1050 lines
47 KiB
Plaintext
1050 lines
47 KiB
Plaintext
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HOW TO BEAT SINGLE DECK BLACKJACK
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Version 1.01
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Copyright 1991, Michael Hall
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----------------> Part 1: The Basics
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Part 2: About the Strategy Charts
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Part 3: The Strategy Charts (LONG)
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Introduction
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============
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Here is the long-awaited article on Hi-Opt I, covering everything
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from the rules of blackjack to basic strategy to card-counting to
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multiparameter tables for experts. Novices should read this article.
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People interested in "just the facts" about the strategy should
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just read Part 2 and Part 3, in separate articles.
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Help for the novice blackjack player
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====================================
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The basic idea of the game is to get a total less than 21 that is
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higher than the dealer OR to not bust (go over 21) when the dealer
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busts.
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All single deck games are dealt face down. You receive the first
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two cards face down, and any subsequent cards face up. Use one
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hand to hold the first two cards. Don't touch the others.
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Insurance is a side bet for up to half of your original bet. It can
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only be placed at the start of a round when the dealer has an ace
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showing. An player who is not counting cards should never take insurance.
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Insurance pays 2-1 only if the dealer has blackjack.
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Splitting can be done 3 times, to produce up to 4 hands. If you have
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a pair and wish to split them, put your cards face up in front of your
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bet, and push out a bet equal to your original. The dealer splits the cards
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apart and deals a card to the first one, which you play normally,
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and then the dealer deals a card to the second one, which again you
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play normally.
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Doubling can be done on any two cards. First put your cards face up
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in front of your bet, and then push out a bet equal to your original,
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and you will receive exactly one more card. (If it is a pair, you
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may have to verbally tell the dealer whether you are doubling or
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splitting.)
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Standing versus hitting is the most common and important decision. To
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hit you scratch your held cards on the surface of the table. Standing is
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indicated by pushing your cards under your bet. When you split,
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you instead use the protocol for face-up games - hitting is indicated
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by tapping the table, and standing is indicated by a waving motion
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parallel to the table.
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Aces can be counted as either 1 or 11. A "soft" total means you have
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an ace and can use it as 11 without going over 21; "hard" means you
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aren't counting an ace as 11 in your total.
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Basic Strategy
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==============
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You must first learn basic strategy, whether your goal is to become
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a professional card counter or just to survive a weekend at
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the blackjack tables.
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With basic strategy, you eliminate the house edge on most Las Vegas
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single deck games. With the Frontier's special rules, you can get
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a +0.3% advantage with just basic strategy. Basic strategy is the
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computer proven *best* way to play, unless you are counting cards.
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The basic strategy for typical single deck blackjack is given in
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another part of this article.
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About Nevada
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============
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Single deck rules and conditions vary tremendously throughout Nevada.
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But yes, Virginia, single deck blackjack is alive and well.
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Vegas Strip rules are dealer stands on soft 17, double any first
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two cards, resplit up to 3 times, no doubling after splitting,
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and blackjack pays 3 to 2. Proper basic strategy on this game
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makes it an even game. Many casinos on the Vegas strip use
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these rules.
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Vegas Downtown rules are like Vegas Strip rules, except that the
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dealer hits soft 17. This swings the odds slightly in the house's
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favor against the basic strategist. Many casinos in downtown Vegas
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use these rules.
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Northern Nevada rules are like Vegas Downtown rules, except that
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doubling is restricted to totals of 10 and 11 only. This really hurts
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the basic strategist.
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Advantage
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=========
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Advantage is your winnings divided by your action. Your action is
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the total amount of money you wager. To find out how much of an
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advantage you have with basic strategy for a single deck game,
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use the table below. Start with +0.02% for Vegas Strip rules,
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and then add the adjustments for rule differences for the game
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you wish to analyze.
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% RULE
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----- ---------------------------------
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-0.78 Doubling on 11 only
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-0.26 Doubling on 10 and 11 only
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-0.21 No non-ace pair splitting
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-0.19 Dealer hits soft 17
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-0.16 No splitting of aces
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-0.13 Doubling on 9, 10, 11 only
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-0.11 No hole card (European)
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-0.02 No resplitting of non-ace pairs
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+0.03 Resplitting of aces
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+0.11 Six card automatic winner
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+0.13 Doubling after splitting (DAS)
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+0.14 Drawing to split aces
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+0.16? Suited BJ pays 2-1
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+0.24 Doubling on 3 or more cards
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Help for the aspiring card-counter
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==================================
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For single deck blackjack, I recommend a simple counting system card
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called Hi-Opt I. Although it is one of the simplest systems to start
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with, it can be extended to be more powerful than nearly any other
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counting system - and you never have to forget what you have already
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learned.
