Knock-Out Blackjack, page 3
In the Knock-Out system, we are striving for the best blend of simplicity and power. Hence, we recommend the use of the generic basic strategy, which is applicable in all games, from hand-held single decks to 8-deck shoes. The complete generic basic strategy chart is presented in the table on page 27.20
To apply the basic strategy table, locate your two-card hand in the leftmost column, then move across to the entry corresponding to the dealer’s upcard. For example, if you’re dealt ace,7 (soft 18) and the dealer has a 5 as his upcard, you should double down if possible; otherwise you should stand. Alternatively, if you hold 7,7 and the dealer shows a 7 as his upcard, you should split the pair instead of hitting the 14.
The basic strategy should be memorized. This is not as daunting a feat as you might first think. In fact, if you’re at least a casual player, you probably know most of it already.
There are several general patterns to observe that will aid in understanding and memorizing the basic strategy. First, most of the splitting occurs against weak dealer upcards. Aces and 8s are always split. The splitting of 8s is often a defensive play, since a poor hand of 16 is potentially converted into two reasonable hands. The splitting of aces is mostly offensive, as a mediocre hand is converted into two strong ones. Pairs of 4s,21 5 s, or tens are never split; doing so would generally weaken the hand.
Of interest is the play with a pair of 9s. We go ahead and split them against a 6 or less. In this case, the split is an offensive maneuver as we’re trying to kick the dealer when he’s down. Against a 7, though, we stand; the chance of a dealer busting with a 7 up is much lower than with a 2 through 6 up (roughly 26% vs. 40%). Furthermore, the chance that a dealer will reach a total of exactly 17 rises dramatically (to 37%), hence there’s a good chance that our 18 will win by the slimmest of margins. Against an 8, we split 9s in an offensive move. Splitting 9s against a 9 is an attempt to salvage a losing hand. Against a ten or ace, we take a deep breath and stand with our 18; there’s not much else to do but wait for the likely coup de grace.
Doubling-down plays typically occur against a weak dealer upcard, where the introduction of an additional wager is most warranted. We generally double down if we expect to win the hand and expect to want only one hit.
Let’s also look at the hitting and standing strategy relative to dealer’s bust percentages by upcard. If you’re holding a stiff hand (12-16), you generally hit against a strong dealer upcard, since he’s likely to reach a pat total of 17 through 21. However, against a weak dealer upcard, you generally stand, forcing the dealer to draw with an increased frequency of busting. Again, a good mnemonic crutch (though not always true) when holding a stiff is to play your hand assuming the dealer has a ten in the hole—a reasonable rule of thumb given that there are four times as many tens as any other card in the pack.
JUDICIOUS BASIC STRATEGY PLAY
Some players have trouble adhering to the basic strategy. One rule in particular that many have a hard time understanding is the hitting of stiff hands. For many, it’s particularly difficult to hit a hard 16. Since the player has such a great chance of busting, it’s easy to balk at taking a hit, especially if the dealer has a 7 showing. The dealer’s 7 is not that strong, they reason, so why risk busting. The ulterior motive, of course, is to last longer. “You stay, you play,” right?
In fact, this strategy will cause them to play less overall because they increase their loss rate. It turns out that by standing with 16 vs. a 7, the player loses about 48¢ for every $1 wagered. On the other hand, by hitting, the loss is only 420¢ Now, a difference of 60 might not seem like much, but it adds up. With a $25 bet out, making the incorrect play in this situation will cost you an average of $1.50.
Looking at the choice in terms of win/loss/tie percentages (rather than dollar amounts), an analysis shows that players who stand will win only if the dealer busts, with probability 26%. By hitting, the chance of winning is increased to 27%, and there is roughly a 4% chance of pushing. Overall, it may seem like you have a better chance by standing with a 16 versus a 7, but most of the time you are gaining only a brief respite before your demise. Sometimes, as in this case, the correct basic strategy play is the lesser of two evils. It’s not that playing correct basic strategy will turn bad hands into good ones; it’s that proper basic strategy tends to minimize losses on those bad hands.
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A similar line of reasoning can be applied to the other basic strategy plays. In the end, it’s a comparison of expected value that determines the best option.
The basic strategy must be followed exactly. There’s no room for superstition or hunches. In the example given earlier, even if you’ve hit 16 vs. 7 three times in a row and busted each time, you’ve got to do it again when presented with the same situation. On the other hand, if the last time you hit 16 vs. 7 you hooked a 5, you may feel inclined not to press your luck. Here again, though, you must; in the long run, it is the best mathematical play. Don’t let your emotions be your guide; this is exactly what the casinos want.
A WORD ON INSURANCE
The basic strategy says to never take insurance. Don’t even consider it. Despite what casinos would have you believe, insurance is a bet solely on whether or not the dealer has a natural. Since the ace is already showing, you’re wagering on whether or not the downcard is a ten.
