HOW TO BEAT SINGLE DECK BLACKJACK
\n Version 1.01
\n Copyright 1991, Michael Hall<\/p>\n
—————-> Part 1: The Basics
\n Part 2: About the Strategy Charts
\n Part 3: The Strategy Charts (LONG)<\/p>\n
Introduction
\n============
\nHere is the long-awaited article on Hi-Opt I, covering everything
\nfrom the rules of blackjack to basic strategy to card-counting to
\nmultiparameter tables for experts. Novices should read this article.
\nPeople interested in “just the facts” about the strategy should
\njust read Part 2 and Part 3, in separate articles.<\/p>\n
Help for the novice blackjack player
\n====================================
\nThe basic idea of the game is to get a total less than 21 that is
\nhigher than the dealer OR to not bust (go over 21) when the dealer
\nbusts.<\/p>\n
All single deck games are dealt face down. You receive the first
\ntwo cards face down, and any subsequent cards face up. Use one
\nhand to hold the first two cards. Don’t touch the others.<\/p>\n
Insurance is a side bet for up to half of your original bet. It can
\nonly be placed at the start of a round when the dealer has an ace
\nshowing. An player who is not counting cards should never take insurance.
\nInsurance pays 2-1 only if the dealer has blackjack.<\/p>\n
Splitting can be done 3 times, to produce up to 4 hands. If you have
\na pair and wish to split them, put your cards face up in front of your
\nbet, and push out a bet equal to your original. The dealer splits the cards
\napart and deals a card to the first one, which you play normally,
\nand then the dealer deals a card to the second one, which again you
\nplay normally.<\/p>\n
Doubling can be done on any two cards. First put your cards face up
\nin front of your bet, and then push out a bet equal to your original,
\nand you will receive exactly one more card. (If it is a pair, you
\nmay have to verbally tell the dealer whether you are doubling or
\nsplitting.)<\/p>\n
Standing versus hitting is the most common and important decision. To
\nhit you scratch your held cards on the surface of the table. Standing is
\nindicated by pushing your cards under your bet. When you split,
\nyou instead use the protocol for face-up games – hitting is indicated
\nby tapping the table, and standing is indicated by a waving motion
\nparallel to the table.<\/p>\n
Aces can be counted as either 1 or 11. A “soft” total means you have
\nan ace and can use it as 11 without going over 21; “hard” means you
\naren’t counting an ace as 11 in your total.<\/p>\n
Basic Strategy
\n==============
\nYou must first learn basic strategy, whether your goal is to become
\na professional card counter or just to survive a weekend at
\nthe blackjack tables.<\/p>\n
With basic strategy, you eliminate the house edge on most Las Vegas
\nsingle deck games. With the Frontier’s special rules, you can get
\na +0.3% advantage with just basic strategy. Basic strategy is the
\ncomputer proven *best* way to play, unless you are counting cards.<\/p>\n
The basic strategy for typical single deck blackjack is given in
\nanother part of this article.<\/p>\n
About Nevada
\n============
\nSingle deck rules and conditions vary tremendously throughout Nevada.
\nBut yes, Virginia, single deck blackjack is alive and well.<\/p>\n
Vegas Strip rules are dealer stands on soft 17, double any first
\ntwo cards, resplit up to 3 times, no doubling after splitting,
\nand blackjack pays 3 to 2. Proper basic strategy on this game
\nmakes it an even game. Many casinos on the Vegas strip use
\nthese rules.<\/p>\n
Vegas Downtown rules are like Vegas Strip rules, except that the
\ndealer hits soft 17. This swings the odds slightly in the house’s
\nfavor against the basic strategist. Many casinos in downtown Vegas
\nuse these rules.<\/p>\n
Northern Nevada rules are like Vegas Downtown rules, except that
\ndoubling is restricted to totals of 10 and 11 only. This really hurts
\nthe basic strategist.<\/p>\n
Advantage
\n=========
\nAdvantage is your winnings divided by your action. Your action is
\nthe total amount of money you wager. To find out how much of an
\nadvantage you have with basic strategy for a single deck game,
\nuse the table below. Start with +0.02% for Vegas Strip rules,
\nand then add the adjustments for rule differences for the game
\nyou wish to analyze.<\/p>\n
% RULE
\n—– ———————————
\n-0.78 Doubling on 11 only
\n-0.26 Doubling on 10 and 11 only
\n-0.21 No non-ace pair splitting
\n-0.19 Dealer hits soft 17
\n-0.16 No splitting of aces
\n-0.13 Doubling on 9, 10, 11 only
\n-0.11 No hole card (European)
\n-0.02 No resplitting of non-ace pairs
\n+0.03 Resplitting of aces
\n+0.11 Six card automatic winner
\n+0.13 Doubling after splitting (DAS)
\n+0.14 Drawing to split aces
\n+0.16? Suited BJ pays 2-1
\n+0.24 Doubling on 3 or more cards<\/p>\n
Help for the aspiring card-counter
\n==================================
\nFor single deck blackjack, I recommend a simple counting system card
\ncalled Hi-Opt I. Although it is one of the simplest systems to start
\nwith, it can be extended to be more powerful than nearly any other
