Multi Parameter Hi Opt 1

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HOW TO BEAT SINGLE DECK BLACKJACKVersion 1.01

Copyright 1991, Michael Hall

----------------> Part 1: The BasicsPart 2: About the Strategy ChartsPart 3: The Strategy Charts (LONG)

Introduction============Here is the long-awaited article on Hi-Opt I, covering everythingfrom the rules of blackjack to basic strategy to card-counting tomultiparameter tables for experts. Novices should read this article.People interested in "just the facts" about the strategy shouldjust 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 ishigher than the dealer OR to not bust (go over 21) when the dealerbusts.

All single deck games are dealt face down. You receive the firsttwo cards face down, and any subsequent cards face up. Use onehand 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 canonly be placed at the start of a round when the dealer has an aceshowing. 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 havea pair and wish to split them, put your cards face up in front of yourbet, and push out a bet equal to your original. The dealer splits the cardsapart 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 youplay normally.

Doubling can be done on any two cards. First put your cards face upin 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 orsplitting.)

Standing versus hitting is the most common and important decision. Tohit you scratch your held cards on the surface of the table. Standing isindicated by pushing your cards under your bet. When you split,you instead use the protocol for face-up games - hitting is indicatedby tapping the table, and standing is indicated by a waving motionparallel to the table.

Aces can be counted as either 1 or 11. A "soft" total means you havean ace and can use it as 11 without going over 21; "hard" means youaren't counting an ace as 11 in your total.

Basic Strategy


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==============You must first learn basic strategy, whether your goal is to becomea professional card counter or just to survive a weekend atthe blackjack tables.

With basic strategy, you eliminate the house edge on most Las Vegassingle deck games. With the Frontier's special rules, you can get

a +0.3% advantage with just basic strategy. Basic strategy is thecomputer proven *best* way to play, unless you are counting cards.

The basic strategy for typical single deck blackjack is given inanother 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 firsttwo cards, resplit up to 3 times, no doubling after splitting,and blackjack pays 3 to 2. Proper basic strategy on this gamemakes it an even game. Many casinos on the Vegas strip usethese rules.

Vegas Downtown rules are like Vegas Strip rules, except that thedealer hits soft 17. This swings the odds slightly in the house'sfavor against the basic strategist. Many casinos in downtown Vegasuse these rules.

Northern Nevada rules are like Vegas Downtown rules, except thatdoubling 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 isthe total amount of money you wager. To find out how much of anadvantage 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 gameyou 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


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Help for the aspiring card-counter==================================For single deck blackjack, I recommend a simple counting system cardcalled Hi-Opt I. Although it is one of the simplest systems to startwith, it can be extended to be more powerful than nearly any other

counting system - and you never have to forget what you have alreadylearned.

Here's an interesting table, drawn from "Theory of Blackjack" and elsewhere:

PLAYING BETTING COUNT VALUESSYSTEM EFFICIENCY CORRELATION A 2 3 4 5 6 7 8 9 10Hi-Opt I .615 .88 0 0 +1 +1 +1 +1 0 0 0 -1Hi-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 -1High-Low + A .61? .97 "Hi-Opt II .67 .91 0 +1 +1 +2 +2 +1 +1 0 0 -2Zen .63 .97 -1 +1 +1 +2 +2 +2 +1 0 0 -2Uston 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 isa strategy, while betting correlation is a measure of how good itis 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 asnearly as good as or better than most systems. Even straight Hi-Opt Iwith no side count of aces is respectable.

Here is how you do the Hi-Opt I count. Initialize "running count" tozero at start. Add one for each 3, 4, 5, or 6 you see and subtractone for each 10 you see. Divide running count by estimated numberof unseen decks to get true count used in the strategy adjustmenttable. 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 theinsure-your-blackjack trap); it's a side bet, so only the countmatters.

The Kelly Criterion is a betting heuristic that minimizes your chanceof going broke while maximizing your long-run profits. To betconsistently with the Kelly Criterion, you should divide your bankrollinto 300-400 units and normally bet 1-4 units on each hand. Youroptimal bet on a hand is a percentage of your *current* bankrollequal to about .5R/D + B, where R is the running count, D is the numberof remaining decks (so R/D is the true count), and B is the basicstrategy 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.


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Of course, if you understand the risks and are willing to accepthigher risks by using fewer units, more power to you.

Playing two hands at once is a often a good idea. You can afford to betaround 30% more on two hands (combined) than on one hand, andso 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 permittedto look at both hands to decide if you want insurance.

