                  HOW TO BEAT SINGLE DECK BLACKJACK 
                           Version 1.01 
                     Copyright 1991, Michael Hall 
 
----------------> Part 1: The Basics 
                  Part 2: About the Strategy Charts 
                  Part 3: The Strategy Charts (LONG) 
 
 
 
Introduction 
============ 
Here is the long-awaited article on Hi-Opt I, covering everything 
from the rules of blackjack to basic strategy to card-counting to 
multiparameter tables for experts.  Novices should read this article. 
People interested in "just the facts" about the strategy should 
just read Part 2 and Part 3, in separate articles. 
 
 
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. 
 
All single deck games are dealt face down.  You receive the first 
two cards face down, and any subsequent cards face up.  Use one 
hand to hold the first two cards. Don't touch the others. 
 
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. An player who is not counting cards should never take insurance. 
Insurance pays 2-1 only if the dealer has blackjack. 
 
Splitting can be done 3 times, to produce up to 4 hands.  If you have 
a pair and wish to split them, put your cards face up in front of your 
bet, and 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, 
and then the dealer deals a card to the second one, which again you 
play normally. 
 
Doubling can be done on any two cards. First put your cards face up 
in front of your bet, and then push out a bet equal to your original, 
and you will receive exactly one more card. (If it is a pair, you 
may have to verbally tell the dealer whether you are doubling or 
splitting.) 
 
Standing versus hitting is the most common and important decision. To 
hit you scratch your held cards on the surface of the table.  Standing is 
indicated by pushing your cards under your bet.  When you split, 
you instead use the protocol for face-up games - hitting is indicated 
by tapping the table, and standing is indicated by a waving motion 
parallel to the table. 
 
Aces can be counted as either 1 or 11. 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. 
 
 
Basic Strategy 
============== 
You must first learn basic strategy, whether your goal is to become 
a professional card counter or just to survive a weekend at 
the blackjack tables. 
 
With basic strategy, you eliminate the house edge on most Las Vegas 
single deck games.  With the Frontier's special rules, you can get 
a +0.3% advantage with just basic strategy.  Basic strategy is the 
computer proven *best* way to play, unless you are counting cards. 
 
The basic strategy for typical single deck blackjack is given in 
another part of this article. 
 
 
About Nevada 
============ 
Single deck rules and conditions vary tremendously throughout Nevada. 
But yes, Virginia, single deck blackjack is alive and well. 
 
Vegas Strip rules are dealer stands on soft 17, double any first 
two cards, resplit up to 3 times, no doubling after splitting, 
and blackjack pays 3 to 2.  Proper basic strategy on this game 
makes it an even game.  Many casinos on the Vegas strip use 
these rules. 
 
Vegas Downtown rules are like Vegas Strip rules, except that the 
dealer hits soft 17.  This swings the odds slightly in the house's 
favor against the basic strategist.  Many casinos in downtown Vegas 
use these rules. 
 
Northern Nevada rules are like Vegas Downtown rules, except that 
doubling is restricted to totals of 10 and 11 only.  This really hurts 
the basic strategist. 
 
 
Advantage 
========= 
Advantage is your winnings divided by your action. Your action is 
the total amount of money you wager.  To find out how much of an 
advantage you have with basic strategy for a single deck game, 
use the table below.  Start with +0.02% for Vegas Strip rules, 
and then add the adjustments for rule differences for the game 
you wish to analyze. 
 
  %                RULE 
-----  --------------------------------- 
-0.78  Doubling on 11 only 
-0.26  Doubling on 10 and 11 only 
-0.21  No non-ace pair splitting 
-0.19  Dealer hits soft 17 
-0.16  No splitting of aces 
-0.13  Doubling on 9, 10, 11 only 
-0.11  No hole card (European) 
-0.02  No resplitting of non-ace pairs 
+0.03  Resplitting of aces 
+0.11  Six card automatic winner 
+0.13  Doubling after splitting (DAS) 
+0.14  Drawing to split aces 
+0.16? Suited BJ pays 2-1 
+0.24  Doubling on 3 or more cards 
 
 
Help for the aspiring card-counter 
================================== 
For single deck blackjack, I recommend a simple counting system card 
called Hi-Opt I.  Although it is one of the simplest systems to start 
with, it can be extended to be more powerful than nearly any other 
counting system - and you never have to forget what you have already 
learned. 
 
Here's an interesting table, drawn from "Theory of Blackjack" and elsewhere: 
 
                      PLAYING    BETTING             COUNT VALUES 
SYSTEM              EFFICIENCY CORRELATION   A  2  3  4  5  6  7  8  9 10 
Hi-Opt I               .615        .88       0  0 +1 +1 +1 +1  0  0  0 -1 
Hi-Opt I + A           .635        .96                    " 
Hi-Opt I + A,7         .736        .97                    " 
Hi-Opt I + A,7,8       .811        .97                    " 
Hi-Opt I + A,7,8,9     .870        .97                    " 
Hi-Opt I + A,7,8,9,2   .891        .98                    " 
 
High-Low               .51         .97      -1 +1 +1 +1 +1 +1  0  0  0 -1 
High-Low + A           .61?        .97                    " 
Hi-Opt II              .67         .91       0 +1 +1 +2 +2 +1 +1  0  0 -2 
Zen                    .63         .97      -1 +1 +1 +2 +2 +2 +1  0  0 -2  
Uston APC + A          .69         .91       0 +1 +2 +2 +3 +2 +2 +1 -1 -3 
 
(Side counted cards are listed after the "+" signs.) 
 