\ncounting system – and you never have to forget what you have already
\nlearned.<\/p>\n
Here’s an interesting table, drawn from “Theory of Blackjack” and elsewhere:<\/p>\n
PLAYING BETTING COUNT VALUES
\nSYSTEM EFFICIENCY CORRELATION A 2 3 4 5 6 7 8 9 10
\nHi-Opt I .615 .88 0 0 +1 +1 +1 +1 0 0 0 -1
\nHi-Opt I + A .635 .96 ”
\nHi-Opt I + A,7 .736 .97 ”
\nHi-Opt I + A,7,8 .811 .97 ”
\nHi-Opt I + A,7,8,9 .870 .97 ”
\nHi-Opt I + A,7,8,9,2 .891 .98 ”<\/p>\n
High-Low .51 .97 -1 +1 +1 +1 +1 +1 0 0 0 -1
\nHigh-Low + A .61? .97 ”
\nHi-Opt II .67 .91 0 +1 +1 +2 +2 +1 +1 0 0 -2
\nZen .63 .97 -1 +1 +1 +2 +2 +2 +1 0 0 -2
\nUston APC + A .69 .91 0 +1 +2 +2 +3 +2 +2 +1 -1 -3<\/p>\n
(Side counted cards are listed after the “+” signs.)<\/p>\n
Playing efficiency is a measure of how good a counting system is
\na strategy, while betting correlation is a measure of how good it
\nis at betting. As you can see, Hi-Opt I + A,7 is better in both
\nrespects than of the listed competitor systems, and Hi-Opt I + A is as
\nnearly as good as or better than most systems. Even straight Hi-Opt I
\nwith no side count of aces is respectable.<\/p>\n
Here is how you do the Hi-Opt I count. Initialize “running count” to
\nzero at start. Add one for each 3, 4, 5, or 6 you see and subtract
\none for each 10 you see. Divide running count by estimated number
\nof unseen decks to get true count used in the strategy adjustment
\ntable. Note that for single deck, this division becomes a multiplication.
\nFor example, if there is 1\/4 deck remaining and the running count is
\n+2, then the true count is +8.<\/p>\n
You should only take insurance if the true count is +2 or above.
\nDon’t be swayed by what cards you have (i.e., don’t fall into the
\ninsure-your-blackjack trap); it’s a side bet, so only the count
\nmatters.<\/p>\n
The Kelly Criterion is a betting heuristic that minimizes your chance
\nof going broke while maximizing your long-run profits. To bet
\nconsistently with the Kelly Criterion, you should divide your bankroll
\ninto 300-400 units and normally bet 1-4 units on each hand. Your
\noptimal bet on a hand is a percentage of your *current* bankroll
\nequal to about .5R\/D + B, where R is the running count, D is the number
\nof remaining decks (so R\/D is the true count), and B is the basic
\nstrategy expectation. Note that on a weekend trip you might not
\nneed access to your whole bankroll, but you may need 100-150 units.
\nIt is wise to limit your top bet to about 1\/100 of your total bankroll,
\nbut you can get away with slightly more for very high true counts.
\nOf course, if you understand the risks and are willing to accept
\nhigher risks by using fewer units, more power to you.<\/p>\n
Playing two hands at once is a often a good idea. You can afford to bet
\naround 30% more on two hands (combined) than on one hand, and
\nso you will make more money per hour without increasing your variance.
\nTo play two hands, each bet must be twice the table minimum at
\nmost casinos. Play the first hand before looking at the second,
\nexcept when the dealer has an ace showing and you are permitted
\nto look at both hands to decide if you want insurance.<\/p>\n
After you have mastered basic strategy and betting according to the
\ncount, you can bet more accurately if you keep a side count of aces.
\nFor each excess seen ace, temporarily subtract 1 from the running count
\n– if there are excess remaining aces, add 1 to the running count.
\nThen compute the true count for betting. For example, suppose you
\nhave seen the first 1\/4 deck, but have not seen any aces. This
\nmeans there is 1 excess remaining ace, since you normally expect
\nto see one ace for every quarter deck (since there are four aces
\nin a deck). So, you would adjust the running count by +1 for betting
\npurposes.<\/p>\n
Strategy adjustments are another improvement. Here you deviate
\nintelligently from basic strategy, according to the true count.
\nThe strategy adjustment table is given and explained in another part of
\nthis article. The strategy adjustment table is refinement; you get
\nmost of the benefit of counting from bet size variation, and you
\nshould do fine if you avoid strategy adjustments at first. The
\nstrategy adjustments will just buy you an extra 0.4% or so.
\nThe multiparameter strategy tables for side counts are a refinement on a
\nrefinement, and should only be attempted by counters with considerable
\nexperience with basic Hi-Opt I. They’ll buy you an extra 0.1% or so.<\/p>\n
Here is what a card counter looks at to rate a blackjack game, in rough
\norder of their importance:<\/p>\n
1. NUMBER OF DECKS. The fewer the better.
\n 2. PENETRATION. The % of cards dealt before the shuffle is very important.
\n The number of spots being played can impact the penetration.
\n 3. RULES. A near zero or positive basic strategy expectation helps.
\n 4. MINIMUMS\/MAXIMUMS. The game must be affordable and profitable, and
\n the player’s betting should not be too much bigger than the minimum,
\n lest he attracts unwanted attention.
