The Number Of Players At Blackjack The Table
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.
Tags: blackjack, online casino, team strategies
The Blackjack Rules Part2
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%