• Appendices
• Miscellaneous
• External Links

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Introduction

The Hi-Lo Count is the most widely written about, and in my judgment, the most commonly used card counting strategy. The High-Low was first introduced in 1963 by Harvey Dubner¹. It has since been discussed by just about all the major blackjack writers. In my opinion, the best introductory treatment is in Professional Blackjack by Stanford Wong, and the most detailed coverage is in Blackjack Attack by Don Schlesinger.

How it Works

Following is a brief explanation of how to use the Hi-Lo.

Step 1: Assign a point value to each rank, as follows.

Step 2: Start with a 'Running Count' of zero at the start of the deck/shoe. As cards are revealed, keep adding or subtracting from the Running Count, according to the point system in step 1. For example, if the first ten cards to come out of the shoe were 3, 5, K, 7, Q, A, 8, 5, 4, 2, then the running count would be 1 +1 -1 +0 -1 -1 +0 +1 +1 +1 = +2.

Step 3: Divide the running count by the number of decks remaining, to get what is known as the 'True Count.' This is the part that beginning counters hate. You don?t need to be exact. A rough estimate will do, in my opinion. Let's look at example. The running count is +7 and there are about 4 decks left. The true count would be 7/4 = 1.75. Round that up to 2, to keep it simple. The more you play the more you will be comfortable eyeballing this adjustment, without doing any real division in your head. Usually the right play is obvious. In borderline cases only will you need to do this True Count conversion.

Step 4: The greater the true count, the more you should bet. This is where card counting becomes more art than science. Some blackjack books give rigid rules on how this should be done. However, the casino managers have read these books too, and the patterns recommended in earlier books now set off red flags. How you do this should depend on your own style, and how much heat you are getting. It helps avoid heat to keep the ratio of maximum bet to minimum bet to a limit, known as the ?Bet Spread.? Only increasing bets after a win, only decreasing after a loss, and staying the same after a push, makes play look more natural, but at a cost to profitability.

Step 5: For some hands, you will play according to the True Count and a table of 'Index Numbers,' rather than basic strategy. The greater the count, the more inclined you will be to stand, double, split, take insurance, and surrender. For example, the Index Number for a player 15 against a dealer 10 is +4. This means the player should stand if the True Count is +4 or higher, otherwise hit.

The following tables are known as the 'Illustrious 18' and 'Fab 4' respectively.² They appear in Blackjack Attack by Don Schlesinger, and are republished here with permission. These are the most important index numbers to remember. Knowing only these will give the counter 80% to 85% of the value of knowing every index number, based on a six-deck game. The difference is more in single and double-deck games. The lists are given in order of value. If you can?t memorize all of them, start at the top, and work your way down.

Illustrious 18

Order	Play	Index
1	Insurance	+3
2	16 Vs. 10	+0
3	15 Vs. 10	+4
4	10,10 Vs. 5	+5
5	10,10 Vs. 6	+4
6	10 Vs. 10	+4
7	12 Vs. 3	+2
8	12 Vs. 2	+3
9	11 Vs. A	+1
10	9 Vs. 2	+1
11	10 Vs. A	+4
12	9 Vs. 7	+3
13	16 Vs. 9	+5
14	13 Vs. 2	-1
15	12 Vs. 4	0
16	12 Vs. 5	-2
17	12 Vs. 6	-1
18	13 Vs. 3	-2

The player should stand/double/split if the True Count equals or exceeds the Index Number, otherwise hit. The player should take insurance if the True Count is +3 or greater.

Fab 4 Surrenders

Order	Play	Index
1	14 Vs. 10	+3
2	15 Vs. 10	+0
3	15 Vs. 9	+2
4	15 Vs. A	+1

The player should surrender if the True Count equals or exceeds the Index Number.

A full table of all index numbers can be found in Chapter 3, and Appendix A, of Professional Blackjack by Stanford Wong.

