Counting Cards in Blackjack
- Part 1 - Part 2 -Card Counting Fundamentals
What do we hope to gain by counting cards? Besides the ultimate goal of kicking the casino's ass and becoming filthy rich in the process, counting cards has as its most fundamental purpose the goal of obtaining better insight into what type of card the dealer deals next. We want to know when we should Hit, when we should Stand, when to Split, when to Double, when to increase our Bet, when to decrease our Bet, and when to walk (or run) away. The card counting method described here will help with all these decisions. The following section introduces definitions and rules that will allow you to count cards effectively.
Plus One, Minus One, or Zero (+1, 0, -1).
The discussion and definitions below easily extend to any size deck (e.g., 2, 3, 4, 5 or 6 decks - a "shoe"). For the moment, though, let's just consider a single deck of cards.
- Definitions 1
- Low Cards - 2s, 3s, 4s, 5s, 6s, and 7s.
- High Cards - 9s, 10s, Jacks, Queens, Kings and Aces.
- Middle Value Cards - 8s. Note: You should consider Jacks, Queens and Kings as 10s, for in the game of Blackjack, they all have equivalent value, the value of 10.
- Fact 1
- In a single deck of cards, before any card is dealt, the number of 2s through 7s equals the number of 9s, 10s and Aces. (This is true for multiple decks as well.) The table below summarizes this fact:
| Prior to 1st Deal - Single Deck | ||||
| Low Cards | High Cards | |||
| Type of Card | Number of Low Cards | Type of Card | Number of High Cards | |
| 2 | 4 | 9 | 4 | |
| 3 | 4 | 10 | 4 | |
| 4 | 4 | Jack | 4 | |
| 5 | 4 | Queen | 4 | |
| 6 | 4 | King | 4 | |
| 7 | 4 | Ace | 4 | |
| Total Number of Low Cards (2s - 7s) | 24 | Total Number of High Cards (9s, 10s, Aces) | 24 | |
You may ask, "What about the 8s?" The 8s represent the exact middle of an un-dealt Deck. In an un-dealt Deck, the number of cards below the 8s equal the number of cards above the 8s. The table below also represents this fact:
| Prior to 1st Deal - Single Deck | High Cards | Aces | 6 sets of 4 cards each = 24 cards | The number of High Cards (24) equals the number of Low Cards (24) |
| Kings | ||||
| Queens | ||||
| Jacks | ||||
| 10s | ||||
| 9s | ||||
| Middle of Deck | 8s | 4 cards | ||
| Low Cards | 7s | 6 sets of 4 cards each = 24 cards | ||
| 6s | ||||
| 5s | ||||
| 4s | ||||
| 3s | ||||
| 2s |
As referred to above, the card counting method we employ must give us an indication as to which type of card the dealer deals next. Before we can determine whether we should Hit, Stand, Split, or Double, or whether we should increase or decrease our Bet, the questions we should ask first are:
- Will the next card be a Low Card, or
- Will the next card be a High Card, or
- Will the next card be an Eight?
This is what we want to determine. We will not know exactly what will happen, but we will be able to determine the likelihood of one event over another.
- Fact 2
- In an un-dealt single deck, the probability of any type of card dealt is equal to the probability of any other type of card dealt. In other words, the probability of receiving any Low Card from an un-dealt Deck is equivalent to the probability of receiving any High Card from that Deck.
- Definitions 2
- Balanced Deck - the number of cards below the 8s (the Low Cards) is equal to the number of cards above the 8s (the High Cards). Unbalanced Deck - either more Low Cards than High Cards remain in the Deck, or vice versa (more High Cards than Low Cards remain).
One should consider an un-dealt deck as being completely balanced. An un-dealt deck is balanced equally on each side of the 8s. There's an equal number of 2s through 7s (Low Cards) as there are 9s, 10s and Aces (High Cards), with equivalent probability of receiving any one of those cards.
- Question
- Suppose the first card dealt from a new deck is a High Card (a 9, 10 or Ace). Then, the total number of High Cards remaining in the Deck is now 23. (For the mathematically challenged, 24 minus 1 equals 23). But there still exists 24 Low Cards in the deck, plus the four 8s. So, what does this imply as to the probability of receiving a certain type of card next?
- If one High Card has been dealt out, then that means the probability of being next dealt a Low Card is greater than the probability of receiving another High Card. The reason rests with the fact that more Low Cards remain in the deck than High Cards. Because the first Card dealt was a High Card, the Deck has now become unbalanced in favor of Low Cards.
- Definitions 3
- Count of the Cards - An Integer value representing whether a Deck is Balanced or Unbalanced. If unbalanced, then this Integer value represents the difference between the number of Low Cards and High Cards remaining to be either seen or dealt out.
- A Positive Count - More Low Cards have been dealt out (or seen) than High Cards.
- A Negative Count - More High Cards have been dealt out (or seen) than Low Cards.
- 0 Count - a Balanced Deck, meaning there exists an equal number of High Cards and Low Cards remaining to be dealt out (or seen).
Basically, only one numbering (counting) system exists to easily capture this concept. And that numbering system is as follows:
- Basic Card Counting Rules - the +1, 0, -1 Number System
- For a Balanced Deck, the Count of the Cards is always 0.
- For every High Card dealt out or seen, decrement the Count by 1 (minus 1).
- For every Low Card dealt out or seen, increment the Count by 1 (plus 1).
- For every 8 dealt out or seen, the Count does NOT change. (8s have 0 Integer value in this card counting method.)
Certainly, we could employ the inverse of rules 2 and 3 above. For example, increase the Count by 1 whenever a High Card is dealt or seen, as opposed to decreasing the Count. It doesn't matter which approach you employ, as long as you're consistent. Throughout this discussion, we will stick to the above rules.
To Be Continued ...