\n 5. CONTENT DEALERS\/PIT CRITTERS. It helps if the employees are happy
\n in general and happy about your business too.<\/p>\n
The importance of playing single deck blackjack with good penetration
\ncannot be overstressed. Sneak some extra effective penetration
\nby sitting towards third base if you are using strategy adjustments –
\nyour adjustments will be more accurate since they will be made after
\nseeing more cards, raising your advantage significantly.<\/p>\n
The maximum edge that you’ll hear knowledgable card counters claim to attain
\nin practice is about 1.5%. Around 0.9%-1.1% is more realistic, winning an
\naverage of about 1.5 units per 100 hands played. Figure on getting in
\nabout 100 hands per hour, so that’s 1.5 units per hour you’ll make. For
\ntypical blackjack games, a 1-4 betting spread is sufficient to beat
\nthe game with a good profit margin. Even flat betting will produce
\na profit, though probably not enough for the average greedy card
\ncounter. If the game has poor penetration or poor rules and a better
\ngame cannot be found, then a betting spread larger than 1-4 will probably
\nbe necessary.<\/p>\n
As far as risk goes, the variance on a hand of blackjack with a
\n1-4 spread is about 15.5. The expected value will form a normal
\ndistribution, as shown on the next page. Study these distributions
\nto get a feel for the kind of negative negative swings you will
\nexperience, purely as a result of variance.<\/p>\n
The game simulated here is Vegas downtown rules, 3 rounds of 3 spots,
\nwith the counter at the last spot using Hi-Opt I, strategy adjustments
\n-6 to +6, ace adjustment for betting, true count accurate to
\na quarter deck, 1-4 betting spread.<\/p>\n
20,000 hands with 300 unit bankroll<\/p>\n
Player #3
\nAverage winnings: 291.90 (variance 15.547404)
\nAverage action: 31582.54 (variance 6.373246)
\nAverage worse loss: -105.47 (variance 31339.356156)
\nAverage advantage: 0.924258 +- 0.072904 % (variance 1.383540)
\nWin\/100 rounds: 1.51<\/p>\n
FINAL BANKROLL DISTRIBUTION CUM %
\n=============== =================================================== ==========
\n BUSTED |********************************************* 7
\n 1 – 50 |* 7
\n 51 – 100 |* 7
\n 101 – 150 |******* 8
\n 151 – 200 |************* 10
\n 201 – 250 |************* 12 LOSS
\n 251 – 300 |********************* 16________
\n 301 – 350 |************************ 19 PROFIT
\n 351 – 400 |************************* 23
\n 401 – 450 |***************************************** 30
\n 451 – 500 |************************************ 35
\n 501 – 550 |************************************************** 43
\n 551 – 600 |*********************************************** 50 –MEAN
\n 601 – 650 |***************************************** 57
\n 651 – 700 |****************************************** 63
\n 701 – 750 |******************************************* 70
\n 751 – 800 |**************************************** 77
\n 801 – 850 |************************************* 82
\n 851 – 900 |***************************** 87
\n 901 – 950 |*********************** 90
\n 951 – 1000 |************* 92
\n 1001 – 1050 |*********** 94
\n 1051 – 1100 |************ 96
\n 1101 – 1150 |******** 97
\n 1151 – 1200 |****** 98
\n 1201+ |************ 100<\/p>\n
Initial bankroll: 300.00
\nMean final bankroll: 591.90<\/p>\n
In a day or two, a player might get in 2,000 hands. With an 80 unit
\nbankroll, the results are shown below:<\/p>\n
2,000 hands with 80 unit bankroll<\/p>\n
Player #3
\nAverage winnings: 29.71 (variance 15.577170)
\nAverage action: 2860.31 (variance 6.363973)
\nAverage worse loss: -44.59 (variance 3387.431404)
\nAverage advantage: 1.038872 +- 0.317410 % (variance 26.225822)
\nWin\/100 rounds: 1.70<\/p>\n
FINAL BANKROLL DISTRIBUTION CUM %
\n=============== =================================================== ==========
\n BUSTED |************************************************** 24
\n 1 – 13 |* 25
\n 14 – 27 |*** 26
\n 28 – 40 |**** 28
\n 41 – 53 |****** 31
\n 54 – 67 |******* 35 LOSS
\n 68 – 80 |********** 40_______
\n 81 – 93 |********* 44 PROFIT
\n 94 – 107 |*********** 50 –MEAN
\n 108 – 120 |*********** 55
\n 121 – 133 |******* 59
\n 134 – 147 |*********** 64
\n 148 – 160 |*********** 70
\n 161 – 173 |********* 74
\n 174 – 187 |********* 78
\n 188 – 200 |********** 83
\n 201 – 213 |***** 86
\n 214 – 227 |******* 89
\n 228 – 240 |******* 92
\n 241 – 253 |***** 95
\n 254 – 267 |**** 97
\n 268 – 280 |** 98
\n 281 – 293 |** 99
\n 294 – 307 |* 99
\n 308 – 320 |* 100
\n 321+ |* 100<\/p>\n
Initial bankroll: 80.00
\nMean final bankroll: 109.72<\/p>\n
Note: different scale than previous graph.<\/p>\n
Team Play
\n=========
\nIf you have studied the above graphs, you may be getting depressed,
\ngiven that the size of your bankroll may imply you will make below
\nminimum wage. Don’t give up hopes of making money with blackjack
\nyet. The way to do it is to form a team.<\/p>\n
Several players can pool their bankrolls and bet as each had the
\nwhole bankroll. If there are N players contributing equally,
\nthen they will each make N times as much together than they would
\nindividually. Or they can make slightly less and reduce the