The next table shows some statistics using the High-Low. The blackjack rules this table is based are liberal Vegas shoe, as follows:

Six decks
Dealer stands on soft 17
Surrender allowed
Double after split allowed
Player may resplit to four hands, including aces

To avoid setting off red flags, the simulation increased the bet after a win only, decreased after a loss only, and always stayed the same after a push, except resetting to a minimum bet after a shuffle. The simulation rounded the remaining decks to the nearest half deck, otherwise playing perfectly.

High-Low Statistics

Spread	Penetration	Index Numbers	Player Adv.	Std. Dev.	Avg.Bet
1 to 5	4	I18+F4	0.157%	1.50	1.35
1 to 10	4	I18+F4	0.368%	2.04	1.57
1 to 15	4	I18+F4	0.578%	2.67	1.73
1 to 5	4.5	I18+F4	0.300%	1.60	1.41
1 to 10	4.5	I18+F4	0.587%	2.27	1.68
1 to 15	4.5	I18+F4	0.834%	3.06	1.90
1 to 5	5	I18+F4	0.469%	1.70	1.47
1 to 10	5	I18+F4	0.837%	2.52	1.80
1 to 15	5	I18+F4	1.147%	3.49	2.10
1 to 5	4.5	All	0.313%	1.61	1.41
1 to 10	4.5	All	0.608%	2.29	1.68
1 to 15	4.5	All	0.862%	3.10	1.91
1 to 5	5	All	0.494%	1.71	1.47
1 to 10	5	All	0.857%	2.55	1.81
1 to 15	5	All	1.182%	3.54	2.11

Explantion of columns

Spread: This is the ratio of the player?s minimum bet to maximum bet. The bigger the range, the greater the player?s advantage, and bankroll volatility. A wide bet spread also sets off a red flag. In a six-deck game, I think a 1 to 15 spread is about the most aggressive the player should get. The simulation played one betting spot only.

Penetration: How many decks played before reaching the cut card. In a six-deck shoe, 4.5 is the norm.

Index Numbers: I already explained index numbers above. Simulations were run using both the Illustrious 18 and Fab 4 (I18+F4) above, and with the full table. The difference is not much, which shows that knowing the top 22 gets you most of the benefit of knowing all of them.

Player Advantage: This is the ratio of net player win to total initial bets. For example, in the last row, the player could expect to win 1.182% of his total initial bets.

Standard Deviation: This is a term for the volatility per initial bet.

Average Bet: The average final bet per hand, compared to the lowest bet For example, in the last row, if the player?s minimum bet were $100, his average bet would be $211. This includes additional money bet due to doubles and splits.

This table was created using CVCX Blackjack Analyzer by Casino Vérité. This software produces hundreds of different statistics for just about any set of rules, betting strategies, and playing strategies. For the player who wants to run these tests, this software is the best there is, in my opinion.

Footnotes

Blackjack Forum Info Free

1. Professional Blackjack by Stanford Wong, page 31, 1994 ed.
2. Blackjack Attack by Don Schlesinger, page 62, 2004 ed.

Acknowledgments

Don Schlesinger: For his permission to reprint the Illustrious 18 and Fab 4 tables from his book, Blackjack Attack.
Norman Wattenberger: For his complimentary use of CVCX Blackjack Analyzer by Casino Vérité.

Practice

Practice your card counting skills with our trainer.

Further Reading

• Card Counting Introduction.
• Wizard Ace-Five Count: Very easy and simple card counting strategy.
• '21' Movie Review: Truth and fiction about the movie about the MIT card counting team.
• Blackjack book reviews.
• Main blackjack page.

Written by:Michael Shackleford

• Appendices
• Miscellaneous
• External Links

Rules

I overhear a lot of bad gambling advice in the casinos. Perhaps the most frequent is this one, 'The object of blackjack is to get as close to 21 as possible, without going over.' No! The object of blackjack is to beat the dealer. To beat the dealer the player must first not bust (go over 21) and second either outscore the dealer or have the dealer bust. Here are the full rules of the game.