After you have mastered basic strategy and betting according to thecount, 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 youhave seen the first 1/4 deck, but have not seen any aces. Thismeans there is 1 excess remaining ace, since you normally expectto 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 bettingpurposes.

Strategy adjustments are another improvement. Here you deviateintelligently from basic strategy, according to the true count.The strategy adjustment table is given and explained in another part ofthis article. The strategy adjustment table is refinement; you getmost of the benefit of counting from bet size variation, and youshould do fine if you avoid strategy adjustments at first. Thestrategy adjustments will just buy you an extra 0.4% or so.The multiparameter strategy tables for side counts are a refinement on arefinement, and should only be attempted by counters with considerableexperience 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 roughorder 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 happyin general and happy about your business too.

The importance of playing single deck blackjack with good penetrationcannot be overstressed. Sneak some extra effective penetrationby sitting towards third base if you are using strategy adjustments -your adjustments will be more accurate since they will be made afterseeing more cards, raising your advantage significantly.

The maximum edge that you'll hear knowledgable card counters claim to attainin practice is about 1.5%. Around 0.9%-1.1% is more realistic, winning anaverage of about 1.5 units per 100 hands played. Figure on getting inabout 100 hands per hour, so that's 1.5 units per hour you'll make. Fortypical blackjack games, a 1-4 betting spread is sufficient to beat

the game with a good profit margin. Even flat betting will producea profit, though probably not enough for the average greedy cardcounter. If the game has poor penetration or poor rules and a better


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game cannot be found, then a betting spread larger than 1-4 will probablybe necessary.

As far as risk goes, the variance on a hand of blackjack with a1-4 spread is about 15.5. The expected value will form a normaldistribution, as shown on the next page. Study these distributionsto 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 toa quarter deck, 1-4 betting spread.


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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 ********************************************* 71 - 50 * 751 - 100 * 7101 - 150 ******* 8

151 - 200 ************* 10201 - 250 ************* 12 LOSS251 - 300 ********************* 16________301 - 350 ************************ 19 PROFIT351 - 400 ************************* 23401 - 450 ***************************************** 30451 - 500 ************************************ 35501 - 550 ************************************************** 43551 - 600 *********************************************** 50 --MEAN601 - 650 ***************************************** 57651 - 700 ****************************************** 63701 - 750 ******************************************* 70751 - 800 **************************************** 77

801 - 850 ************************************* 82851 - 900 ***************************** 87901 - 950 *********************** 90951 - 1000 ************* 921001 - 1050 *********** 941051 - 1100 ************ 961101 - 1150 ******** 971151 - 1200 ****** 981201+ ************ 100

Initial bankroll: 300.00Mean final bankroll: 591.90


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In a day or two, a player might get in 2,000 hands. With an 80 unitbankroll, 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 ************************************************** 241 - 13 * 2514 - 27 *** 2628 - 40 **** 28

41 - 53 ****** 3154 - 67 ******* 35 LOSS68 - 80 ********** 40_______81 - 93 ********* 44 PROFIT94 - 107 *********** 50 --MEAN108 - 120 *********** 55121 - 133 ******* 59134 - 147 *********** 64148 - 160 *********** 70161 - 173 ********* 74174 - 187 ********* 78188 - 200 ********** 83201 - 213 ***** 86

214 - 227 ******* 89228 - 240 ******* 92241 - 253 ***** 95254 - 267 **** 97268 - 280 ** 98281 - 293 ** 99294 - 307 * 99308 - 320 * 100321+ * 100

Initial bankroll: 80.00Mean final bankroll: 109.72

Note: different scale than previous graph.


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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 belowminimum wage. Don't give up hopes of making money with blackjackyet. The way to do it is to form a team.

Several players can pool their bankrolls and bet as each had thewhole bankroll. If there are N players contributing equally,then they will each make N times as much together than they wouldindividually. Or they can make slightly less and reduce thevariance 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 youout for whatever reason they choose. If they read you the TrespassAct, *then* it will be illegal for you to return to the casinoand they can have you arrested. In extreme cases, casinos havebeen known to break the bones of card counters, but if you areplaying for low stakes at a reputable casino, you shouldn't haveany such physical problems.

There are many things that a casino can do besides kick you outto make it not worth your while to stay. They can shuffle thedeck any time the cards favor you, which will cost you 1-2% inadvantage, making the game unbeatable. Even if they are not

card counting, the dealer can simply shuffle any time a largebet is placed. Or they can simply stop dealing deep into thedeck altogether.

