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- Appendices
- Miscellaneous
- External Links
Introduction
Basic strategy blackjack players sometimes ask me for a simple way to overcome the small house edge in blackjack, with little worry over being recognized as a card counter. This is often done with the motive of milking the casinos for comps and offers. What follows is, in my opinion, the easiest card counting strategy to achieve the above goal and still put the odds in the player's favor.
How It Works
- Establish what your minimum and maximum bets will be. Usually the maximum will be 8, 16, or 32 times the minimum bet, or any power of 2, but you can use whatever bet spread you wish.
- At the beginning of each shoe, start with your minimum bet, and a count of zero.
- For each five observed, add one to the count.
- For each ace observed, subtract one from the count.
- If the count is greater than or equal to two, then double your last bet, up to your maximum bet.
- If the count is less than or equal to one, then make the minimum bet.
- Use basic strategy for all playing decisions.
This strategy was designed to be most effective on a six- or eight-deck game. I recommend playing only on games with liberal Strip rules, which are as follows:
- 4-8 decks
- Blackjack pays 3 to 2
- Dealer stands on soft 17
- Double after split allowed
- Late surrender allowed
- Re-splitting aces allowed
- 75%+ penetration
Such games are easy to find in Las Vegas, although sometimes a higher minimum bet is required. In the low-roller pits, the dealer will usually hit on a soft 17, which is bad, costing the player 0.22%.
Simulation Results
The following results were provided by Norm Wattenberger using his Casino Vérité software. The rules above were used, with six decks, and 75% penetration. In my opinion, Casino Vérité is the most robust and accurate blackjack simulation software on the market. It can be used to test just about any card counting strategy under any set of rules and conditions.
Ace/Five Count Statistics
Spread | Player Advantage | Average Initial Bet | SCORE |
---|---|---|---|
1-8 | 0.30% | 2.7 | 3.1 |
1-16 | 0.45% | 4.2 | 5.3 |
1-32 | 0.57% | 7.1 | 6.5 |
SCORE is an acronym, coined by Don Schlesinger, for Standardized Comparison Of Risk and Expectation. It is defined as the advantage squared divided by the variance. The SCORE may also be interpreted as the expected hourly win per hand for a player with a $10,000 bankroll, who sizes his bets according to the Kelly Criterion, to achieve a 13.5% risk of ruin. As a basis of comparison, a Hi-Lo counter, with a 1 to 8 spread, under the same rules, has a SCORE of 8.40, compared to the 3.1 of the Ace/Five count.
Source: 'Blackjack Attack,' third edition by Don Schlesinger.
Earlier Strategies
Blackjack Ace Queen
After publishing this section, somebody accused me of stealing the idea from Edward Thorp. Indeed, in 1969 Thorp did discuss a similar strategy in his book 'Beat the Dealer,' in the fourth chapter titled 'A Winning Strategy.' The difference is that Thorp's strategy tracks fives remaining against total cards remaining. Later, in 1971, Lawrence Revere published a similar strategy as Thorp's in 'Playing Blackjack as a Business,' chapter 7 titled 'The Revere Five Count Strategy.'
Practice
Practice your card counting skills with our trainer.
Acknowledgments
- Norm Wattenberger: For the simulation results, using his Casino Vérité software.
- Don Schlesinger: For his many edits to this page.
Written by: Michael Shackleford
Ace-seven is by far the most difficult hand for the professional blackjack player to handle. Depending on what the dealer is showing, you will either hit, stand, or double down.
Basic Strategy tells us that we should double if the dealer is showing 3 through 6, stand on 2, 7, and 8, and hit on 9, 10, and A. This may come as a shock to some since common sense tells us to stay with an 18 regardless of what the dealer has. Let's look at the math behind the strategy.
First, we must look at A-7 as a plain old 18. Basic Strategy dictates that we stand on a pat 18 regardless of what the dealer is showing; we want to get to 17 or higher and then let Lady Luck determine the outcome. This isn't necessarily the case for a soft 18.
- If the dealer is showing a 2, the return on an 18 is $.12 for each dollar invested.
- For 3 through 6, this jumps up ranging from $0.40 to $0.50 per dollar.
- 7 is also $0.40.
- At 8, it goes back down to $0.11.
- 9 through A plummets into a negative return of $0.18 to $0.10 loss per dollar.
So is it really worthwhile to go against the common sense factor and hit an 18 if the dealer is showing 9-A?
- Hitting A-7 on a dealers 9 gives us a negative return of $0.10,
- 10 a negative return of $0.14, and
- Ace a negative return of $0.09.
The spread here, while not seeming like much, is less than the -$0.18 to -$0.10 return of staying. To minimize the damage, hitting on these cards is a necessity.
Doubling is the third option with this hand. In this case, you count the hand as an 8 and pray for a 9 or 10, or you count it as an 18 and hope for an Ace through 3.
First of all, doubling when the dealer is showing:
- 9 through A gives us a -$0.29 to -$0.36 return, far greater of a loss than hitting. So doubling on those cards is out of the question.
- Doubling on 8 is also a negative return (-$0.03), whereas it's a positive return to hit. Again, out of the question.
- Doubling on 7 is a positive return of $0.22, which is less than the $0.40 you will get with staying. If the dealer is showing a 7, it makes economic sense to stand.
- Doubling on the dealer's 2 is also $0.12 return, but it is less than a cent less difference of a return than standing. In the long run, this adds up to major dollars, believe me. You will want to stay rather than risking the double in this case.
- That leaves 3 through 6. The math here gets tricky, so pay careful attention. The numbers above regarding standing on 18 don't take into account the power of the Ace. As you know, the Ace can be counted as either a 1 or an 11, and because of this, hitting on A-7 is not nearly as dangerous as hitting a pat 18. In fact, the 23% (3/13) chance of drawing a card to better your 18 makes the diminished return on doubling the right move.
While the return ranges from $0.18 to $0.38 (compared to the $0.40 to $0.50 of staying), the 23% odds of improving plus the doubled amount of money pumped into the hand make doubling the most profitable choice.
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