\nvariance significantly.<\/p>\n
There are also schemes of cooperative play at the same table,
\nbut it’s usually best to have the players play at separate tables.<\/p>\n
Barring and Countermeasures
\n===========================
\nCard counting is not illegal. However, the casino can kick you
\nout for whatever reason they choose. If they read you the Trespass
\nAct, *then* it will be illegal for you to return to the casino
\nand they can have you arrested. In extreme cases, casinos have
\nbeen known to break the bones of card counters, but if you are
\nplaying for low stakes at a reputable casino, you shouldn’t have
\nany such physical problems.<\/p>\n
There are many things that a casino can do besides kick you out
\nto make it not worth your while to stay. They can shuffle the
\ndeck any time the cards favor you, which will cost you 1-2% in
\nadvantage, making the game unbeatable. Even if they are not
\ncard counting, the dealer can simply shuffle any time a large
\nbet is placed. Or they can simply stop dealing deep into the
\ndeck altogether.<\/p>\n
When the pit critters (properly known as floor managers or sometimes
\na pit boss) are hanging around your table, eyeing you, looking
\nthrough the discards or obviously card counting during play,
\ntelling the dealer to shuffle early, restricting your betting
\nspread, etc. then this is called “heat”.<\/p>\n
Since heat results in poor playing conditions and may preceed
\na barring, you should try to avoid it. Don’t look like you
\nare counting cards! Become good enough at card counting that
\nyou can simultaneously carry on a conversation. Talk to the
\nother players, the dealer, and the pit critters. Mix up your
\nbetting pattern. Don’t always bet the same at the top of
\nthe deck. Limit your betting spread, as spreads wider
\nthan 1-4 are usually not necessary to have a good advantage
\nand wider spreads will usually not be tolerated by the pit
\ncritters. You can make an okay profit with even a 1-2 spread,
\nthough 1-4 should be your goal. Use a lot of different colors of
\nchips, representing different dollar amounts, so that a pit critter
\ncannot at a glance figure out whether you raised or lowered your
\nbet from the previous hand. Try switching back between 1 and
\n2 hands to range your bet that way, unless this causes heat
\nitself.<\/p>\n
Many casinos like for you to “color up” when you leave. This
\nmeans to exchange your chips for ones of higher denominations,
\nmaking it easier for you to carry, and trivial for the pit critters
\nto count. It’s a good idea to leave a table with no chips, if possible.
\nYou can accomplish this without losing by *discretely* squirreling chips
\ninto yourclothes during play. Even if you can’t get rid of all your chips,
\nyour coloring up will be less embarassing. If you run out of chips
\non the table before you’re ready to go, pull out more cash. Make
\nsure you do color up if you leave with only a few chips on the
\ntable – you want them to know that you took a “loss”.<\/p>\n
If you have been squirreling chips, then be discrete about cashing
\nthem in. Only cash in initially what you had showing on the table.
\nCome back later to cash in the rest, or try to get rid of the chips
\nat another casino.<\/p>\n
Comps
\n=====
\nYou can generate extra low variance income via “comps” – complimentary
\nrooms, food, and other hotel services. Four hours of betting $25
\nminimums is enough to get a free room at most casinos in Vegas.
\nLower levels of betting will get you a free meel. Even higher levels
\nof betting will prompt the casino to comp *everything* – room,
\nfood, and even your plane tickets.<\/p>\n
To be eligible for comps, just ask a floor manager to “rate” your
\nplay. He will record your buy-in, betting level, and color-out
\n(chips you take with you.) After you have played for a while,
\nask a floor manager or the pit boss for a meal or whatever.<\/p>\n
This is a great way to reduce expenses and hence essentially get
\nsome guarenteed income. Unfortunately, it’s also a great way to
\nget nailed by the casinos, since you’ll be in their computers,
\nand it will take just one pit critter comment “card counter”
\nappended to your record to ruin your play there until they
\nforget your face and you use a new name.<\/p>\n
Further reading for the aspiring card counter
\n=============================================
\nAlthough this article gives you enough information to make money off
\nthe casinos, I recommend purchasing at least two of these three books:<\/p>\n
“Blackbelt in Blackjack” by Snyder
\n “Fundamentals of Blackjack” by Chambliss and Rogenski
\n “The World’s Greatest Blackjack Book” by Humble & Cooper<\/p>\n
These are available from the Gambler’s Book Club in Las Vegas,
\n(800) 634-6243. You have a decent shot at finding the last book
\nin your local book store.<\/p>\n
“Blackbelt in Blackjack” has a couple of good counting systems,
\nRed 7’s and Zen. In addition, Snyder gives many good suggestions
\nfor achieving an advantage in single deck blackjack without looking
\nlike a typical counter.<\/p>\n
“Fundamentals of Blackjack” is a new book with lots of useful tables.