When the pit critters (properly known as floor managers or sometimesa pit boss) are hanging around your table, eyeing you, lookingthrough the discards or obviously card counting during play,telling the dealer to shuffle early, restricting your bettingspread, etc. then this is called "heat".

Since heat results in poor playing conditions and may preceeda barring, you should try to avoid it. Don't look like youare counting cards! Become good enough at card counting thatyou can simultaneously carry on a conversation. Talk to theother players, the dealer, and the pit critters. Mix up yourbetting pattern. Don't always bet the same at the top ofthe deck. Limit your betting spread, as spreads widerthan 1-4 are usually not necessary to have a good advantageand wider spreads will usually not be tolerated by the pitcritters. 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 ofchips, representing different dollar amounts, so that a pit crittercannot at a glance figure out whether you raised or lowered yourbet from the previous hand. Try switching back between 1 and2 hands to range your bet that way, unless this causes heat

itself.

Many casinos like for you to "color up" when you leave. This


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means to exchange your chips for ones of higher denominations,making it easier for you to carry, and trivial for the pit crittersto count. It's a good idea to leave a table with no chips, if possible.You can accomplish this without losing by *discretely* squirreling chipsinto 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 chipson 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 thetable - you want them to know that you took a "loss".

If you have been squirreling chips, then be discrete about cashingthem 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 chipsat another casino.

Comps=====You can generate extra low variance income via "comps" - complimentary

rooms, food, and other hotel services. Four hours of betting $25minimums is enough to get a free room at most casinos in Vegas.Lower levels of betting will get you a free meel. Even higher levelsof 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" yourplay. 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 getsome 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 theyforget 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 offthe 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 bookin 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 suggestionsfor achieving an advantage in single deck blackjack without lookinglike 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


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counting system that I advocate. It has lots of general informationthat any card counter should know, though the authors of this book area little too paranoid about getting cheated.

Good luck and on to the tables! The strategy tables, that is. Seethe next two articles.


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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 tablesfor single deck blackjack, Vegas Strip rules. The strategy informationwas compiled from a variety of sources, including "The World'sGreatest Blackjack Book", Steve Markowitz's analytic strategy adjustmentprogram, and my empirical strategy adjustment program.

Caveats=======I do not guarantee that these tables are correct. If you find anymistakes, or have any suggestions, please let me know, and I willrepost if necessary.

How to read the Basic Strategy table====================================Cross index your hand with the dealer's face-up card. If there issomething 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 10showing. You first check splitting - the table shows that you alwayssplit 8's, since it has an "spl" for every dealer up card. Asanother 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 ifyou should "soft hit" it. Ace-7 is soft 18, which when cross-refencedwith 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 basicstrategy, except possibly when there is a number there. If thereis a number and the true count is greater than or equal to it,it means yes, do the corresponding action. Exception: when thereis 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 basicstrategy and hit soft 18 vs. Ace if the true count were belowzero, 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 adjustmentsin preference to basic strategy. As another example, supposeyou have 8-8 vs. dealer 10 (no double after split). The number there


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is "+5*", meaning that for true counts of 5 or less, you split, butfor true counts of +6 or more, you would not split. (Exercise forthe 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 Snydershowed that such a simplication resulted in no measurable loss in

performance. However, I have included a finer granularity of numbersfor hard standing, because my empirical results produced statisticallysignificant settings of these adjustments to their exact values.Whether this will make a statistically difference in the overall resultsof a few million hands, I rather doubt, but since it definitely makesa difference in the results for these particular hands, I can't bearto throw away that gain. If you wish, you may round the restof 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 forhard 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 inaddition to the normal Hi-Opt I strategy adjustment table. The bestorder to learn the side counts is given in the first part of thearticle 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 youbecomes 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 givesHi-Opt I strategy adjustments outside of -6 to +6, and no bookgives multiparameter adjustments for anything other than aces.(Currently just aces and 7's are here, but I'll add the other cardsin later editions of this article.)

You find the side count strategy adjustment number the same way you findthe Hi-Opt I strategy adjustment number, by cross-indexing on theappropriate table.

For strategy, you adjust the running count by the number of excess seencards for the side count times the side count strategy adjustment number.