Playing efficiency is a measure of how good a counting system is 
a strategy, while betting correlation is a measure of how good it 
is at betting.  As you can see, Hi-Opt I + A,7 is better in both 
respects than of the listed competitor systems, and Hi-Opt I + A is as 
nearly as good as or better than most systems.  Even straight Hi-Opt I 
with no side count of aces is respectable. 
 
Here is how you do the Hi-Opt I count. Initialize "running count" to 
zero at start. Add one for each 3, 4, 5, or 6 you see and subtract 
one for each 10 you see. Divide running count by estimated number 
of unseen decks to get true count used in the strategy adjustment 
table. Note that for single deck, this division becomes a multiplication. 
For example, if there is 1/4 deck remaining and the running count is 
+2, then the true count is +8. 
 
You should only take insurance if the true count is +2 or above. 
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 Kelly Criterion is a betting heuristic that minimizes your chance 
of going broke while maximizing your long-run profits.  To bet 
consistently with the Kelly Criterion, you should divide your bankroll 
into 300-400 units and normally bet 1-4 units on each hand.  Your 
optimal bet on a hand is a percentage of your *current* bankroll 
equal to about .5R/D + B, where R is the running count, D is the number 
of remaining decks (so R/D is the true count), and B is the basic 
strategy expectation. Note that on a weekend trip you might not 
need access to your whole bankroll, but you may need 100-150 units. 
It is wise to limit your top bet to about 1/100 of your total bankroll, 
but you can get away with slightly more for very high true counts. 
Of course, if you understand the risks and are willing to accept 
higher risks by using fewer units, more power to you. 
 
Playing two hands at once is a often a good idea.  You can afford to bet 
around 30% more on two hands (combined) than on one hand, and 
so you will make more money per hour without increasing your variance. 
To play two hands, each bet must be twice the table minimum at 
most casinos.  Play the first hand before looking at the second, 
except when the dealer has an ace showing and you are permitted 
to look at both hands to decide if you want insurance. 
 
After you have mastered basic strategy and betting according to the 
count, you can bet more accurately if you keep a side count of aces. 
For each excess seen ace, temporarily subtract 1 from the running count 
- if there are excess remaining aces, add 1 to the running count. 
Then compute the true count for betting.  For example, suppose you 
have seen the first 1/4 deck, but have not seen any aces.  This 
means there is 1 excess remaining ace, since you normally expect 
to see one ace for every quarter deck (since there are four aces 
in a deck).  So, you would adjust the running count by +1 for betting 
purposes. 
 
Strategy adjustments are another improvement.  Here you deviate 
intelligently from basic strategy, according to the true count. 
The strategy adjustment table is given and explained in another part of 
this article. The strategy adjustment table is 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 
strategy adjustments will just buy you an extra 0.4% or so. 
The multiparameter strategy tables for side counts are a refinement on a 
refinement, and should only be attempted by counters with considerable 
experience with basic Hi-Opt I.  They'll buy you an extra 0.1% or so. 
 
Here is what a card counter looks at to rate a blackjack game, in rough 
order of their importance: 
 
  1. NUMBER OF DECKS.  The fewer the better. 
  2. PENETRATION.  The % of cards dealt before the shuffle is very important. 
     The number of spots being played can impact the penetration. 
  3. RULES.  A near zero or positive basic strategy expectation helps. 
  4. MINIMUMS/MAXIMUMS.  The game must be affordable and profitable, and 
     the player's betting should not be too much bigger than the minimum, 
     lest he attracts unwanted attention. 
  5. CONTENT DEALERS/PIT CRITTERS.  It helps if the employees are happy 
     in general and happy about your business too. 
 
The importance of playing single deck blackjack with good penetration 
cannot be overstressed.  Sneak some extra effective penetration 
by sitting towards third base if you are using strategy adjustments - 
your adjustments will be more accurate since they will be made after 
seeing more cards, raising your advantage significantly. 
 
The maximum edge that you'll hear knowledgable card counters claim to attain 
in practice is about 1.5%.  Around 0.9%-1.1% is more realistic, winning an 
average of about 1.5 units per 100 hands played.  Figure on getting in 
about 100 hands per hour, so that's 1.5 units per hour you'll make.  For 
typical blackjack games, a 1-4 betting spread is sufficient to beat 
the game with a good profit margin.  Even flat betting will produce 
a profit, though probably not enough for the average greedy card 
counter. If the game has poor penetration or poor rules and a better 
game cannot be found, then a betting spread larger than 1-4 will probably 
be necessary. 
 
As far as risk goes, the variance on a hand of blackjack with a 
1-4 spread is about 15.5.  The expected value will form a normal 
distribution, as shown on the next page.  Study these distributions 
to get a feel for the kind of negative negative swings you will 
experience, purely as a result of variance. 
 
The game simulated here is Vegas downtown rules, 3 rounds of 3 spots, 
with the counter at the last spot using Hi-Opt I, strategy adjustments 
-6 to +6, ace adjustment for betting, true count accurate to 
a quarter deck, 1-4 betting spread. 
 