1. Blackjack may be played with one to eight decks of 52-card decks.
2. Aces may be counted as 1 or 11 points, 2 to 9 according to pip value, and tens and face cards count as ten points.
3. The value of a hand is the sum of the point values of the individual cards. Except, a 'blackjack' is the highest hand, consisting of an ace and any 10-point card, and it outranks all other 21-point hands.
4. After the players have bet, the dealer will give two cards to each player and two cards to himself. One of the dealer cards is dealt face up. The facedown card is called the 'hole card.'
5. If the dealer has an ace showing, he will offer a side bet called 'insurance.' This side wager pays 2 to 1 if the dealer's hole card is any 10-point card. Insurance wagers are optional and may not exceed half the original wager.
6. If the dealer has a ten or an ace showing (after offering insurance with an ace showing), then he will peek at his facedown card to see if he has a blackjack. If he does, then he will turn it over immediately.
7. If the dealer does have a blackjack, then all wagers (except insurance) will lose, unless the player also has a blackjack, which will result in a push. The dealer will resolve insurance wagers at this time.
8. Play begins with the player to the dealer's left. The following are the choices available to the player:
   • Stand: Player stands pat with his cards.
   • Hit: Player draws another card (and more if he wishes). If this card causes the player's total points to exceed 21 (known as 'breaking' or 'busting') then he loses.
   • Double: Player doubles his bet and gets one, and only one, more card.
   • Split: If the player has a pair, or any two 10-point cards, then he may double his bet and separate his cards into two individual hands. The dealer will automatically give each card a second card. Then, the player may hit, stand, or double normally. However, when splitting aces, each ace gets only one card. Sometimes doubling after splitting is not allowed. If the player gets a ten and ace after splitting, then it counts as 21 points, not a blackjack. Usually the player may keep re-splitting up to a total of four hands. Sometimes re-splitting aces is not allowed.
   • Surrender: The player forfeits half his wager, keeping the other half, and does not play out his hand. This option is only available on the initial two cards, and depending on casino rules, sometimes it is not allowed at all.
9. After each player has had his turn, the dealer will turn over his hole card. If the dealer has 16 or less, then he will draw another card. A special situation is when the dealer has an ace and any number of cards totaling six points (known as a 'soft 17'). At some tables, the dealer will also hit a soft 17.
10. If the dealer goes over 21 points, then any player who didn't already bust will win.
11. If the dealer does not bust, then the higher point total between the player and dealer will win.
12. Winning wagers pay even money, except a winning player blackjack usually pays 3 to 2. Some casinos have been short-paying blackjacks, which is a rule strongly in the casino's favor.

Wizard's Simple Strategy

I've been preaching for years that to play blackjack properly requires memorizing the basic strategy. However, after pitching the basic strategy for 20 years, I've learned that few people have the will to memorize it. In my book, Gambling 102, I presented a 'Simple Strategy,' which is seven simple rules to playing blackjack. The cost due to incorrect plays with the Simple Strategy is 0.53%, under liberal Vegas Strip rules.

Ever since my book was published it has bothered me that the cost in errors to my Simple Strategy was too high. So in September 2009 I developed the following 'Wizard's Strategy.' The cost due to imperfect plays is 0.14% only, relative to liberal Vegas Strip rules. That is the cost of one hand for about every 12 hours of play. Compared to the 250 cells in the Basic Strategy, the Wizard's Strategy has only 21, as follows.

Let me be perfectly clear that this strategy is not right 100% of the time. I continue to get Emails saying that when this strategy was used with my practice game, the player was corrected for following it. For example, my simple strategy says to stand on 12 against a 2, when it is mathematically better to hit. If you want to learn a strategy that is correct all the time you should use the appropriate basic strategy for the set of rules you are playing.

Here are some comments of clarification.

• A 'hard' hand is one that either has no aces, or has aces that are forced to count as point, lest the hand bust. A 'soft' hand is one with at least one ace, which may still count as one or eleven points.
• With a hard 10 or 11, double if you have more points than the dealer, treating a dealer ace as 11 points. Specifically, double with 10 against a 2 to 9, and with 11 against 2 to 10.
• If the strategy says to double, but you have three or more cards, or table rules don't allow soft doubling, then hit, except stand with a soft 18.
• If the strategy says to surrender (16 vs. 10), but you can't for whatever reason, then hit.
• If the strategy says to 'not split,' then treat the hand has a hard total of 8, 10, or 20, according to the pair in question.