\nThe counting system (C&R count) is not recommended, however.<\/p>\n
“The World’s Best Blackjack Book” focuses on the Hi-Opt I
\ncounting system that I advocate. It has lots of general information
\nthat any card counter should know, though the authors of this book are
\na little too paranoid about getting cheated.<\/p>\n
Good luck and on to the tables! The strategy tables, that is. See
\nthe next two articles.<\/p>\n
HOW TO BEAT SINGLE DECK BLACKJACK
\n Version 1.01
\n Copyright 1991, Michael Hall<\/p>\n
Part 1: The Basics
\n—————-> Part 2: About the Strategy Charts
\n Part 3: The Strategy Charts (LONG)<\/p>\n
Description
\n===========
\nThis article describes basic strategy and Hi-Opt I strategy tables
\nfor single deck blackjack, Vegas Strip rules. The strategy information
\nwas compiled from a variety of sources, including “The World’s
\nGreatest Blackjack Book”, Steve Markowitz’s analytic strategy adjustment
\nprogram, and my empirical strategy adjustment program.<\/p>\n
Caveats
\n=======
\nI do not guarantee that these tables are correct. If you find any
\nmistakes, or have any suggestions, please let me know, and I will
\nrepost if necessary.<\/p>\n
How to read the Basic Strategy table
\n====================================
\nCross index your hand with the dealer’s face-up card. If there is
\nsomething other than “…”, it means “yes, do the corresponding decision”
\n– conversely, a “…” means “no, *don’t* do the corresponding decision.”
\nRead from the bottom up. First see if you should split (“spl”), then double
\n(“dbl”), then stand (“sta”). If nothing applies, then hit. <\/p>\n
For example, suppose you have two 8’s, and the dealer has a 10
\nshowing. You first check splitting – the table shows that you always
\nsplit 8’s, since it has an “spl” for every dealer up card. As
\nanother example, if you Ace-7 vs. Ace, you first check to see if you double.
\nThere is a “…” there, so you don’t double, and so you check to see if
\nyou should “soft hit” it. Ace-7 is soft 18, which when cross-refenced
\nwith the dealer’s ace has a “sta”, indicating you should stand on versus ace.<\/p>\n
How to read the Hi-Opt I Strategy table
\n=======================================
\nCross index as with the basic strategy table. Follow the basic
\nstrategy, except possibly when there is a number there. If there
\nis a number and the true count is greater than or equal to it,
\nit means yes, do the corresponding action. Exception: when there
\nis an asterisk (*) after the number it means just the opposite –
\ndo the decision only when the true count that number or below.<\/p>\n
For example, using the previous example, you would deviate from basic
\nstrategy and hit soft 18 vs. Ace if the true count were below
\nzero, since there is a 0 in that box. For counts of zero and above,
\nyou would stand. Note that the strategy with a count of zero is
\nnot always the same as basic strategy – use the strategy adjustments
\nin preference to basic strategy. As another example, suppose
\nyou have 8-8 vs. dealer 10 (no double after split). The number there
\nis “+5*”, meaning that for true counts of 5 or less, you split, but
\nfor true counts of +6 or more, you would not split. (Exercise for
\nthe reader: what play would you do in that case of a true count of +6?)<\/p>\n
Most of the numbers are rounded off to -20,-15,-10,-5,-1,0,+1,+5,+10,+15,
\nor +20. In the September 1991 issue of Blackjack Forum, Arnold Snyder
\nshowed that such a simplication resulted in no measurable loss in
\nperformance. However, I have included a finer granularity of numbers
\nfor hard standing, because my empirical results produced statistically
\nsignificant settings of these adjustments to their exact values.
\nWhether this will make a statistically difference in the overall results
\nof a few million hands, I rather doubt, but since it definitely makes
\na difference in the results for these particular hands, I can’t bear
\nto throw away that gain. If you wish, you may round the rest
\nof the numbers off the multiples of 5 (or +1\/-1) to make things easier.<\/p>\n
Learn the adjustments gradually, starting with 0, then adding +1, then
\n-1, then +5, and so on. The most important adjustments are the ones for
\nhard standing and doubling. You can and probably should completely ignore
\nthe ones for splitting, except for the hand 10-10.<\/p>\n
How to read the side count strategy tables
\n==========================================
\nThe side count tables are for experts only. They are memorized in
\naddition to the normal Hi-Opt I strategy adjustment table. The best
\norder to learn the side counts is given in the first part of the
\narticle in the table that compares the various card counting systems.
\nFirst learn to side count aces, then add 7’s and other side counts as you
\nbecomes a grandmaster of blackjack.<\/p>\n
As far as I know, this article is the only place you can easily
\nmultiparameter Hi-Opt I in its full glory. No book I’ve seen gives
\nHi-Opt I strategy adjustments outside of -6 to +6, and no book
\ngives multiparameter adjustments for anything other than aces.
\n(Currently just aces and 7’s are here, but I’ll add the other cards
\nin later editions of this article.)<\/p>\n
You find the side count strategy adjustment number the same way you find
\nthe Hi-Opt I strategy adjustment number, by cross-indexing on the
\nappropriate table.<\/p>\n
For strategy, you adjust the running count by the number of excess seen
\ncards for the side count times the side count strategy adjustment number.<\/p>\n
As an example of how to use the side count adjustment number, suppose
\nyou are side-counting 7’s and are faced with 14 vs. 10 and a running
\ncount of -1 at the 1\/2 deck level. The Hi-Opt I strategy adjustment
\nnumber for standing hard 14 vs. 10 is +15, and the seven adjustment
\nnumber for this play is +5. Suppose you have seen all four 7’s
\nremaining at the 1\/2 deck level, meaning that there are two excess
\n7’s removed from the deck. For strategy, you then must adjust the
\n*running* count, not the true count, and not the strategy adjustment
\nnumber. From the running count, you *subtract* the number of excess
\n*remaining* 7’s times the 7-adjustment index (or *add* the number of
\nexcess *seen* 7’s times the 7-adjustment index.) In this case
\nthat’s -1 + 2*(+5) = +9. You then convert to true count by dividing
\nby the number of remaining decks (1\/2), yielding +9\/(1\/2) = 9*2 = +18,
\nwhich is the true count you would compare to the normal Hi-Opt I strategy
\nadjustment number of +15. Since +18 is more than +15, you would
\nstand. Imagine that, standing on hard 14 vs. 10 with a negative Hi-Opt I
\ncount!<\/p>\n
Let R be the running count,
\n X be the number of excess seen side count cards times the adjustment number
\n N be the number of remaining decks<\/p>\n
Then the adjusted count for strategy is:<\/p>\n
R+X
\n —
\n N <\/p>\n
If you are good enough to keep several side counts for strategy,
\nthen X will be the sum of all these adjustments.<\/p>\n
Confused?