  
 
 
 
              20,000 hands with 300 unit bankroll 
 
Player #3 
Average winnings:   291.90 (variance 15.547404) 
Average action:     31582.54 (variance 6.373246) 
Average worse loss: -105.47 (variance 31339.356156) 
Average advantage:  0.924258 +- 0.072904 % (variance 1.383540) 
Win/100 rounds:     1.51 
 
FINAL BANKROLL  DISTRIBUTION                                        CUM % 
=============== =================================================== ========== 
         BUSTED |*********************************************        7 
     1 -     50 |*                                                    7 
    51 -    100 |*                                                    7 
   101 -    150 |*******                                              8 
   151 -    200 |*************                                       10 
   201 -    250 |*************                                       12  LOSS 
   251 -    300 |*********************                               16________ 
   301 -    350 |************************                            19 PROFIT 
   351 -    400 |*************************                           23 
   401 -    450 |*****************************************           30 
   451 -    500 |************************************                35 
   501 -    550 |**************************************************  43 
   551 -    600 |***********************************************     50 --MEAN 
   601 -    650 |*****************************************           57 
   651 -    700 |******************************************          63 
   701 -    750 |*******************************************         70 
   751 -    800 |****************************************            77 
   801 -    850 |*************************************               82 
   851 -    900 |*****************************                       87 
   901 -    950 |***********************                             90 
   951 -   1000 |*************                                       92 
  1001 -   1050 |***********                                         94 
  1051 -   1100 |************                                        96 
  1101 -   1150 |********                                            97 
  1151 -   1200 |******                                              98 
  1201+         |************                                       100 
 
Initial bankroll:    300.00 
Mean final bankroll: 591.90 
 
  
In a day or two, a player might get in 2,000 hands.  With an 80 unit 
bankroll, the results are shown below: 
 
               2,000 hands with 80 unit bankroll 
 
Player #3 
Average winnings:   29.71 (variance 15.577170) 
Average action:     2860.31 (variance 6.363973) 
Average worse loss: -44.59 (variance 3387.431404) 
Average advantage:  1.038872 +- 0.317410 % (variance 26.225822) 
Win/100 rounds:     1.70 
 
FINAL BANKROLL  DISTRIBUTION                                        CUM % 
=============== =================================================== ========== 
         BUSTED |**************************************************  24 
     1 -     13 |*                                                   25 
    14 -     27 |***                                                 26 
    28 -     40 |****                                                28 
    41 -     53 |******                                              31 
    54 -     67 |*******                                             35 LOSS 
    68 -     80 |**********                                          40_______ 
    81 -     93 |*********                                           44 PROFIT 
    94 -    107 |***********                                         50 --MEAN 
   108 -    120 |***********                                         55  
   121 -    133 |*******                                             59 
   134 -    147 |***********                                         64 
   148 -    160 |***********                                         70 
   161 -    173 |*********                                           74 
   174 -    187 |*********                                           78 
   188 -    200 |**********                                          83 
   201 -    213 |*****                                               86 
   214 -    227 |*******                                             89 
   228 -    240 |*******                                             92 
   241 -    253 |*****                                               95 
   254 -    267 |****                                                97 
   268 -    280 |**                                                  98 
   281 -    293 |**                                                  99 
   294 -    307 |*                                                   99 
   308 -    320 |*                                                  100 
   321+         |*                                                  100 
 
Initial bankroll:     80.00 
Mean final bankroll: 109.72 
 
Note: different scale than previous graph. 
  
Team Play 
========= 
If you have studied the above graphs, you may be getting depressed, 
given that the size of your bankroll may imply you will make below 
minimum wage.  Don't give up hopes of making money with blackjack 
yet.  The way to do it is to form a team. 
 
Several players can pool their bankrolls and bet as each had the 
whole bankroll.  If there are N players contributing equally, 
then they will each make N times as much together than they would 
individually.  Or they can make slightly less and reduce the 
variance significantly. 
 
There are also schemes of cooperative play at the same table, 
but it's usually best to have the players play at separate tables. 
 
 
Barring and Countermeasures 
=========================== 
Card counting is not illegal.  However, the casino can kick you 
out for whatever reason they choose.  If they read you the Trespass 
Act, *then* it will be illegal for you to return to the casino 
and they can have you arrested.  In extreme cases, casinos have 
been known to break the bones of card counters, but if you are 
playing for low stakes at a reputable casino, you shouldn't have 
any such physical problems. 
 
There are many things that a casino can do besides kick you out 
to make it not worth your while to stay.  They can shuffle the 
deck any time the cards favor you, which will cost you 1-2% in 
advantage, making the game unbeatable.  Even if they are not 
card counting, the dealer can simply shuffle any time a large 
bet is placed.  Or they can simply stop dealing deep into the 
deck altogether. 
 
When the pit critters (properly known as floor managers or sometimes 
a pit boss) are hanging around your table, eyeing you, looking 
through the discards or obviously card counting during play, 
telling the dealer to shuffle early, restricting your betting 
spread, etc. then this is called "heat". 
 
Since heat results in poor playing conditions and may preceed 
a barring, you should try to avoid it.  Don't look like you 
are counting cards!  Become good enough at card counting that 
you can simultaneously carry on a conversation. Talk to the 
other players, the dealer, and the pit critters. Mix up your 
betting pattern.  Don't always bet the same at the top of 
the deck.  Limit your betting spread, as spreads wider 
than 1-4 are usually not necessary to have a good advantage 
and wider spreads will usually not be tolerated by the pit 
critters.  You can make an okay profit with even a 1-2 spread, 
though 1-4 should be your goal.  Use a lot of different colors of 
chips, representing different dollar amounts, so that a pit critter 
cannot at a glance figure out whether you raised or lowered your 
bet from the previous hand.  Try switching back between 1 and 
2 hands to range your bet that way, unless this causes heat 
itself. 
 