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Here's an interesting table, drawn from "Theory of Blackjack" and elsewhere:
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PLAYING BETTING COUNT VALUES
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SYSTEM EFFICIENCY CORRELATION A 2 3 4 5 6 7 8 9 10
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Hi-Opt I .615 .88 0 0 +1 +1 +1 +1 0 0 0 -1
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Hi-Opt I + A .635 .96 "
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Hi-Opt I + A,7 .736 .97 "
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Hi-Opt I + A,7,8 .811 .97 "
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Hi-Opt I + A,7,8,9 .870 .97 "
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Hi-Opt I + A,7,8,9,2 .891 .98 "
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High-Low .51 .97 -1 +1 +1 +1 +1 +1 0 0 0 -1
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High-Low + A .61? .97 "
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Hi-Opt II .67 .91 0 +1 +1 +2 +2 +1 +1 0 0 -2
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Zen .63 .97 -1 +1 +1 +2 +2 +2 +1 0 0 -2
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Uston APC + A .69 .91 0 +1 +2 +2 +3 +2 +2 +1 -1 -3
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(Side counted cards are listed after the "+" signs.)
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Playing efficiency is a measure of how good a counting system is
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a strategy, while betting correlation is a measure of how good it
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is at betting. As you can see, Hi-Opt I + A,7 is better in both
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respects than of the listed competitor systems, and Hi-Opt I + A is as
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nearly as good as or better than most systems. Even straight Hi-Opt I
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with no side count of aces is respectable.
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Here is how you do the Hi-Opt I count. Initialize "running count" to
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zero at start. Add one for each 3, 4, 5, or 6 you see and subtract
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one for each 10 you see. Divide running count by estimated number
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of unseen decks to get true count used in the strategy adjustment
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table. Note that for single deck, this division becomes a multiplication.
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For example, if there is 1/4 deck remaining and the running count is
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+2, then the true count is +8.
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You should only take insurance if the true count is +2 or above.
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Don't be swayed by what cards you have (i.e., don't fall into the
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insure-your-blackjack trap); it's a side bet, so only the count
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matters.
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The Kelly Criterion is a betting heuristic that minimizes your chance
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of going broke while maximizing your long-run profits. To bet
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consistently with the Kelly Criterion, you should divide your bankroll
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into 300-400 units and normally bet 1-4 units on each hand. Your
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optimal bet on a hand is a percentage of your *current* bankroll
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equal to about .5R/D + B, where R is the running count, D is the number
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of remaining decks (so R/D is the true count), and B is the basic
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strategy expectation. Note that on a weekend trip you might not
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need access to your whole bankroll, but you may need 100-150 units.
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It is wise to limit your top bet to about 1/100 of your total bankroll,
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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 accept
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higher risks by using fewer units, more power to you.
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Playing two hands at once is a often a good idea. You can afford to bet
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around 30% more on two hands (combined) than on one hand, and
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so you will make more money per hour without increasing your variance.
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To play two hands, each bet must be twice the table minimum at
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most casinos. Play the first hand before looking at the second,
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except when the dealer has an ace showing and you are permitted
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to look at both hands to decide if you want insurance.
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After you have mastered basic strategy and betting according to the
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count, you can bet more accurately if you keep a side count of aces.
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For each excess seen ace, temporarily subtract 1 from the running count
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- if there are excess remaining aces, add 1 to the running count.
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Then compute the true count for betting. For example, suppose you
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have seen the first 1/4 deck, but have not seen any aces. This
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means there is 1 excess remaining ace, since you normally expect
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to see one ace for every quarter deck (since there are four aces
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in a deck). So, you would adjust the running count by +1 for betting
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purposes.
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Strategy adjustments are another improvement. Here you deviate
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intelligently from basic strategy, according to the true count.
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The strategy adjustment table is given and explained in another part of
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this article. The strategy adjustment table is refinement; you get
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most of the benefit of counting from bet size variation, and you
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should do fine if you avoid strategy adjustments at first. The
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strategy adjustments will just buy you an extra 0.4% or so.
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The multiparameter strategy tables for side counts are a refinement on a
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refinement, and should only be attempted by counters with considerable
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experience with basic Hi-Opt I. They'll buy you an extra 0.1% or so.
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Here is what a card counter looks at to rate a blackjack game, in rough
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order of their importance:
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1. NUMBER OF DECKS. The fewer the better.