\n=========
\nYou can send e-mail to hall@rocky.bellcore.com if you have any
\nquestions on these charts.<\/p>\n
HOW TO BEAT SINGLE DECK BLACKJACK
\n Version 1.01
\n Copyright 1991, Michael Hall<\/p>\n
Part 1: The Basics
\n Part 2: About the Strategy Charts
\n—————-> Part 3: The Strategy Charts (LONG)<\/p>\n
What follows are several tables for single deck blackjack and
\nmulti-parameter Hi-Opt I.<\/p>\n
* Basic Strategy for Single Deck
\n * Hi-Opt I Blackjack Count Strategy Adjustments
\n * Hi-Opt I Ace Side Count Strategy Adjustments
\n * Hi-Opt I Seven Side Count Strategy Adjustments<\/p>\n
Basic Strategy for Single Deck<\/p>\n
Hard Hit\/Stand Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Hard 18+ sta sta sta sta sta sta sta sta sta sta
\n Hard 17 sta sta sta sta sta sta sta sta sta sta
\n Hard 16 sta sta sta sta sta … … … … …
\n Hard 15 sta sta sta sta sta … … … … …
\n Hard 14 sta sta sta sta sta … … … … …
\n Hard 13 sta sta sta sta sta … … … … …
\n Hard 12 … … sta sta sta … … … … …<\/p>\n
Soft Hit\/Stand Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Soft 19+ sta sta sta sta sta sta sta sta sta sta
\n Soft 18 sta sta sta sta sta sta sta … … sta
\n Soft 17- … … … … … … … … … … <\/p>\n
Hard Double Down Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Hard 11 dbl dbl dbl dbl dbl dbl dbl dbl dbl dbl
\n Hard 10 dbl dbl dbl dbl dbl dbl dbl dbl … …
\n Hard 9 dbl dbl dbl dbl dbl … … … … …
\n Hard 8 … … … dbl dbl … … … … …
\n Hard 7 … … … … … … … … … …
\n Hard 6 … … … … … … … … … …
\n Hard 5 … … … … … … … … … …
\n Hard 4 … … … … … … … … … … <\/p>\n
Soft Double Down Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
A9 … … … … … … … … … …
\n A8 … … … … dbl … … … … …
\n A7 … dbl dbl dbl dbl … … … … …
\n A6 dbl dbl dbl dbl dbl … … … … …
\n A5 … … dbl dbl dbl … … … … …
\n A4 … … dbl dbl dbl … … … … …
\n A3 … … dbl dbl dbl … … … … …
\n A2 … … dbl dbl dbl … … … … …<\/p>\n
Basic Strategy for Single Deck<\/p>\n
Pair Split Strategy (non-DAS)<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Pair 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Ace,Ace spl spl spl spl spl spl spl spl spl spl
\n 10,10 … … … … … … … … … …
\n 9,9 spl spl spl spl spl … spl spl … …
\n 8,8 spl spl spl spl spl spl spl spl spl spl
\n 7,7 spl spl spl spl spl spl … … … …
\n 6,6 spl spl spl spl spl … … … … …
\n 5,5 … … … … … … … … … …
\n 4,4 … … … … … … … … … …
\n 3,3 … … spl spl spl spl
\n 2,2 … spl spl spl spl spl … … … … <\/p>\n
Pair Split Strategy (DAS)<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Pair 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Ace,Ace spl spl spl spl spl spl spl spl spl spl
\n 10,10 … … … … … … … … … …
\n 9,9 spl spl spl spl spl … spl spl … …
\n 8,8 spl spl spl spl spl spl spl spl spl spl
\n 7,7 spl spl spl spl spl spl spl … … …
\n 6,6 spl spl spl spl spl spl … … … …
\n 5,5 … … … … … … … … … …
\n 4,4 … … spl spl spl … … … … …
\n 3,3 spl spl spl spl spl spl spl … … …
\n 2,2 spl spl spl spl spl spl … … … … <\/p>\n
Take insurance: Never (unless card counting)<\/p>\n
Hi-Opt I Blackjack Count Strategy Adjustments<\/p>\n
Cards: 2 3 4 5 6 7 8 9 10 Ace
\n Values: 0 1 1 1 1 0 0 0 -1 0<\/p>\n
1 deck, dealer stands on soft 17<\/p>\n
Hard Hit\/Stand Strategy (-20 to +20)<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Hard 18+ sta sta sta sta sta sta sta sta sta sta
\n Hard 17 -20 -20 sta -20 sta -20 -15 -15 -20 -6