Many casinos like for you to "color up" when you leave.  This 
means to exchange your chips for ones of higher denominations, 
making it easier for you to carry, and trivial for the pit critters 
to count.  It's a good idea to leave a table with no chips, if possible. 
You can accomplish this without losing by *discretely* squirreling chips 
into yourclothes during play.  Even if you can't get rid of all your chips, 
your coloring up will be less embarassing.  If you run out of chips 
on the table before you're ready to go, pull out more cash.  Make 
sure you do color up if you leave with only a few chips on the 
table - you want them to know that you took a "loss". 
 
If you have been squirreling chips, then be discrete about cashing 
them in.  Only cash in initially what you had showing on the table. 
Come back later to cash in the rest, or try to get rid of the chips 
at another casino. 
 
 
Comps 
===== 
You can generate extra low variance income via "comps" - complimentary 
rooms, food, and other hotel services.  Four hours of betting $25 
minimums is enough to get a free room at most casinos in Vegas. 
Lower levels of betting will get you a free meel.  Even higher levels 
of betting will prompt the casino to comp *everything* - room, 
food, and even your plane tickets. 
 
To be eligible for comps, just ask a floor manager to "rate" your 
play.  He will record your buy-in, betting level, and color-out 
(chips you take with you.)  After you have played for a while, 
ask a floor manager or the pit boss for a meal or whatever. 
 
This is a great way to reduce expenses and hence essentially get 
some guarenteed income.  Unfortunately, it's also a great way to 
get nailed by the casinos, since you'll be in their computers, 
and it will take just one pit critter comment "card counter" 
appended to your record to ruin your play there until they 
forget your face and you use a new name. 
 
 
Further reading for the aspiring card counter 
============================================= 
Although this article gives you enough information to make money off 
the casinos, I recommend purchasing at least two of these three books: 
 
    "Blackbelt in Blackjack" by Snyder 
    "Fundamentals of Blackjack" by Chambliss and Rogenski 
    "The World's Greatest Blackjack Book" by Humble & Cooper 
 
These are available from the Gambler's Book Club in Las Vegas, 
(800) 634-6243.  You have a decent shot at finding the last book 
in your local book store. 
 
"Blackbelt in Blackjack" has a couple of good counting systems, 
Red 7's and Zen.  In addition, Snyder gives many good suggestions 
for achieving an advantage in single deck blackjack without looking 
like a typical counter. 
 
"Fundamentals of Blackjack" is a new book with lots of useful tables. 
The counting system (C&R count) is not recommended, however. 
 
"The World's Best Blackjack Book" focuses on the Hi-Opt I 
counting system that I advocate.  It 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. 
 
Good luck and on to the tables! The strategy tables, that is.  See 
the next two articles. 
  
                  HOW TO BEAT SINGLE DECK BLACKJACK 
                           Version 1.01 
                     Copyright 1991, Michael Hall 
 
                  Part 1: The Basics 
----------------> Part 2: About the Strategy Charts 
                  Part 3: The Strategy Charts (LONG) 
 
 
 
Description 
=========== 
This article describes basic strategy and Hi-Opt I strategy tables 
for single deck blackjack, Vegas Strip rules.  The strategy information 
was compiled from a variety of sources, including "The World's 
Greatest Blackjack Book", Steve Markowitz's analytic strategy adjustment 
program, and my empirical strategy adjustment program. 
 
 
Caveats 
======= 
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. 
 
 
How to read the Basic Strategy table 
==================================== 
Cross index your hand with the dealer's face-up card. If there is 
something other than "...", it means "yes, do the corresponding decision" 
- conversely, a "..." means "no, *don't* do the corresponding decision." 
Read from the bottom up. First see if you should split ("spl"), then double 
("dbl"), then stand ("sta"). If nothing applies, then hit.  
 
For example, suppose you have two 8's, and the dealer has a 10 
showing. You first check splitting - the table shows that you always 
split 8's, since it has an "spl" for every dealer up card.  As 
another example, if you Ace-7 vs. Ace, you first check to see if you double. 
There is a "..." there, so you don't double, and so you check to see if 
you should "soft hit" it.  Ace-7 is soft 18, which when cross-refenced 
with the dealer's ace has a "sta", indicating you should stand on versus ace. 
 
 
How to read the Hi-Opt I Strategy table 
======================================= 
Cross index as with the basic strategy table. Follow the basic 
strategy, except possibly when there is a number there. If there 
is a number and the true count is greater than or equal to it, 
it means yes, do the corresponding action.  Exception: when there 
is an asterisk (*) after the number it means just the opposite - 
do the decision only when the true count that number or below. 
 
For example, using the previous example, you would deviate from basic 
strategy and hit soft 18 vs. Ace if the true count were below 
zero, since there is a 0 in that box.  For counts of zero and above, 
you would stand.  Note that the strategy with a count of zero is 
not always the same as basic strategy - use the strategy adjustments 
in preference to basic strategy.  As another example, suppose 
you have 8-8 vs. dealer 10 (no double after split).  The number there 
is "+5*", meaning that for true counts of 5 or less, you split, but 
for true counts of +6 or more, you would not split.  (Exercise for 
the reader: what play would you do in that case of a true count of +6?) 
 
