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Three Sides of the Same Coin |
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The old adage that there are two sides to every story certainly applies to recaps of the ensuing events after the publication of Beat the Dealer. Below is a sampling of spin (or perhaps revisionist history) provided by the feuding sides in the casino/card counter battle (underlined emphasis courtesy of your authors). The card counter’s side: Carlson writes, in Blackjack for Blood, “Their paranoia out of control, the Las Vegas casinos snapped! On April Fool’s Day 1964, the casinos on the Las Vegas Strip changed the rules of blackjack. The first (and only) time the rules of a major casino game had ever been significantly altered. And the changes were drastic. Doubling down was restricted to two-card totals of 11 only, and a pair of Aces could no longer be split. The effect on the average player was disastrous, and play at the tables all but vanished. The casino’s side: A “suave PR man,” in a Newsweek article dated April 13, 1964, indicates that the operators eliminated the “fringe benefits” of the game, namely “the right to double most bets and to split hands of two Aces.” A third side to the story? Thorp’s nonchalant reply (in the same Newsweek article) to all the hoopla: “Instead of five hours, now I’ll have to play seven to make the same money.” |
The most popular counts today are, perhaps surprisingly, variations of the original point-count systems. For all the improvements and simplifications that have occurred in the last 35 years, card-counting still remains relatively inaccessible to most of us. It’s simply too much to do, what with all the bells clanging, dealers talking, cocktail waitresses jiggling, pit bosses staring, eyes-in-the-sky watching, players chatting, and money changing hands.
So have we exhausted the possibilities? Has blackjack been milked for all it’s worth? Thankfully no. Is there anything left for the rest of us? The answer is yes!
Necessity is the mother of invention, and the need for simplicity is why the Knock-Out method was conceived. We believe the Knock-Out system is, to date, the easiest professional-level card-counting system. It is the system capable of making better players out of almost all of us. The ease of play makes card-counting a “fun” event for even the casual player. And the simplicity does not come at the expense of performance. The K-O system is a top caliber tool at your disposal. Let’s get ready for round 2.
Ease of Use
The unbalanced nature of the Knock-Out count (which eliminates the need for remaining deck estimation and a true count conversion), the natural level-1 card values, the lack of any side counts, the innovation of a reduced and rounded matrix (which eases the effort to memorize and apply the strategy matrix), and the ability for you, as a player, to custom tailor the Preferred system, makes the K-O system unique. To date, no other system has all, or even three, of these attributes.
The following table compares the most popular systems today in terms of ease of use. The three comparison parameters left of the solid bar (type, level, and whether or not a side count is employed) are intrinsic properties for each particular system and are therefore fixed3.
The comparison parameter to the right of the bar (whether or not a rounded matrix exists) is included for the present-day version of these systems. In principle, any system developer so inclined could develop a rounded matrix for a system, hence this is not an intrinsic property of the system per se. But of course this requires effort, whereas the K-O system has already been designed with ease of use in mind.
System Comparison: Ease of Use | ||||
System | Type | Level | Side count? | Round matrix? |
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K-O | U | 1 | N | Y |
Red 7 | U | 1+* | N | N |
UZ II | U | 2 | N | N |
Hi-Opt I | B | 1 | Y | N |
High-Low | B | 1 | N | N |
Omega II | B | 2 | Y | N |
*Red 7 requires the player to keep track of colors on 7-valued cards. |
Performance
We’ve demonstrated that the K-O system is easy to apply. But how well does it perform? Below we give comparison tables to demonstrate the power of the K-O system.
We note that our rounding of the K-O matrix comes at the expense of expectation. In the “Reduced” comparisons which follow, we will always be adopting the top 16 plays of the K-O Preferred system. Thus, we are comparing the Knock-Out rounded matrices to the unrounded top 16 matrix plays of the other systems, in effect giving the other systems the benefit of a slight edge.
Let’s first consider a 2-deck game with the benchmark rules. We choose the 2-deck game to study in detail because it is a compromise between single-deck and multiple-deck games. To remind you, our benchmark 2-decker included the dealer standing on soft 17 (S17), doubling down on any first two cards (DOA), no doubling after splitting (noDAS), and no surrender. We have fixed the penetration at 75%4.