\n Hard 16 -7 -7 -9 -10 -10 +10 +10 +6 +2 +7
\n Hard 15 -5 -5 -5 -8 -8 +10 +10 +6 +3 +8
\n Hard 14 -3 -3 -5 -5 -5 +10 +20 … +13 +10
\n Hard 13 0 0 -1 -4 -4 … … … … +15
\n Hard 12 +3 +3 +1 -1 +1 … … … … … <\/p>\n
Soft Hit\/Stand Strategy (-5 to +5)<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Soft 19+ sta sta sta sta sta sta sta sta sta sta
\n Soft 18 sta sta sta sta sta sta sta … … 0
\n Soft 17- … … … … … … … … … … <\/p>\n
Hard Double Down Strategy (-10 to +15)<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Hard 11 -10 -10 -10 -10 -10 -5 -5 -5 -5 0
\n Hard 10 -10 -10 -10 -10 -10 -5 -5 -1 +5 +5
\n Hard 9 +1 0 0 -5 -5 +5 +10 … … …
\n Hard 8 +10 +10 +5 +5 +1 +15 … … … …
\n Hard 7 … +15 +10 +10 +10 … … … … …
\n Hard 6 … +15 +15 +10 +15 … … … … …
\n Hard 5 … … +15 +10 +15 … … … … …
\n Hard 4 … … +15 +15 +15 … … … … … <\/p>\n
Soft Double Down Strategy (-10 to +15)<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
A9 +10 +10 +5 +5 +5 +15 … … … …
\n A8 +5 +5 +5 +1 +1 +15 … … … …
\n A7 +1 -1 -5 -10 -10 +15 … … … …
\n A6 +1 -1 -5 -10 -10 +10 … … … …
\n A5 +10 +5 -1 -5 -10 … … … … …
\n A4 +15 +5 -1 -5 -5 … … … … …
\n A3 +10 +5 +1 -5 -5 … … … … …
\n A2 +10 +5 +1 -1 -5 … … … … … <\/p>\n
Hi-Opt I Blackjack Count Strategy Adjustments<\/p>\n
Cards: 2 3 4 5 6 7 8 9 10 Ace
\n Values: 0 1 1 1 1 0 0 0 -1 0<\/p>\n
1 deck, dealer stands on soft 17<\/p>\n
Pair Split Strategy (non-DAS) (-5 to +5 except 10’s)<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Pair 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Ace,Ace spl spl spl spl spl spl spl spl spl -5
\n 10,10 +10 +10 +5 +5 +5 +10 +20 … … …
\n 9,9 -1 -1 -1 -5 -5 +5 spl spl … +1
\n 8,8 spl spl spl spl spl spl spl spl +5* spl
\n 7,7 spl spl spl spl spl spl … … … …
\n 6,6 +1 0 -5 -5 -5 +1* … … … …
\n 5,5 … … … … … … … … … …
\n 4,4 … … … … … … … … … …
\n 3,3 +5 +5 0 spl spl spl +1* … … …
\n 2,2 +5 +1 -5 spl spl spl … … … … <\/p>\n
Pair Split Strategy (DAS) (-5 to +5 except 10’s)<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Pair 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Ace,Ace spl spl spl spl spl spl spl spl spl -5
\n 10,10 +10 +10 +5 +5 +5 +10 +20 … … …
\n 9,9 -5 -5 -5 -5 -5 +5 spl spl … +1
\n 8,8 spl spl spl spl spl spl spl spl spl spl
\n 7,7 spl spl spl spl spl spl -1 … … …
\n 6,6 -5 -5 -5 spl spl spl … … … …
\n 5,5 … … … … … … … … … …
\n 4,4 … +5 +1 -1 0 … … … … …
\n 3,3 -5 spl spl spl spl spl +5* … … …
\n 2,2 -5 -5 spl spl spl spl +5 … … … <\/p>\n
Take insurance: true counts +2 and above<\/p>\n
Modifications if dealer hits soft 17:<\/p>\n
Hard 17 vs. A -4
\nHard 16 vs. A +3
\nHard 15 vs. A +4
\nHard 14 vs. 6 S
\nHard 13 vs. 6 -5
\nHard 12 vs. 6 -3<\/p>\n
Soft 18 vs. A H
\n 9-9 vs. 6 -4
\n 9-9 vs. A +5<\/p>\n
AAAAAAAAAAAAAAA Hi-Opt I Ace Side Count Strategy Adjustments AAAAAAAAAAAAAAA<\/p>\n
Cards: 2 3 4 5 6 7 8 9 10 Ace
\n Values: 0 1 1 1 1 0 0 0 -1 0<\/p>\n
1 deck, dealer stands on soft 17<\/p>\n
Hard Hit\/Stand Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Hard 18+ sta sta sta sta sta sta sta sta sta sta
\n Hard 17 +1 +1 sta +1 sta +3 +6 +3 +2 0
\n Hard 16 +1 0 0 +1 +1 +2 +1 +1 +1 0
\n Hard 15 0 0 0 0 +1 +1 0 0 0 0
\n Hard 14 0 0 0 0 +1 +1 0 … 0 0
\n Hard 13 0 0 0 0 +1 … … … … 0
\n Hard 12 0 0 0 0 +1 … … … … … <\/p>\n
Soft Hit\/Stand Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Soft 19+ sta sta sta sta sta sta sta sta sta sta
