The third condition you must take into account is the number of players at the table. The more hands you play per-hour, assuming you have an advantage, the faster your win rate. If crowded tables keep you from seeing and counting all the cards played, which is a common problem in facedown hand-held games, the effect of this is the same as the effect of an inadequate depth of deal ("bad penetration").

Consider, for instance, a single-deck game where there are seven players at the table. Two rounds will consume about 83% of the cards, which makes this game appear attractive. Who can complain about 83% penetration? Isn't that as good as it gets? But remember that your second (and last) bet before the shuffle will be made after having seen only about 42% of the cards, assuming you are able to see and count all cards from the first round. If you are at a table where players are hiding their hands, this cuts further into the amount of usable information you can actually process.

Let's also consider the effect the number of players at the table has on the speed of the game.

# Players Hands/Hour
l 200
2 160
3 140
4 120
5 100
6 80
7 65

So, assuming all other factors are equal, including the advantage you gain over the house from card counting, and the average amount you bet per hand, you may expect to win three times as much money per hour if you are going head-to-head with the dealer than if you are playing at a full table.

I'm not saying you should always play head-to-head—there are many other factors that must enter into this decision. Some team strategies only work well in crowded casinos, and most big-money counters find it useful to play with other players around, since blending into a crowd is always good camouflage. There is also the simple fact that it's all too often impossible to find heads-up games in most casinos, as they tend to open new tables on an as-needed basis. Analyzing your expected hourly return, however, you must take into account the amount of action you are putting on the tables. This is always strongly affected by the crowd conditions.

• The Number Of Decks In Play (0)
• The Blackjack Rules Part2 (0)
• The Blackjack Rules (0)

Most of these rule effects have been calculated by using data from Peter Griffin's Theory of Blackjack. Note that the last five rules show effects of 00.00% for basic strategy players. Also, when it comes to the "bonus" rules, such as 6,7,8 suited or 7,7,7 pays 2 to 1, the general rule is to never change your basic strategy to try for a bonus payout.

In some cases, when a specific dollar amount is awarded for the bonus hand, the value is dependent on the player's bet size. For instance, if 6,7,8 suited pays a $100 bonus, then the percentage will be quite different for a player who has a $2 bet and a player who has a $200 bet. The first player would receive a 50 to 1 payout on his hand, while the second player would receive only an extra half-bet. The $2 bettor would likely be right to hit his hand against any dealer upcard, if his hand contained two of the needed suited cards. The $200 bettor would usually be in error if he hit the hand in violation of his basic/count strategy.

The best source book for determining the value of weird bonuses, and how to adjust your strategy when appropriate, is Stanford Wong's Basic Blackjack. All players who travel frequently to foreign countries, where some of the more unusual rules are in play, should have this book in their libraries; it defines the esoteric rules at work around the world, and provides the strategies for playing them.

Returning to the chart, note the huge negative effect of "BJ Pays 6 to 5," a rule now common in many Las Vegas single-deck games. This rule is a killer, and it's worse yet when BJ pays 1 to 1 (even money), as is standard in all "Super Fun 21" games. All those other "good" rules that the "Super Fun" game allows do not make up for this single punitive one. Serious card counters should stick with the traditional "BJ Pays 3 to 2" games.

