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Table of Contents

                    Copyright 1991, Michael Hall

—————→ Part 1: The Basics

                Part 2: About the Strategy Charts
                Part 3: Postscript Strategy Charts (LONG)

Help for the novice blackjack player

The basic idea of the game is to get a total less than 21 that is higher than the dealer OR to not bust (go over 21) when the dealer busts. With basic strategy, you reduce the house edge to about -.45% in Atlantic City (or -.40% where late surrender is offered); it is the *best* way to play, unless you are counting cards. All hands are dealt face up in Atlantic City; don't touch the cards. A "soft" total means you have an ace and can use it as 11 without going over 21; hard means you aren't counting an ace as 11 in your total.

Insurance is a side bet for up to half of your original bet. It can only be placed at the start of a round when the dealer has an ace showing. A basic strategy player should never take insurance. Insurance pays 2-1 only if the dealer has blackjack.

With early surrender, you can give up half your bet to avoid playing your first two cards; late surrender is the same, except you still lose you whole bet if the dealer has blackjack. To surrender, just say "surrender."

Splitting can be done only on your first two cards in Atlantic City. You push out a bet equal to your original, the dealer splits the cards apart and deals a card to the first one, which you play normally except that you can't resplit, and then the dealer deals a card to the second one, which again you play normally without resplitting.

Doubling can be done on any two cards. You push out a bet equal to your original, and you will receive exactly one more card.

Standing versus hitting is the most common and important decision. To hit you tap the table or draw your fingers towards you. Standing is indicated by a waving motion parallel to the table.

About Atlantic City

All Atlantic City casinos use the same rules, except when they get special permission from the Gaming Commission to try something else. Atlantic City rules are no resplitting, split aces get only one card each, double down allowed after split, dealer stands on soft 17, blackjack pays 3 to 2, insurance pays 2 to 1, and 4, 6, or 8 decks are used, but you will find only 8 decks for less than $25 minimums. Until recently the absolute lowest minimums were $5, but now the Taj Mahal offers $3 tables during the day on weekdays. Late surrender was found only at the Claridge until recently, when Trump Plaza announced that it is offering it too. It is unlikely that early surrender will ever be offered again, because the casinos lost so much money when it was offered that the Gaming Commission declared a state financial crisis (or some such) in order to get rid of it and protect this source of New Jersey tax revenue.

Help for the aspiring card counter

I recommend Stanford Wong's book, "Professional Blackjack" as a reference on the High-Low counting system; it is finally out as a paperback after 9 years of being a hardback. I also recommend Humble's "The World's Best Blackjack Book", which focuses on the Hi-Opt I counting system but which has lots of general information that any card counter should know, though the authors of this book are a little too paranoid about getting cheated. Hi-Opt I and High-Low counts are very similar, but I feel that High-Low is marginally better for most players. More advanced counts do exist (using more numbers than -1, 0, and +1), but they offer very little theoretical gain coupled with an increased chance for errors. Most professional card counters use High-Low or Hi-Opt I. An additional reference containing useful tables of information is "Fundamentals of Blackjack" by Chambliss & Rogenski. For example, they give a table that shows the effects of various rules on basic strategy expectation for 1, 2, 4, 6, or 8 decks.

Here is how you do the High-Low count. Initialize running count to zero at start. Add one for each 2, 3, 4, 5, or 6 you see and subtract one for each 10 or Ace you see. Divide running count by estimated number of unseen decks to get true count used in the strategy adjustment table. The strategy adjustment table is just a minor refinement; you get most of the benefit of counting from bet size variation, and you should do fine if you avoid strategy adjustments at first.

The Kelly Criterion is a betting heuristic that minimizes your chance of going broke while maximizing your long-run profits, and for Atlantic City, this heuristic dictates that you should bet approximately (TC*0.5 - 0.5)*.0077*BR, where TC is the True Count and BR is your BankRoll (i.e., how much money you've got on you.)

On games with large numbers of decks, it is absolutely imperative that you abandon the table when the count goes negative. How negative? That's a personal decision and depends on your betting spread (difference between your lowest bet and your highest), but I would advise leaving eight deckers when the count hits -1.

You should only take insurance if the TC is above +3 (more precisely, +2.8 for four decks, +3.0 for six decks, and +3.1 for eight decks). Don't be swayed by what cards you have (i.e., don't fall into the insure-your-blackjack trap); it's a side bet, so only the count matters.

The maximum edge that most card counters claim to attain in practice is about 1.5%. In Atlantic City, you will need about a 1-8 spread (i.e., highest bet is eight times your lowest) to grind out any profit at all. My simulations show a .5% advantage (ratio of winnings to total amount bet) for a 1-8 betting spread, 7 players, -1 to +10 strategy adjustments, and abandoning counts of -1 or worse. If late surrender is available, the edge improves to .66%.