\n Soft 18 sta sta sta sta sta sta sta … … +1
\n Soft 17- … … … … … … … … … … <\/p>\n
Hard Double Down Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Hard 11 +1 +1 +1 +1 +1 +1 +1 +2 +1 +1
\n Hard 10 0 0 0 0 0 0 -1 0 -2 -1
\n Hard 9 0 0 0 0 0 0 0? … … …
\n Hard 8 0 0 0 0 0 0 … … … …
\n Hard 7 … 0 0 0 0 … … … … …<\/p>\n
Soft Double Down Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
A9 -1 -1 -1 -1 0 0 … … … …
\n A8 -1 -1 -1 0 0 0 … … … …
\n A7 -1 -1 0 0 0 -1 … … … …
\n A6 +1 0 0 0 +1 +1 … … … …
\n A5 +2 +2 +1 +1 +2 … … … … …
\n A4 +4 +3 +2 +2 +3 … … … … …
\n A3 +2 +2 +1 +1 +2 … … … … …
\n A2 +1 +1 +1 +1 +2 … … … … … <\/p>\n
AAAAAAAAAAAAAAA Hi-Opt I Ace Side Count Strategy Adjustments AAAAAAAAAAAAAAA<\/p>\n
Cards: 2 3 4 5 6 7 8 9 10 Ace
\n Values: 0 1 1 1 1 0 0 0 -1 0<\/p>\n
1 deck, dealer stands on soft 17<\/p>\n
Pair Split Strategy (non-DAS)<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Pair 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Ace,Ace spl spl spl spl spl spl spl spl spl +1
\n 10,10 0? 0? 0? 0? 0? 0? 0? … … …
\n 9,9 -1 -1 -1 0 0 -4 spl spl … -4
\n 8,8 spl spl spl spl spl spl spl spl +2 spl
\n 7,7 spl spl spl spl spl spl … … … …
\n 6,6 +1 0 0? 0? 0? +2 … … … …
\n 5,5 … … … … … … … … … …
\n 4,4 … … … … … … … … … …
\n 3,3 0 0 0 spl spl spl 0 … … …
\n 2,2 -1 -1 -1 spl spl spl … … … … <\/p>\n
777777777777777 Hi-Opt I Seven Side Count Strategy Adjustments 777777777777777<\/p>\n
Cards: 2 3 4 5 6 7 8 9 10 Ace
\n Values: 0 1 1 1 1 0 0 0 -1 0<\/p>\n
1 deck, dealer stands on soft 17<\/p>\n
Hard Hit\/Stand Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Hard 18+ sta sta sta sta sta sta sta sta sta sta
\n Hard 17 0 0 sta -1 sta -2 -5 -4 -2 +1
\n Hard 16 0 0 0 -1 -1 -2 -2 -2 +1 0
\n Hard 15 0 0 0 -1 -1 -2 -2 -2 0 0
\n Hard 14 +2 +1 +1 +1 +1 +2 +2 … +5 +2
\n Hard 13 +1 +1 +1 +1 +1 … … … … +2
\n Hard 12 +1 +1 +1 +1 +1 … … … … … <\/p>\n
Soft Hit\/Stand Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Soft 19+ sta sta sta sta sta sta sta sta sta sta
\n Soft 18 sta sta sta sta sta sta sta … … 0
\n Soft 17- … … … … … … … … … … <\/p>\n
Hard Double Down Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Hard 11 +1 +1 +1 0 0 0 0 0 +1 +1
\n Hard 10 +1 +1 +1 0 0 0 0 0 +2 +1
\n Hard 9 +1 +1 +1 0 0 0 0? … … …
\n Hard 8 +1 +1 +1 0 0 0 … … … …
\n Hard 7 … +1 +1 0 0 … … … … …<\/p>\n
Soft Double Down Strategy<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Total 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
A9 +1 +1 +1 0 0 0? … … … …
\n A8 +1 +1 +1 0 0 0? … … … …
\n A7 +2 +2 +2 +1 +1 +2 … … … …
\n A6 +3 +2 +2 0 0 +1 … … … …
\n A5 +3 +3 +2 0 0 … … … … …
\n A4 +3 +3 +2 0 0 … … … … …
\n A3 -1 0 0 -2 -2 … … … … …
\n A2 0 0 0 -1 -1 … … … … … <\/p>\n
777777777777777 Hi-Opt I Seven Side Count Strategy Adjustments 777777777777777<\/p>\n
Cards: 2 3 4 5 6 7 8 9 10 Ace
\n Values: 0 1 1 1 1 0 0 0 -1 0<\/p>\n
1 deck, dealer stands on soft 17<\/p>\n
Pair Split Strategy (non-DAS)<\/p>\n
Dealer’s Upcard<\/p>\n
Player’s Pair 2 3 4 5 6 7 8 9 10 Ace<\/p>\n
Ace,Ace spl spl spl spl spl spl spl spl spl +1
\n 10,10 0? 0? 0? 0? 0? 0? 0? … … …
\n 9,9 +1 +1 +1 0 0 +2 spl spl … 0
\n 8,8 spl spl spl spl spl spl spl spl +3 spl
\n 7,7 spl spl spl spl spl spl … … … …
\n 6,6 +2 +2 0? 0? 0? -3 … … … …
\n 5,5 … … … … … … … … … …
\n 4,4 … … … … … … … … … …
\n 3,3 -2 0 0 spl spl spl +8 … … …
\n 2,2 0 +2 +1 spl spl spl … … … … <\/p>\n