Most of the numbers are rounded off to -20,-15,-10,-5,-1,0,+1,+5,+10,+15, 
or +20. In the September 1991 issue of Blackjack Forum, Arnold Snyder 
showed that such a simplication resulted in no measurable loss in 
performance.  However, I have included a finer granularity of numbers 
for hard standing, because my empirical results produced statistically 
significant settings of these adjustments to their exact values. 
Whether this will make a statistically difference in the overall results 
of a few million hands, I rather doubt, but since it definitely makes 
a difference in the results for these particular hands, I can't bear 
to throw away that gain.  If you wish, you may round the rest 
of the numbers off the multiples of 5 (or +1/-1) to make things easier. 
 
Learn the adjustments gradually, starting with 0, then adding +1, then 
-1, then +5, and so on.  The most important adjustments are the ones for 
hard standing and doubling.  You can and probably should completely ignore 
the ones for splitting, except for the hand 10-10. 
 
 
How to read the side count strategy tables 
========================================== 
The side count tables are for experts only.  They are memorized in 
addition to the normal Hi-Opt I strategy adjustment table. The best 
order to learn the side counts is given in the first part of the 
article in the table that compares the various card counting systems. 
First learn to side count aces, then add 7's and other side counts as you 
becomes a grandmaster of blackjack. 
 
As far as I know, this article is the only place you can easily 
multiparameter Hi-Opt I in its full glory.  No book I've seen gives 
Hi-Opt I strategy adjustments outside of -6 to +6, and no book 
gives multiparameter adjustments for anything other than aces. 
(Currently just aces and 7's are here, but I'll add the other cards 
in later editions of this article.) 
 
You find the side count strategy adjustment number the same way you find 
the Hi-Opt I strategy adjustment number, by cross-indexing on the 
appropriate table. 
 
For strategy, you adjust the running count by the number of excess seen 
cards for the side count times the side count strategy adjustment number. 
 
As an example of how to use the side count adjustment number, suppose 
you are side-counting 7's and are faced with 14 vs. 10 and a running 
count of -1 at the 1/2 deck level.  The Hi-Opt I strategy adjustment 
number for standing hard 14 vs. 10 is +15, and the seven adjustment 
number for this play is +5.  Suppose you have seen all four 7's 
remaining at the 1/2 deck level, meaning that there are two excess 
7's removed from the deck.  For strategy, you then must adjust the 
*running* count, not the true count, and not the strategy adjustment 
number.  From the running count, you *subtract* the number of excess 
*remaining* 7's times the 7-adjustment index (or *add* the number of 
excess *seen* 7's times the 7-adjustment index.) In this case 
that's -1 + 2*(+5) = +9.  You then convert to true count by dividing 
by the number of remaining decks (1/2), yielding +9/(1/2) = 9*2 = +18, 
which is the true count you would compare to the normal Hi-Opt I strategy 
adjustment number of +15.  Since +18 is more than +15, you would 
stand.  Imagine that, standing on hard 14 vs. 10 with a negative Hi-Opt I 
count! 
 
Let R be the running count, 
    X be the number of excess seen side count cards times the adjustment number 
    N be the number of remaining decks 
 
Then the adjusted count for strategy is: 
 
    R+X 
    --- 
     N  
 
If you are good enough to keep several side counts for strategy, 
then X will be the sum of all these adjustments. 
 
 
Confused? 
========= 
You can send e-mail to hall@rocky.bellcore.com if you have any 
questions on these charts. 
  
                  HOW TO BEAT SINGLE DECK BLACKJACK 
                           Version 1.01 
                     Copyright 1991, Michael Hall 
 
                  Part 1: The Basics 
                  Part 2: About the Strategy Charts 
----------------> Part 3: The Strategy Charts (LONG) 
 
 
What follows are several tables for single deck blackjack and 
multi-parameter Hi-Opt I. 
 
   * Basic Strategy for Single Deck 
   * Hi-Opt I Blackjack Count Strategy Adjustments 
   * Hi-Opt I Ace Side Count Strategy Adjustments 
   * Hi-Opt I Seven Side Count Strategy Adjustments 
  
                          Basic Strategy for Single Deck 
 
 
 
 
 
 
 
                            Hard Hit/Stand Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Hard 18+       sta   sta   sta   sta   sta   sta   sta   sta   sta   sta    
   Hard 17        sta   sta   sta   sta   sta   sta   sta   sta   sta   sta 
   Hard 16        sta   sta   sta   sta   sta   ...   ...   ...   ...   ... 
   Hard 15        sta   sta   sta   sta   sta   ...   ...   ...   ...   ... 
   Hard 14        sta   sta   sta   sta   sta   ...   ...   ...   ...   ... 
   Hard 13        sta   sta   sta   sta   sta   ...   ...   ...   ...   ... 
   Hard 12        ...   ...   sta   sta   sta   ...   ...   ...   ...   ... 
 