Effects in Percent
Common Rules 1-Deck 2-Deck Multi-Deck
Double on 10-11 only: -0.26 -0.21 -0.18
Double on 9-10-11 only: -0.13 -0.11 -0.09
Hits Soft 17: -0.19 -0.20 -0.21
No Re-splits: -0.02 -0.03 -0.04
Double After Splits: +0.14 +0.14 +0.14
Re-split Aces: +0.03 +0.05 +0.07
Draw to Split Aces: +0.14 +0.14 +0.14
Late Surrender: +0.02 +0.05 +0.08
Late Surrender (H softl7): +0.03 +0.06 +0.09
Less Common Rules
Double on 8-9-10-11 only: -0.13 -0.11 -0.09
Double on 11 only: -0.78 -0.69 -0.64
Double after Ace splits: +0.10 +0.10 +0.10
Double on 3+ cards: +0.24 +0.23 +0.23
No Ace Splits: -0.16 -0.17 -0.18
Early Surrender: +0.62 +0.62 +0.63
Early Surrender (H soft 17): +0.70 +0.71 +0.72
Early Surrender v. 10 only: +0.19 +0.21 +0.24
BJ Pays 6 to 5: -1.40 -1.37 -1.36
BJ Pays 1 to 1: -2.32 -2.28 -2.26
BJ Pays 2 to 1: +2.32 +2.28 +2.26
Suited BJ Pays 2 to 1: +0.58 +0.57 +0.56
21 Pushes Dir. 10-up BJ: +0.20 +0.20 +0.20
No Hole Card (European): -0.10 -0.11 -0.11
5-card21 Pays 2 to 1: +0.20 +0.20 +0.20
6-card21 Pays 2 to 1: +0.10 +0.10 +0.10
Suited 678 Pays 2 to 1: +0.01 +0.01 +0.01
7-7-7 Pays 3 to 2: +0.01 +0.01 +0.01
6 Cards Un-busted Wins: +0.10 +0.10 +0.10
No Insurance: 00.00 00.00 00.00
Multi-Action: 00.00 00.00 00.00
Over/Under: 00.00 00.00 00.00
Royal Match 00.00 00.00 00.00
Super 7s: 00.00 00.00 00.00

Let's walk through the "off the top" expectations in a more typical blackjack game. Consider a standard Atlantic City 8-deck game, which allows double after splits, but no re-splits. The basic strategy expectation is derived by adding together the effects of both the number of decks in play, and the rules being used (from the multi-deck column):

8 Decks: -0.57
Double After Splits: +0.14
No Re-splits: -0.04
House Advantage: -0.47%

• The Number Of Decks In Play (0)
• The Blackjack Rules (0)
• The Number Of Players At Blackjack The Table (0)

The second condition you must consider is the set of rules used in the game. Some rules, notably those that offer more options, favor the player, assuming he applies the correct strategy. Among those options are surrender, doubling after splitting allowed, and re-splitting aces allowed.

Those rules that limit the player's options, such as doubling down on 10-11 only, or no re-splits, are disadvantageous to the player.

Some rules neither limit nor offer options to the player, but alter the dealer's procedure. An example of one such rule would be dealer hits soft seventeen. That's disadvantageous to the player. An advantageous dealer rule, used occasionally in short-term special promotions, would be "blackjack pays 2 to 1."

Another set of rules that work in the player's favor are the "bonus" rules, such as "dealer pays $XXX bonus to player hand of 6, 7, 8 same suit." Most bonuses, due to the rarity of bonus hands, have very small dollar value to the player.

Earlier, most of the common rules were explained. In this chapter, we'll look at the approximate effect of each rule on your basic strategy expectation. By adding the effect of the number of decks in play to the effects of the rule variations, you will know the house advantage against basic strategy players. Card counters call this the "starting advantage," or the advantage off the top.

Most rules, to be sure, affect card counters differently than they affect basic strategy players. The house edge off the top, however, is always an important consideration, as that's what you're working to overcome. For instance, insurance has no value to a basic strategy player, since correct basic strategy is to never take insurance. If a casino disallows insurance, however, this hurts card counters, since they profit from their selective insurance bets. Likewise, the surrender option has little value to basic strategy players—less than one-tenth of 1% increase in expectation. For a card counter, however, surrender is, like insurance, very valuable.

In order to figure out the starting advantage of a game, you should begin by defining a benchmark game—i.e., a set of standard rules, which you can then add to or subtract from. Most authors define this benchmark game as Vegas Strip rules:

1. Dealer stands on soft 17.
2. You may double down on any 2 original cards.
3. You may not double down after splitting a pair.
4. You may split any pair.
5. You may re-split any pair except aces.
6. Split aces receive only one card each.
7. No surrender.
8. Dealer either receives a hole card, or the player's original bet only is lost if the player doubles down or splits a pair and the dealer gets a blackjack (and the extra amount bet is returned to the player).
9. Insurance is allowed up to one-half the player's bet, and pays 2 to 1.
10. Player blackjack is paid 3 to 2.
The effect of any other rules must be accounted for in determining your starting advantage. The chart below shows how these rules affect the game.

• The Number Of Decks In Play (0)
• The Blackjack Rules Part2 (0)
• The Number Of Players At Blackjack The Table (0)

First consider the effect of the number of decks shuffled together. All other conditions being equal, single-deck games would be the most profitable for card counters.