Below is a table which summarizes the 2-deck results. Each entry in the following table is based on a simulation of at least several hundred million hands. As before, perfect play was assumed; no betting or playing errors were introduced. To be fair to each system, we have placed the different systems on the same scale in a modified proportional betting fashion, as described in the last chapter. Note that by doing so, we force each system to have nearly the same chance of ruin5.
We have adopted the benchmark of the last chapter; each entry was calculated based on a spread of 1 to 5 units. As before, intermediate values rise linearly with the player’s expectation, with a constant of proportionality (ramp) of 3, such that the minimum wager is 1 unit, and the maximum wager of 5 units is made at an expectation of +1.67%6.
Simulation Results: 2-deck game (7) (DOA, noDAS, S17, 75% pen; Spread 1 to 5 w/ ramp of 3) | |||
Expectation | |||
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System | Core | Reduced | Full |
Knock-Out | 0.86 | 1.14 | 1.23 |
Red 7 | 0.82 | 1.08 | 1.12 |
UZ II | 0.85 | 1.16 | N/A |
Hi-Opt I | 0.80 | 1.09 | 1.19 |
High-Low | 0.81 | 1.08 | 1.17 |
Omega II | 0.85 | 1.15 | 1.28 |
In constructing this table and those that follow, we have sought to place the systems on an even playing field. As such, each system’s variation (of Core, Reduced, or Full) has approximately the same number of strategic plays to memorize that potentially deviate from the basic strategy:
The “Core” column, for each system, assumes that the only strategy deviation from basic strategy is the insurance wager.
The “Reduced” column includes only the 16 most significant matrix entries when comparing to the basic strategy. For the unbalanced systems (which behave very similarly strategically), we have adopted the 16 positions which exist in the Preferred form of the Knock-Out system (of course each system has different numerical values as appropriate for the 16 matrix positions). For the Knock-Out 6- and 8-deck simulations, only 14 plays are used (the C value is omitted). For the balanced systems, we have adopted Don Schlesinger’s “Sweet 16” set of 16 plays which are the most rewarding to memorize.
The “Full” column includes the 40 or so most significant matrix entries for all systems (much less than 40 entries for the K-O and unbalanced systems in the case of 6 and 8 decks; see Appendix III).
As you can see, the systems’ expectations are all bunched together fairly tightly. No system’s performance stands out as superior over all the rest.
Note in particular that K-O compares admirably with all other systems. Indeed, the two most popular systems in use today, the Hi-Opt I and the High-Low, are both edged slightly by the Knock-Out system. This is despite the fact that the Knock-Out system is vastly simpler to employ.
Footnotes
1 Bryce Carlson, Blackjack for Blood, 1994, CompuStar Press.
2 Lance Humble & Carl Cooper, The World’s Greatest Blackjack Book, 1980, Doubleday.
3 The side count, in principle, can be discontinued by a player. Since side counts require so much effort to implement, some may argue that a proper comparison between systems thus should be made without any such extra counts. Qualitatively, the elimination of side counts (for those systems which employ them) comes at considerable expense in expectation. In our comparison, eliminating all side counts would serve to enhance the relative performance of K-O and other singular-count systems.
4 See Appendix IV for a discussion of the effect on K-O of varying penetration.
5 See Appendix V for confirmation of this statement.
6 As mentioned in the last chapter, varying the ramping factor has little effect on the relative performance of the systems.
7 Sources for all comparisons in this chapter– Red 7: Core adapted from Arnold Snyder’s Blackbelt in Blackjack; Reduced and Full plays for 1 and 2 decks adapted from Arnold Snyder’s “The Big Tilt” article in Blackjack Forum, March, 1994; Reduced and Full plays for 6 and 8 decks based on applicable extrapolations from K-O. Unbalanced Zen II: All versions adapted from George C’s The Unbalanced Zen II. Hi-Opt I: Core and Full adapted from Lance Humble and Carl Cooper’s The World’s Greatest Blackjack Book; Reduced plays are Humble and Cooper’s matrix entries for Don Schlesinger’s “Illustrious 18” less the two splitting Tens plays, hereinafter referred to as the “Sweet 16.” High-Low: Core and Full adapted from Stanford Wong’s Professional Blackjack; Reduced plays are Wong’s matrix entries for Schlesinger’s “Sweet 16.” Omega II: Core and Full adapted from Bryce Carlson’s Blackjack for Blood; Reduced plays are Carlson’s matrix entries for Schlesinger’s “Sweet 16.”