The insurance bet neither increases nor decreases your chances of winning the main bet. As such, taking insurance is strictly a side bet. Whether or not you win it, the main hand will be played to its completion. If the dealer has the natural, then insurance pays 2 to 1, but the main hand is lost (unless you, too, have a natural and push); if the dealer doesn’t have the blackjack, the insurance bet is lost and the main hand is played out in the normal fashion. Either way, you can see that your insurance bet doesn’t “buy” you anything on the main hand.
We can easily estimate the disadvantage of taking insurance. With no knowledge of cards played, we can assume that the remaining cards are in roughly the same proportion as in the full pack. Thus, regardless of the number of decks in use, the chance of the downcard being a ten (10, jack, queen, or king) is roughly 4/13. On the other hand, the chance that the downcard is not a ten (ace through 9) is roughly 9/13. The expected outcome for each dollar wagered on insurance is then roughly:
You can expect to lose 1/13 of every $1 wagered on insurance, corresponding to an expectation of nearly –7.7% (or a loss of 7.7¢ per $1). Without any other information about deck composition, insurance should never be taken.
BASIC STRATEGY STRENGTH
What can you expect (in terms of return percentages) when you play blackjack by the basic strategy? It depends on the game you’re playing; the number of decks being dealt and the rules in force affect the expected return. For almost all games you encounter, the basic strategy player’s expectation is between –0.7% and +0.1%. The majority will actually be between –0.6% and 0.0%.
We’ve generated the following table to guide you in estimating the approximate effects of rules variations on the basic strategy player. (The table was generated by simulation assuming our generic basic strategy and should be used only as a guide. The effects of rules variations often depend on the number of decks in play. We have assumed the average effect for the purposes of constructing the table on pg. 36.)
The benchmark is for the set of rules often referred to as the “Las Vegas Strip game.” The top-of-the-deck expectation is effectively –0.02%, making it nearly an even game.23
To estimate the expectation for a particular game, we can, to a good approximation, start with the benchmark and adjust for any rules changes by simply adding their effects.
For a typical Atlantic City (or Foxwoods, Conn.) game, the difference from our benchmark is the use of 6 or 8 decks and the allowance of doubling after splitting. Hence we can estimate our expectation for the 8-decker to be the following:
Benchmark –0.02%
Eight decks –0.55%
Double down after pair splitting +0.13%
Approx. player expectation –0.44%
For a downtown Reno game, typical rules are dealer hits soft 17 (the other dealer hit/stand rules remain the same) and players may double down only on two-card totals of 10 or 11. For a 2-deck Reno game, the expectation is significantly worse:
Benchmark –0.02%
Two decks –0.32%
Dealer hits soft 17–0.20%
Double down only on 10 or 11 –0.21%
Approx. player expectation –0.75%
For a single-deck Reno game, the expectation is about –0.43%, in the ballpark of a multiple-deck shoe game on the East Coast or in Las Vegas. Trade-offs like this, where multiple-deck games have more liberal doubling and splitting rules (or alternatively, single-deck games impose restrictive doubling), are commonplace and can often be found within the same casino.
Rules variations from casino to casino can have a significant impact on your expectation, hence earnings. Independent of finding favorable card-counting conditions as described later in this book, we recommend always playing the best available game. Though this may require going to a different casino, often all that’s needed is a short walk around the pit. It’s not uncommon for a single casino to offer a range of games with basic strategy expectations that differ by 0.3% or more.
Before we take a look at some of the entries in the “Effect of Rules Variations” table, a few words on the effects of multiple decks are in order. Why, for the same basic strategy, does a multiple-deck game have a worse expectation than a single-deck game? Peter Griffin, in The Theory of Blackjack, gives three primary reasons: natural 21s occur less frequently in multiple-deck packs; doubling down is less advantageous in multiple-deck packs; and “judicious standing with stiff totals” is less advantageous.
These consequences each occur because, as you might expect, the effect of removing individual cards is more pronounced in single-deck than in multiple-deck games. For example, when doubling with a hand of 7,3 against a dealer upcard of 4, the player is hoping to get either an ace or a ten. Considering the three cards in play, the player still has four aces and sixteen tens available. The chance of drawing one of them in a single-deck game is therefore 20/49 (or 0.408). In an 8-deck game, on the other hand, the chance would be considerably less at 160/413 (0.387), a success rate only 95% that of the single-deck game. You can see that the three cards already in play (in this example) improve the player’s chances for success in the single-deck case.
Here’s another example of this effect. Consider one of the key advantages afforded the player: the bonus paid on naturals. In an 8-deck game, the “off-the-top” chance of receiving a two-card total of 21 is 4.75%, while in a single deck it’s 4.83%. Even more striking, assuming we have a natural in hand, the chance that the dealer also possesses one is a sensitive function of the number of decks in play. In an 8-deck game, the dealer’s chance of duplicating our natural is 4.61%, while in a single deck, it drops precipitously to 3.67%.