The more decks being used, the less profitable the game becomes, not only for card counters, but for basic strategy players as well. A single-deck Vegas Strip game (blackjack pays 3 to 2, double down on any two cards, and dealer stands on soft 17), is pretty close to being a break even proposition for a basic strategy player. With four or more decks in play, and the same set of rules, the house has about a 1/2% edge. Use this chart to estimate your basic strategy (dis)advantage due to the number of decks in play:

# Decks Advantage
l +0.02%
2 -0.31%
3 -0.43%
4 -0.48%
5 -0.52%
6 -0.54%
7 -0.55%
8 -0.57%

• The Blackjack Rules Part2 (0)
• The Blackjack Rules (0)
• The Number Of Players At Blackjack The Table (0)

Counting Is Not Enough
Many card counters believe that as long as a game is called "blackjack," and is being offered by a legitimate casino, they can win by applying their counting systems. But the fact is that while some games can be beaten by card counting strategies many can't, and table conditions make the difference. I've written two books on this subject already, my first two books, The Blackjack Formula, and Blackjack for Profit, plus five technical reports: "Beat the 1-Deck Game," "Beat the 2-Deck Game," "Beat the 4-Deck Game," "Beat the 6-Deck Game," and "Beat the 8-Deck Game." The first two books are now out of print, but the reports have been recently updated and are available (See the reference section in the back of this book).

In this chapter, I will attempt to update and condense some of the most important information from these books and reports so that you may choose your games wisely. There are simple guidelines you can follow that will help to keep you from throwing your money away in unbeatable games.

First, let's define table conditions. There are four distinct conditions of any blackjack game that directly affect the profit potential for card counters:

1. The number of decks in play: In U.S. casinos, this may range from one to eight.
2. Rules: There are about a dozen common rule variations, and dozens more uncommon variations in U.S. casinos.
3. Crowd conditions: You may be the only player at the table, or one of as many as seven.
4. Depth of deal, or deck penetration, between shuffles: Anywhere from 2% to 90% of the cards may be dealt out.
Let's go through these conditions one at a time.

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• The Number Of Decks In Play (0)
• The Blackjack Rules Part2 (0)

Another player's question:

I purchased a blackjack system through the mail about six months ago. It was very expensive, and in order to obtain it I had to sign a contract stating that I would never disclose the system to anyone else, and that I would never show the materials I received to any other blackjack system seller. The advertising materials made a big issue of the fact that some other system seller might try to steal his system, and that the author would prosecute any purchaser who revealed his secrets to competitors. After six months of losing with this system, I feel I've been had. I would like to get a professional opinion on whether or not this system has any value, but how can I get an opinion if I can't even show this system to anyone else?

My answer:

"You've been had, in my opinion. Over the years I've seen photocopies of about a dozen different systems sold with some kind of binding contract stating that the purchaser would never reveal the system to anyone else, and in every case so far, my opinion has been that the system was worthless. My cynical opinion of the secrecy contract is that its sole purpose is to keep you from obtaining a professional opinion, not to keep unscrupulous peddlers from stealing the system.

"There are very few blackjack books or systems that have been published in the past decade that I haven't had a chance to examine. Most authors send me their books for review. Those systems that aren't sent to me by the authors or publishers are usually sent to me by players who want to know my professional opinion. Secrecy contract or not, I think just about everything published on blackjack crosses my desk eventually.

"Some system-sellers write long treatises on how you will be violating international copyright laws if you photocopy their material; you'll be investigated by the FBI, the CIA, the Federal Trade Commission.. .and it's all nonsense.

"The copyright laws are written to protect authors and publishers from losing income. If you photocopy something for the purpose of obtaining a professional opinion from an expert in that field, you haven't violated copyright laws. You're not selling the photocopies for any personal gain, nor are you in any way affecting the copyright owner's income from the sale of his work.

"Signing a contract not to disclose information is something else again. I'm no attorney, and I'm not going to get into my understanding of the validity of inane contracts. My advice to anyone who is required to sign a secrecy contract in order to purchase a gambling system is simple. Don't do it. The system is probably worthless. The system seller is probably trying to keep you from obtaining honest expert opinions. The system seller probably doesn't care if the secrecy contract you signed is valid, so long as the check you signed is."

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• The Number Of Decks In Play (0)
• The Blackjack Rules Part2 (0)