As far as risk goes, a 500 unit bankroll (e.g. $2500 for $5 minimums) has a 81.5% chance of doubling before going broke. If late surrender is available, this improves to 89.3%. You are risking quite a bit to win how much? 0.9 units is the average win per 100 hands; 1.3 units with late surrender. So you could make about $5 an hour or so if you are willing to have more than a 10% chance of losing $2500 before doubling it.

If you want to make money at blackjack, either join a blackjack team or play the single or double deckers in Vegas.

                    Copyright 1991, Michael Hall
                Part 1: The Basics

—————→ Part 2: About the Strategy Charts

                Part 3: Postscript Strategy Charts (LONG)


This article describes basic and High-Low strategy tables for Atlantic City rules with four or more decks. The strategy information was taken from Stanford Wong's book, "Professional Blackjack". The tables tell you the mathematically best play given a certain circumstance - whether to surrender, split, double-down, hit, or stand.


I made these tables for myself, because I was unsatisfied with any I could find in published books. I am very satisfied with the result, so I thought I would share it with y'all. You may wish to modify the tables for your particular situation (different counting system, different casino rules, etc.) If so, you'll need to get the troff source from me, or else you can use the "Do Your Own Strategy" blank chart that is included.


I do not guarantee that these tables are correct. If you find any mistakes, or have any suggestions, please let me know, and I will repost if necessary. Also, note that Wong computed his numbers for 4 decks, and he assumes 4 decks = 6 decks = 8 decks for purposes of strategy adjustments. If anyone has High-Low strategy numbers that have *proved* to be more accurate for 6 or 8 decks, then let me know.

How to print the tables

In a subsequent article, you'll find the Postscript gobble-dee-gook that hopefully can be understood by your printer. However, it's uuencoded and compressed. Save the article to a file. "uudecode" the file. "uncompress" the resulting file, ("uudecode" and "uncompress" are UNIX programs that you hopefully have. There is no need to strip out the article header before running uudecode. If everything works, then you should wind up with a file named that has "%!PS-Adobe-1.0" as its first line.) Send to a printer that understands Postscript. (This includes the popular Apple Laserwriter II printer and many others.) There will be a few semi-blank pages, because the original text formatter, troff, is brain-damaged. What you want are the pages with the tables for "High-Low", "Basic Strategy", and "Do Your Own Strategy".

How to use the Do Your Own Strategy table

Use the Do Your Own Strategy table for memory recall practice or to devise a table with a different set of strategy adjustment numbers, perhaps for a counting system other than High-Low.

How to read the Basic Strategy table

Cross index your hand with the dealer's face-up card. If there is an "X", it means "yes, do the corresponding decision" - conversely, a blank means "no, *don't* do the corresponding decision." Read from the bottom up. First see if you should surrender (if this option is available), then split, then double, then stand. If nothing applies, then hit.

For example, suppose you have two 8's, and the dealer has a 10 showing. If you are playing at the Claridge (or Trump Plaza), you first see if you should late surrender, but cross indexing 8-8 with 10 under late surrender shows that you should not. You then check splitting - the table shows that you always split 8's, since there are X's all the way across. However, if you split 8's and get another hand of 8's, then you cannot resplit. You then look up to see if you should double - of course not - and then you look up to see if you should stand; 8-8 versus 10 is blank, so you don't stand and instead you take a hit.

How to read the High-Low Strategy table

Cross index as with the basic strategy table. Follow the basic strategy, except in these cases:

1) If there is a positive number in the box and the true count is greater

 than it, it means "override basic strategy, so yes, do the corresponding

2) If there is a negative number in the box and the true count is lower

 than it means "override basic strategy, so no, *don't* do the corresponding

To conform to the above and to avoid confusion, zeros are noted as positive or negative. The somewhat counterintuitive use of a "Stand" decision as opposed to a "Hit" decision is again to conform to the above and to avoid confusion in the long run.

This all sounds complicated, but it's simple once you get used to it.

For example, using the previous example, you would deviate from basic strategy and surrender 8-8 against 10 if the running count were positive (greater than +0). You would always split 8's, but you would deviate from basic strategy and stand on hard 16 when the running count were positive.

How to highlight the High-Low Strategy table

I highly recommended that you use a highlighting pen to indicate basic strategy on the High-Low Strategy tables. Overlay your High-Low printed page on top of your Basic Strategy page. Press down so you can the X's through the High-Low page. Highlight everywhere an X shows through. Note that there is a basic strategy X everywhere there is a negative High-Low Strategy number, and there is a basic strategy blank everywhere there is a positive High-Low Strategy number (this would not be true for some ranges of counts larger than -1 to +6.)

Still confused?

You can send e-mail to if you have any questions on these charts.

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