Clearly, the more restrictive the doubling-down rules, the more the player is hurt—though not badly. It may seem that restricting doubling down to only 10 and 11 should “cost” us more than 0.21%. But in reality, most of the gain in doubling down comes from these two plays. In addition, it may seem that allowing double downs on any number of cards should be worth more than 0.24%. However, on soft hands, the double has usually occurred (if at all) on the initial two cards. Furthermore, being dealt a three-card total of 10 or 11 happens very infrequently.
A game where the dealer wins all ties is catastrophic to a player’s profitability. Even card counters will be unable to beat this game. Charity-night blackjack games often incorporate this “feature” to ensure that the house makes money during the event.
A SIMPLIFIED BASIC STRATEGY
For those new to the game, the basic strategy as presented may seem a bit intimidating. As such, we’ve boiled down the rules to a simplified set for novices. While the simplified set is sufficient for casual play, the simplification does come at the expense of power. For a typical game, using the simplified basic strategy costs you an extra 0.35%, compared to our generic basic strategy expectation. Thus, in a benchmark 6-deck game, your expectation would be roughly –0.90%, still an expected payback in excess of 99%, which is better than almost any other game you can play in a casino.
SUMMARY
• Basic strategy is a set of playing rules based on the cards in your hand and the dealer’s upcard.
• Deviation from the basic strategy, without any other information about deck composition, will cost you in the long run.
• In principle, the basic strategy matrix is slightly different for different playing conditions. However, the differences are subtle and minor. The change in expectation between applying our generic basic strategy table and the appropriate exact table, which is a function of the number of decks and rules in force, is typically 0.03% or less, and therefore, not worth the effort to remember.
Round 3
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An Introduction to Card Counting
Chance favors the prepared mind.
—Louis Pasteur
You may be wondering what makes blackjack different from other gambling games. Why is it that a skilled player can beat blackjack, but has no hope of ever beating a game like craps over the long term? It boils down to the mathematical concept of independent and dependent trials.
In games like craps, roulette, slot machines, big six, Let It Ride, and Caribbean Stud, each and every round is independent from all other rounds. Even if a shooter has thrown a natural on four straight crap hands, the chances of success or failure on the next hand do not change. In fact, there is no information whatsoever to be gained by studying the outcome of previous trials.24 There is no point in trying to jump in on “hot” streaks and exit early on “cold” streaks; there is no predictive ability.
In blackjack, successive hands are dependent events. This means that past events can and do influence what happens in the future. Specifically, the cards already played affect the composition of the remaining deck, which in turn affects your future chances of winning.
Consider a single-deck blackjack game. If, in the first round after a shuffle, player one is dealt a pair of aces, while players two and three each receive naturals, then we have useful information about what may take place in the future. First, we know that no naturals can appear in the second round. Why? Because all four aces have already appeared in round one. In this instance, the players are at a severe disadvantage (and the house is at a correspondingly high advantage). Card counting identifies those times when the deck composition favors the player, allowing us to bet more when we have the advantage.
We note that baccarat, like blackjack, is a game of dependent events. However, in the case of baccarat, only a tiny advantage can be gained through the tracking of cards. This comes about because the banker and player draw to very similar fixed sets of rules, the result being that no card strongly favors either the player or the dealer.25
In Chapter 2 we learned that by finding a good blackjack game and playing basic strategy, we can chop the house advantage down to between 0% and 0.5%. Keeping track of the cards (counting) will allow us to push over the top to secure an advantage.
COUNTING GUMBALLS
To illustrate the concept of dependent trials, let’s take a step back into our childhood.
You’re at the local grocery store, and standing before you is a gumball machine filled with exactly 10 white and 10 black gumballs. You know this because you saw the store manager refill it just five minutes ago. All the balls are thoroughly mixed together, and there’s a line of kids waiting to purchase them.
Your friend, being the betting type and needing only a couple more dollars to buy that model airplane he’s been eyeing, makes the following proposition. You are allowed to bet $1 (let’s pretend we’re rich kids) whenever you wish that the next ball to come out will be white. If a white ball comes out, you win $1. If a black ball comes out, you lose $1. Sounds like a simple enough game, you say to yourself.
If you bet right off the top, there are a total of 20 gumballs, of which 10 will win for you. Your chance of winning is thus 10/20, or simply 1/2. Not surprisingly, your chance of losing is also 1/2. So your expected outcome is simply:
The expected outcome of 0 implies that, over the long run, you are expected to neither win nor lose money if you bet on the very first ball. Of course, each individual wager will result in either a $1 win or a $1 loss, but over time your expectation is to net 0 on this 50/50 proposition.
Let’s say, however, that one gumball has already come out, and you know that it was white.
Since there are now 10 black balls (losers) and only 9 white balls (winners) left, making the bet would place you at a disadvantage. Your chance of winning is 9/19, but your chance of losing is 10/19. The expected outcome has become:
For every $1 you wager on white at this point, you expect to lose 1/19 of $1, or a little more than 5¢. That is, in the long run your expectation is to lose 5.26% of your wager. Again, each individual wager will result in either a $1 win or a $1 loss, but over the long haul you will lose more often than win, which leads to your demise at an average rate of 5¢ per play.
