophisticated strategy.  But here is all you need to do:

 Count every card 6 or under (except red 2's) as a -1.  Count every face card as a +1.    It's an unbalanced system for a reason.  You have 4 different face cards (10, J, Q, K) and 5 cards under 6.  You unbalance for reasons that are complicated that I won't explain here, but you only want to unbalance it by a couple of cards, so you cut out two cards from the -1 count.   I chose red 2's.  There is nothing special about red 2's.  If could be black 2's, but you want it to be 2's.  You definitely want to count all the 4,5 and 6.'s because they are the most powerful of the -1 cards. The 2's are the least poweful (the 6's will f' you more than the 2's when it comes to making your hand.)      If you count this way, and only raise your bet when the count gets to +10 or better, you will gain a 2% advantage over the house.  With patience, you can make money this way.  The only thing that is going to screw you is if you get superstitious, or cave to the pressure of other superstitious players and do two bad things:  1) play not according to the book, and 2) not raise your bet when you are +10.  The other way you can gain advantage is to stop playing when the deck is -10).  

Simple math will save you, superstition, as in most places in life, will screw you.