As an example of how to use the side count adjustment number, supposeyou are side-counting 7's and are faced with 14 vs. 10 and a runningcount of -1 at the 1/2 deck level. The Hi-Opt I strategy adjustmentnumber for standing hard 14 vs. 10 is +15, and the seven adjustmentnumber for this play is +5. Suppose you have seen all four 7'sremaining at the 1/2 deck level, meaning that there are two excess7's removed from the deck. For strategy, you then must adjust the*running* count, not the true count, and not the strategy adjustmentnumber. From the running count, you *subtract* the number of excess*remaining* 7's times the 7-adjustment index (or *add* the number ofexcess *seen* 7's times the 7-adjustment index.) In this casethat'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 strategyadjustment number of +15. Since +18 is more than +15, you would


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stand. Imagine that, standing on hard 14 vs. 10 with a negative Hi-Opt Icount!

Let R be the running count,X be the number of excess seen side count cards times the adjustment numberN 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 [email protected] if you have anyquestions on these charts.


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Part 1: The BasicsPart 2: About the Strategy Charts

----------------> Part 3: The Strategy Charts (LONG)

What follows are several tables for single deck blackjack andmulti-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


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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 staHard 17 sta sta sta sta sta sta sta sta sta staHard 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


Soft 19+ sta sta sta sta sta sta sta sta sta staSoft 18 sta sta sta sta sta sta sta ... ... sta

Soft 17- ... ... ... ... ... ... ... ... ... ...

Hard Double Down Strategy

Dealer's Upcard


Hard 11 dbl dbl dbl dbl dbl dbl dbl dbl dbl dblHard 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


A9 ... ... ... ... ... ... ... ... ... ...A8 ... ... ... ... dbl ... ... ... ... ...A7 ... dbl dbl dbl dbl ... ... ... ... ...


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A6 dbl dbl dbl dbl dbl ... ... ... ... ...A5 ... ... dbl dbl dbl ... ... ... ... ...A4 ... ... dbl dbl dbl ... ... ... ... ...A3 ... ... dbl dbl dbl ... ... ... ... ...A2 ... ... dbl dbl dbl ... ... ... ... ...


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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 spl10,10 ... ... ... ... ... ... ... ... ... ...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 spl2,2 ... 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 spl10,10 ... ... ... ... ... ... ... ... ... ...9,9 spl spl spl spl spl ... spl spl ... ...8,8 spl spl spl spl spl spl spl spl spl spl7,7 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)


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Hi-Opt I Blackjack Count Strategy Adjustments

Cards: 2 3 4 5 6 7 8 9 10 AceValues: 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


Hard 18+ sta sta sta sta sta sta sta sta sta staHard 17 -20 -20 sta -20 sta -20 -15 -15 -20 -6Hard 16 -7 -7 -9 -10 -10 +10 +10 +6 +2 +7Hard 15 -5 -5 -5 -8 -8 +10 +10 +6 +3 +8

Hard 14 -3 -3 -5 -5 -5 +10 +20 ... +13 +10Hard 13 0 0 -1 -4 -4 ... ... ... ... +15Hard 12 +3 +3 +1 -1 +1 ... ... ... ... ...

Soft Hit/Stand Strategy (-5 to +5)

Dealer's Upcard


Soft 19+ sta sta sta sta sta sta sta sta sta staSoft 18 sta sta sta sta sta sta sta ... ... 0

Soft 17- ... ... ... ... ... ... ... ... ... ...

Hard Double Down Strategy (-10 to +15)

Dealer's Upcard


Hard 11 -10 -10 -10 -10 -10 -5 -5 -5 -5 0Hard 10 -10 -10 -10 -10 -10 -5 -5 -1 +5 +5Hard 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


A9 +10 +10 +5 +5 +5 +15 ... ... ... ...A8 +5 +5 +5 +1 +1 +15 ... ... ... ...A7 +1 -1 -5 -10 -10 +15 ... ... ... ...


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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 ... ... ... ... ...


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Hi-Opt I Blackjack Count Strategy Adjustments

Cards: 2 3 4 5 6 7 8 9 10 AceValues: 0 1 1 1 1 0 0 0 -1 0


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 -510,10 +10 +10 +5 +5 +5 +10 +20 ... ... ...9,9 -1 -1 -1 -5 -5 +5 spl spl ... +18,8 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 -510,10 +10 +10 +5 +5 +5 +10 +20 ... ... ...9,9 -5 -5 -5 -5 -5 +5 spl spl ... +18,8 spl spl spl spl spl spl spl spl spl spl7,7 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 -4Hard 16 vs. A +3Hard 15 vs. A +4Hard 14 vs. 6 SHard 13 vs. 6 -5Hard 12 vs. 6 -3