 
                            Soft Hit/Stand Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Soft 19+       sta   sta   sta   sta   sta   sta   sta   sta   sta   sta    
   Soft 18        sta   sta   sta   sta   sta   sta   sta   ...   ...   sta    
   Soft 17-       ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
 
 
                           Hard Double Down Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Hard 11        dbl   dbl   dbl   dbl   dbl   dbl   dbl   dbl   dbl   dbl 
   Hard 10        dbl   dbl   dbl   dbl   dbl   dbl   dbl   dbl   ...   ... 
   Hard  9        dbl   dbl   dbl   dbl   dbl   ...   ...   ...   ...   ... 
   Hard  8        ...   ...   ...   dbl   dbl   ...   ...   ...   ...   ... 
   Hard  7        ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
   Hard  6        ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
   Hard  5        ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
   Hard  4        ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
 
 
                           Soft Double Down Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
        A9        ...   ...   ...   ...   ...   ...   ...   ...   ...   ... 
        A8        ...   ...   ...   ...   dbl   ...   ...   ...   ...   ... 
        A7        ...   dbl   dbl   dbl   dbl   ...   ...   ...   ...   ... 
        A6        dbl   dbl   dbl   dbl   dbl   ...   ...   ...   ...   ... 
        A5        ...   ...   dbl   dbl   dbl   ...   ...   ...   ...   ... 
        A4        ...   ...   dbl   dbl   dbl   ...   ...   ...   ...   ... 
        A3        ...   ...   dbl   dbl   dbl   ...   ...   ...   ...   ... 
        A2        ...   ...   dbl   dbl   dbl   ...   ...   ...   ...   ... 
  
                          Basic Strategy for Single Deck 
 
 
 
 
 
 
 
                           Pair Split Strategy (non-DAS) 
 
                                Dealer's Upcard 
 
Player's Pair      2     3     4     5     6     7     8     9    10    Ace 
 
   Ace,Ace        spl   spl   spl   spl   spl   spl   spl   spl   spl   spl 
    10,10         ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     9,9          spl   spl   spl   spl   spl   ...   spl   spl   ...   ... 
     8,8          spl   spl   spl   spl   spl   spl   spl   spl   spl   spl    
     7,7          spl   spl   spl   spl   spl   spl   ...   ...   ...   ...    
     6,6          spl   spl   spl   spl   spl   ...   ...   ...   ...   ... 
     5,5          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     4,4          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     3,3          ...   ...   spl   spl   spl   spl 
     2,2          ...   spl   spl   spl   spl   spl   ...   ...   ...   ...    
 
 
 
                            Pair Split Strategy (DAS) 
 
                                Dealer's Upcard 
 
Player's Pair      2     3     4     5     6     7     8     9    10    Ace 
 
   Ace,Ace        spl   spl   spl   spl   spl   spl   spl   spl   spl   spl 
    10,10         ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     9,9          spl   spl   spl   spl   spl   ...   spl   spl   ...   ... 
     8,8          spl   spl   spl   spl   spl   spl   spl   spl   spl   spl    
     7,7          spl   spl   spl   spl   spl   spl   spl   ...   ...   ...    
     6,6          spl   spl   spl   spl   spl   spl   ...   ...   ...   ...    
     5,5          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     4,4          ...   ...   spl   spl   spl   ...   ...   ...   ...   ...    
     3,3          spl   spl   spl   spl   spl   spl   spl   ...   ...   ...    
     2,2          spl   spl   spl   spl   spl   spl   ...   ...   ...   ...    
 
 
 
Take insurance: Never (unless card counting) 
  
                 Hi-Opt I Blackjack Count Strategy Adjustments 
 
                Cards:    2   3   4   5   6   7   8   9  10 Ace 
                Values:   0   1   1   1   1   0   0   0  -1   0 
 
                     1 deck, dealer stands on soft 17 
 
 
                            Hard Hit/Stand Strategy  (-20 to +20) 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Hard 18+       sta   sta   sta   sta   sta   sta   sta   sta   sta   sta    
   Hard 17        -20   -20   sta   -20   sta   -20   -15   -15   -20    -6    
   Hard 16         -7    -7    -9   -10   -10   +10   +10    +6    +2    +7    
   Hard 15         -5    -5    -5    -8    -8   +10   +10    +6    +3    +8    
   Hard 14         -3    -3    -5    -5    -5   +10   +20   ...   +13   +10    
   Hard 13          0     0    -1    -4    -4   ...   ...   ...   ...   +15    
   Hard 12         +3    +3    +1    -1    +1   ...   ...   ...   ...   ...    
 
 
                            Soft Hit/Stand Strategy (-5 to +5) 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Soft 19+       sta   sta   sta   sta   sta   sta   sta   sta   sta   sta    
   Soft 18        sta   sta   sta   sta   sta   sta   sta   ...   ...     0    
   Soft 17-       ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
 
 
                           Hard Double Down Strategy (-10 to +15) 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Hard 11        -10   -10   -10   -10   -10    -5    -5    -5    -5     0    
   Hard 10        -10   -10   -10   -10   -10    -5    -5    -1    +5    +5    
   Hard  9         +1     0     0    -5    -5    +5   +10   ...   ...   ...    
   Hard  8        +10   +10    +5    +5    +1   +15   ...   ...   ...   ...    
   Hard  7        ...   +15   +10   +10   +10   ...   ...   ...   ...   ...    
   Hard  6        ...   +15   +15   +10   +15   ...   ...   ...   ...   ...    
   Hard  5        ...   ...   +15   +10   +15   ...   ...   ...   ...   ...    
   Hard  4        ...   ...   +15   +15   +15   ...   ...   ...   ...   ...    
 