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2. PENETRATION. The % of cards dealt before the shuffle is very important.
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The number of spots being played can impact the penetration.
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3. RULES. A near zero or positive basic strategy expectation helps.
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4. MINIMUMS/MAXIMUMS. The game must be affordable and profitable, and
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the player's betting should not be too much bigger than the minimum,
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lest he attracts unwanted attention.
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5. CONTENT DEALERS/PIT CRITTERS. It helps if the employees are happy
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in general and happy about your business too.
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The importance of playing single deck blackjack with good penetration
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cannot be overstressed. Sneak some extra effective penetration
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by sitting towards third base if you are using strategy adjustments -
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your adjustments will be more accurate since they will be made after
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seeing more cards, raising your advantage significantly.
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The maximum edge that you'll hear knowledgable card counters claim to attain
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in practice is about 1.5%. Around 0.9%-1.1% is more realistic, winning an
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average of about 1.5 units per 100 hands played. Figure on getting in
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about 100 hands per hour, so that's 1.5 units per hour you'll make. For
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typical blackjack games, a 1-4 betting spread is sufficient to beat
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the game with a good profit margin. Even flat betting will produce
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a profit, though probably not enough for the average greedy card
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counter. 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 probably
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be necessary.
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As far as risk goes, the variance on a hand of blackjack with a
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1-4 spread is about 15.5. The expected value will form a normal
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distribution, as shown on the next page. Study these distributions
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to get a feel for the kind of negative negative swings you will
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experience, purely as a result of variance.
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The game simulated here is Vegas downtown rules, 3 rounds of 3 spots,
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with the counter at the last spot using Hi-Opt I, strategy adjustments
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-6 to +6, ace adjustment for betting, true count accurate to
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a quarter deck, 1-4 betting spread.
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20,000 hands with 300 unit bankroll
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Player #3
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Average winnings: 291.90 (variance 15.547404)
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Average action: 31582.54 (variance 6.373246)
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Average worse loss: -105.47 (variance 31339.356156)
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Average advantage: 0.924258 +- 0.072904 % (variance 1.383540)
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Win/100 rounds: 1.51
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FINAL BANKROLL DISTRIBUTION CUM %
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=============== =================================================== ==========
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BUSTED |********************************************* 7
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1 - 50 |* 7
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51 - 100 |* 7
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101 - 150 |******* 8
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151 - 200 |************* 10
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201 - 250 |************* 12 LOSS
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251 - 300 |********************* 16________
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301 - 350 |************************ 19 PROFIT
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351 - 400 |************************* 23
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401 - 450 |***************************************** 30
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451 - 500 |************************************ 35
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501 - 550 |************************************************** 43
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551 - 600 |*********************************************** 50 --MEAN
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601 - 650 |***************************************** 57
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651 - 700 |****************************************** 63
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701 - 750 |******************************************* 70
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751 - 800 |**************************************** 77
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801 - 850 |************************************* 82
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851 - 900 |***************************** 87
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901 - 950 |*********************** 90
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951 - 1000 |************* 92
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1001 - 1050 |*********** 94
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1051 - 1100 |************ 96
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1101 - 1150 |******** 97
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1151 - 1200 |****** 98
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1201+ |************ 100
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Initial bankroll: 300.00
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Mean final bankroll: 591.90
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In a day or two, a player might get in 2,000 hands. With an 80 unit
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bankroll, the results are shown below:
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2,000 hands with 80 unit bankroll
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Player #3
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Average winnings: 29.71 (variance 15.577170)
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Average action: 2860.31 (variance 6.363973)
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Average worse loss: -44.59 (variance 3387.431404)
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Average advantage: 1.038872 +- 0.317410 % (variance 26.225822)
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Win/100 rounds: 1.70
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FINAL BANKROLL DISTRIBUTION CUM %
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=============== =================================================== ==========
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BUSTED |************************************************** 24
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1 - 13 |* 25
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14 - 27 |*** 26
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28 - 40 |**** 28
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41 - 53 |****** 31
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54 - 67 |******* 35 LOSS
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68 - 80 |********** 40_______
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81 - 93 |********* 44 PROFIT
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94 - 107 |*********** 50 --MEAN
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108 - 120 |*********** 55
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121 - 133 |******* 59
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134 - 147 |*********** 64
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148 - 160 |*********** 70
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161 - 173 |********* 74
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174 - 187 |********* 78
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188 - 200 |********** 83
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201 - 213 |***** 86
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214 - 227 |******* 89
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|
|
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 ... ... ... ...
|
|||
|
|
|