Soft 18 vs. A H9-9 vs. 6 -4


21/27

9-9 vs. A +5


22/27

AAAAAAAAAAAAAAA Hi-Opt I Ace Side Count Strategy Adjustments AAAAAAAAAAAAAAA

Cards: 2 3 4 5 6 7 8 9 10 AceValues: 0 1 1 1 1 0 0 0 -1 0



Dealer's Upcard


Hard 18+ sta sta sta sta sta sta sta sta sta staHard 17 +1 +1 sta +1 sta +3 +6 +3 +2 0Hard 16 +1 0 0 +1 +1 +2 +1 +1 +1 0Hard 15 0 0 0 0 +1 +1 0 0 0 0

Hard 14 0 0 0 0 +1 +1 0 ... 0 0Hard 13 0 0 0 0 +1 ... ... ... ... 0Hard 12 0 0 0 0 +1 ... ... ... ... ...


Dealer's Upcard


Soft 19+ sta sta sta sta sta sta sta sta sta staSoft 18 sta sta sta sta sta sta sta ... ... +1

Soft 17- ... ... ... ... ... ... ... ... ... ...


Dealer's Upcard


Hard 11 +1 +1 +1 +1 +1 +1 +1 +2 +1 +1Hard 10 0 0 0 0 0 0 -1 0 -2 -1Hard 9 0 0 0 0 0 0 0? ... ... ...Hard 8 0 0 0 0 0 0 ... ... ... ...Hard 7 ... 0 0 0 0 ... ... ... ... ...


Dealer's Upcard


A9 -1 -1 -1 -1 0 0 ... ... ... ...A8 -1 -1 -1 0 0 0 ... ... ... ...A7 -1 -1 0 0 0 -1 ... ... ... ...


23/27

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 ... ... ... ... ...


24/27

AAAAAAAAAAAAAAA Hi-Opt I Ace Side Count Strategy Adjustments AAAAAAAAAAAAAAA

Cards: 2 3 4 5 6 7 8 9 10 AceValues: 0 1 1 1 1 0 0 0 -1 0



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 +110,10 0? 0? 0? 0? 0? 0? 0? ... ... ...9,9 -1 -1 -1 0 0 -4 spl spl ... -48,8 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 ... ... ... ...


25/27

777777777777777 Hi-Opt I Seven Side Count Strategy Adjustments 777777777777777

Cards: 2 3 4 5 6 7 8 9 10 AceValues: 0 1 1 1 1 0 0 0 -1 0



Dealer's Upcard


Hard 18+ sta sta sta sta sta sta sta sta sta staHard 17 0 0 sta -1 sta -2 -5 -4 -2 +1Hard 16 0 0 0 -1 -1 -2 -2 -2 +1 0Hard 15 0 0 0 -1 -1 -2 -2 -2 0 0

Hard 14 +2 +1 +1 +1 +1 +2 +2 ... +5 +2Hard 13 +1 +1 +1 +1 +1 ... ... ... ... +2Hard 12 +1 +1 +1 +1 +1 ... ... ... ... ...


Dealer's Upcard


Soft 19+ sta sta sta sta sta sta sta sta sta staSoft 18 sta sta sta sta sta sta sta ... ... 0

Soft 17- ... ... ... ... ... ... ... ... ... ...


Dealer's Upcard


Hard 11 +1 +1 +1 0 0 0 0 0 +1 +1Hard 10 +1 +1 +1 0 0 0 0 0 +2 +1Hard 9 +1 +1 +1 0 0 0 0? ... ... ...Hard 8 +1 +1 +1 0 0 0 ... ... ... ...Hard 7 ... +1 +1 0 0 ... ... ... ... ...


Dealer's Upcard


A9 +1 +1 +1 0 0 0? ... ... ... ...A8 +1 +1 +1 0 0 0? ... ... ... ...A7 +2 +2 +2 +1 +1 +2 ... ... ... ...


26/27

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 ... ... ... ... ...


27/27

777777777777777 Hi-Opt I Seven Side Count Strategy Adjustments 777777777777777

Cards: 2 3 4 5 6 7 8 9 10 AceValues: 0 1 1 1 1 0 0 0 -1 0



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 +110,10 0? 0? 0? 0? 0? 0? 0? ... ... ...9,9 +1 +1 +1 0 0 +2 spl spl ... 08,8 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 ... ... ... ...

Multi Parameter Hi Opt 1

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