A reader named Jeff provided another table of my simple strategy, with exceptions in small print. Details about the Wizard's Simple Strategy can be found in my Blackjack appendix 21.

Basic Strategy

For the appropriate basic strategy for just about any set of rules, please visit my basic strategy calculator. I still have my traditional charts too:

House Edge

See my Blackjack House Edge Calculator to determine the house edge under 6,912 possible rule combinations.

Blackjack Forum Online

Rule Surveys

Las Vegas: I'm proud to feature up date blackjack rules for every casino in Las Vegas. The list is updated monthly, based on Stanford Wong's Current Blackjack Newsletter. Effective November 2009 the survey has been moved to my companion site, WizardOfVegas.com.

Rule Variations

Following is a list of some common rule variations and the effect on the player's expected return compared to standard U.S. rules (8 decks, dealer stands on soft 17, double after split allowed).

Rule Variations

Rule	Effect
Single deck	0.48%
Early surrender against ten	0.24%
Player may double on any number of cards	0.23%
Double deck	0.19%
Player may draw to split aces	0.19%
Six-card Charlie	0.16%
Player may resplit aces	0.08%
Late surrender	0.08%
Four decks	0.06%
Five decks	0.03%
Six decks	0.02%
Split to only 3 hands	-0.01%
Player may double on 9-11 only	-0.09%
Split to only 2 hands	-0.10%
European no hole card	-0.11%
Player may not double after splitting	-0.14%
Player may double on 10,11 only	-0.18%
Dealer hits on soft 17	-0.22%
Blackjack pays 7-5	-0.45%
Blackjack pays 6-5	-1.39%
Blackjacks pay 1 to 1	-2.27%

I also have a longer list of rule variations.

Beware Short Pays on a Blackjack

More and more tables are showing up that pay less than the full 3 to 2 on a blackjack. Most of these tables pay 6 to 5, but some even money and 7 to 5 tables are known to exist. I would estimate that 10% of '21' tables in Las Vegas now pay less than 3 to 2. In my opinion, only games that pay 3 to 2 deserve to be called 'blackjack,' the rest fall under '21' games, including Super Fun 21 and Spanish 21. Regardless of the other rules, you should demand nothing less than 3 to 2 blackjack. You should always check the felt to be sure, and if the felt doesn't say, look for a sign. If nothing says the win on a blackjack, then ask.

Articles about 6-5 Blackjack:

• Taking a hit: New blackjack odds further tilt advantage toward the house, Las Vegas Sun, Nov. 13, 2003.
• Tighter blackjack rules would hurt players' bankroll, Pittsburgh Tribune-Review, Feb. 4, 2011.

Bad Strategies

Three popular bad strategies encountered at the blackjack table are: never bust, mimic the dealer, and always assume the dealer has a ten in the hole. All three are very bad strategies. Following are my specific comments on each of them, including the house edge under Atlantic City rules (dealer stands on soft 17, split up to 4 hands, double after split, double any two cards) of 0.43%.

Never bust: For my analysis of this strategy I assumed the player would never hit a hard 12 or more. All other decisions were according to correct basic strategy. This 'never bust' strategy results in a house edge of 3.91%.

Mimic the dealer: For my analysis of this strategy I assumed the player would always hit 16 or less and stand on17 or more, including a soft 17. The player never doubled or split, since the dealer is not allowed to do so. This 'mimic the dealer' strategy results in a house edge of 5.48%.

Assume a ten in the hole: For this strategy I first figured out the optimal basic strategy under this assumption. If the dealer had an ace up, then I reverted to proper basic strategy, because the dealer would have peeked for blackjack, making a 10 impossible. This 'assume a ten' strategy results in a house edge of 10.03%.

Play Blackjack

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Written by: Michael Shackleford