 
                           Soft Double Down Strategy (-10 to +15) 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
        A9        +10   +10    +5    +5    +5   +15   ...   ...   ...   ...    
        A8         +5    +5    +5    +1    +1   +15   ...   ...   ...   ...    
        A7         +1    -1    -5   -10   -10   +15   ...   ...   ...   ...    
        A6         +1    -1    -5   -10   -10   +10   ...   ...   ...   ...    
        A5        +10    +5    -1    -5   -10   ...   ...   ...   ...   ...    
        A4        +15    +5    -1    -5    -5   ...   ...   ...   ...   ...    
        A3        +10    +5    +1    -5    -5   ...   ...   ...   ...   ...    
        A2        +10    +5    +1    -1    -5   ...   ...   ...   ...   ...    
  
                 Hi-Opt I Blackjack Count Strategy Adjustments 
 
                Cards:    2   3   4   5   6   7   8   9  10 Ace 
                Values:   0   1   1   1   1   0   0   0  -1   0 
 
                         1 deck, dealer stands on soft 17 
 
 
                           Pair Split Strategy (non-DAS) (-5 to +5 except 10's) 
 
                                Dealer's Upcard 
 
Player's Pair      2     3     4     5     6     7     8     9    10    Ace 
 
   Ace,Ace        spl   spl   spl   spl   spl   spl   spl   spl   spl    -5    
    10,10         +10   +10    +5    +5    +5   +10   +20   ...   ...   ...    
     9,9           -1    -1    -1    -5    -5    +5   spl   spl   ...    +1    
     8,8          spl   spl   spl   spl   spl   spl   spl   spl    +5*  spl    
     7,7          spl   spl   spl   spl   spl   spl   ...   ...   ...   ...    
     6,6           +1     0    -5    -5    -5    +1*  ...   ...   ...   ...    
     5,5          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     4,4          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     3,3           +5    +5     0   spl   spl   spl    +1*  ...   ...   ...    
     2,2           +5    +1    -5   spl   spl   spl   ...   ...   ...   ...    
 
 
 
                            Pair Split Strategy (DAS) (-5 to +5 except 10's) 
 
                                Dealer's Upcard 
 
Player's Pair      2     3     4     5     6     7     8     9    10    Ace 
 
   Ace,Ace        spl   spl   spl   spl   spl   spl   spl   spl   spl    -5 
    10,10         +10   +10    +5    +5    +5   +10   +20   ...   ...   ...    
     9,9           -5    -5    -5    -5    -5    +5   spl   spl   ...    +1    
     8,8          spl   spl   spl   spl   spl   spl   spl   spl   spl   spl    
     7,7          spl   spl   spl   spl   spl   spl    -1   ...   ...   ...    
     6,6           -5    -5    -5   spl   spl   spl   ...   ...   ...   ...    
     5,5          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     4,4          ...    +5    +1    -1     0   ...   ...   ...   ...   ...    
     3,3           -5    spl  spl   spl   spl   spl    +5*  ...   ...   ...    
     2,2           -5    -5   spl   spl   spl   spl    +5   ...   ...   ...    
 
 
 
Take insurance: true counts +2 and above 
 
Modifications if dealer hits soft 17: 
 
Hard 17 vs. A  -4 
Hard 16 vs. A  +3 
Hard 15 vs. A  +4 
Hard 14 vs. 6   S 
Hard 13 vs. 6  -5 
Hard 12 vs. 6  -3 
 
Soft 18 vs. A   H 
    9-9 vs. 6  -4 
    9-9 vs. A  +5 
  
AAAAAAAAAAAAAAA  Hi-Opt I Ace Side Count Strategy Adjustments   AAAAAAAAAAAAAAA 
 
                Cards:    2   3   4   5   6   7   8   9  10 Ace 
                Values:   0   1   1   1   1   0   0   0  -1   0 
 
                     1 deck, dealer stands on soft 17 
 
 
                            Hard Hit/Stand Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Hard 18+       sta   sta   sta   sta   sta   sta   sta   sta   sta   sta    
   Hard 17         +1    +1   sta    +1   sta    +3    +6    +3    +2     0    
   Hard 16         +1     0     0    +1    +1    +2    +1    +1    +1     0 
   Hard 15          0     0     0     0    +1    +1     0     0     0     0 
   Hard 14          0     0     0     0    +1    +1     0   ...     0     0 
   Hard 13          0     0     0     0    +1   ...   ...   ...   ...     0    
   Hard 12          0     0     0     0    +1   ...   ...   ...   ...   ...    
 
 
                            Soft Hit/Stand Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Soft 19+       sta   sta   sta   sta   sta   sta   sta   sta   sta   sta    
   Soft 18        sta   sta   sta   sta   sta   sta   sta   ...   ...    +1    
   Soft 17-       ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
 
 
                           Hard Double Down Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Hard 11         +1    +1    +1    +1    +1    +1    +1    +2    +1    +1 
   Hard 10          0     0     0     0     0     0    -1     0    -2    -1 
   Hard  9          0     0     0     0     0     0     0?  ...   ...   ... 
   Hard  8          0     0     0     0     0     0   ...   ...   ...   ... 
   Hard  7        ...     0     0     0     0   ...   ...   ...   ...   ... 
 
 
 
 
 
                           Soft Double Down Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
        A9         -1    -1    -1    -1     0     0   ...   ...   ...   ...    
        A8         -1    -1    -1     0     0     0   ...   ...   ...   ...    
        A7         -1    -1     0     0     0    -1   ...   ...   ...   ...    
        A6         +1     0     0     0    +1    +1   ...   ...   ...   ...    
        A5         +2    +2    +1    +1    +2   ...   ...   ...   ...   ...    
        A4         +4    +3    +2    +2    +3   ...   ...   ...   ...   ...    
        A3         +2    +2    +1    +1    +2   ...   ...   ...   ...   ...    
        A2         +1    +1    +1    +1    +2   ...   ...   ...   ...   ...    
  
AAAAAAAAAAAAAAA  Hi-Opt I Ace Side Count Strategy Adjustments   AAAAAAAAAAAAAAA 
 
                Cards:    2   3   4   5   6   7   8   9  10 Ace 
                Values:   0   1   1   1   1   0   0   0  -1   0 
 
                         1 deck, dealer stands on soft 17 
 
 
                           Pair Split Strategy (non-DAS) 
 
                                Dealer's Upcard 
 
Player's Pair      2     3     4     5     6     7     8     9    10    Ace 
 
   Ace,Ace        spl   spl   spl   spl   spl   spl   spl   spl   spl    +1 
    10,10           0?    0?    0?    0?    0?    0?    0?  ...   ...   ...    
     9,9           -1    -1    -1     0     0    -4   spl   spl   ...    -4    
     8,8          spl   spl   spl   spl   spl   spl   spl   spl    +2   spl    
     7,7          spl   spl   spl   spl   spl   spl   ...   ...   ...   ...    
     6,6           +1     0     0?    0?    0?   +2   ...   ...   ...   ...    
     5,5          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     4,4          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     3,3            0     0     0   spl   spl   spl     0   ...   ...   ...    
     2,2           -1    -1    -1   spl   spl   spl   ...   ...   ...   ...    
  
777777777777777  Hi-Opt I Seven Side Count Strategy Adjustments 777777777777777 
 
                Cards:    2   3   4   5   6   7   8   9  10 Ace 
                Values:   0   1   1   1   1   0   0   0  -1   0 
 
                     1 deck, dealer stands on soft 17 
 
 
                            Hard Hit/Stand Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Hard 18+       sta   sta   sta   sta   sta   sta   sta   sta   sta   sta    
   Hard 17          0     0   sta    -1   sta    -2    -5    -4    -2    +1    
   Hard 16          0     0     0    -1    -1    -2    -2    -2    +1     0 
   Hard 15          0     0     0    -1    -1    -2    -2    -2     0     0 
   Hard 14         +2    +1    +1    +1    +1    +2    +2   ...    +5    +2 
   Hard 13         +1    +1    +1    +1    +1   ...   ...   ...   ...    +2    
   Hard 12         +1    +1    +1    +1    +1   ...   ...   ...   ...   ...    
 
 
                            Soft Hit/Stand Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Soft 19+       sta   sta   sta   sta   sta   sta   sta   sta   sta   sta    
   Soft 18        sta   sta   sta   sta   sta   sta   sta   ...   ...     0    
   Soft 17-       ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
 
 
                           Hard Double Down Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
   Hard 11         +1    +1    +1     0     0     0     0     0    +1    +1 
   Hard 10         +1    +1    +1     0     0     0     0     0    +2    +1 
   Hard  9         +1    +1    +1     0     0     0     0?  ...   ...   ... 
   Hard  8         +1    +1    +1     0     0     0   ...   ...   ...   ... 
   Hard  7        ...    +1    +1     0     0   ...   ...   ...   ...   ... 
 
 
 
 
 
                           Soft Double Down Strategy 
 
                                Dealer's Upcard 
 
Player's Total     2     3     4     5     6     7     8     9    10    Ace 
 
        A9         +1    +1    +1     0     0     0?  ...   ...   ...   ...    
        A8         +1    +1    +1     0     0     0?  ...   ...   ...   ...    
        A7         +2    +2    +2    +1    +1    +2   ...   ...   ...   ...    
        A6         +3    +2    +2     0     0    +1   ...   ...   ...   ...    
        A5         +3    +3    +2     0     0   ...   ...   ...   ...   ...    
        A4         +3    +3    +2     0     0   ...   ...   ...   ...   ...    
        A3         -1     0     0    -2    -2   ...   ...   ...   ...   ...    
        A2          0     0     0    -1    -1   ...   ...   ...   ...   ...    
  
777777777777777  Hi-Opt I Seven Side Count Strategy Adjustments 777777777777777 
 
                Cards:    2   3   4   5   6   7   8   9  10 Ace 
                Values:   0   1   1   1   1   0   0   0  -1   0 
 
                         1 deck, dealer stands on soft 17 
 
 
                           Pair Split Strategy (non-DAS) 
 
                                Dealer's Upcard 
 
Player's Pair      2     3     4     5     6     7     8     9    10    Ace 
 
   Ace,Ace        spl   spl   spl   spl   spl   spl   spl   spl   spl    +1 
    10,10           0?    0?    0?    0?    0?    0?    0?  ...   ...   ...    
     9,9           +1    +1    +1     0     0    +2   spl   spl   ...     0    
     8,8          spl   spl   spl   spl   spl   spl   spl   spl    +3   spl    
     7,7          spl   spl   spl   spl   spl   spl   ...   ...   ...   ...    
     6,6           +2    +2     0?    0?    0?   -3   ...   ...   ...   ...    
     5,5          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     4,4          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...    
     3,3           -2     0     0   spl   spl   spl    +8   ...   ...   ...    
     2,2            0    +2    +1   spl   spl   spl   ...   ...   ...   ...    
 
