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Winning at blackjack: how much is luck and how much is skill?14 June 2010
What causes players to win at blackjack? An amalgam of luck and skill. Luck: getting a healthy helping of highly hopeful hands. Skill: knowing how to handle whatever comes along, to maximize the expected profit or minimize the expected loss inherent in the cards involved in each decision. The first, they can't control. The second is where Basic Strategy enters the picture.
A decent proportion of blackjacks is critical. Uncontested blackjacks are not simply clean wins. The 3-to-2 payoffs sharply lower house advantage. By the numbers, in eight-deck games, players average uncontested blackjacks approximately once every 22 hands – a frequency of about 4.5 percent. Ditto for dealers, to be sure. The difference is that solid citizens are paid an extra half bet, while dealers get only what's at risk. Multiply the bonus half unit by the frequency; the resulting 2.25 percent is the decrease in what otherwise would be the casino's edge.
If, by random chance, players receive blackjacks appreciably more often than once every 22 hands, the payoff bonuses can quickly mount and the edge in the game could easily shift to their favor. The converse is likewise true. Substantially fewer blackjacks than 4.5 percent can make a table seem bankroll-breakingly cold.
Blackjacks are gimme's. Well, almost. Two issues do arise. First, whether to trade payoffs below 3-to-2 for other goodies (the extras typically cut edge less than the 3-to-2 payoff). Second, whether to insure a blackjack when the dealer has ace-up (this returns edge to the house, but guaranteed even money sometimes has more utility to a person than a statistically better nine ways to earn 3-to-2 versus four to push and none to lose).
Hands appropriate for doubling under Basic Strategy are also important. On the average, players will have this opportunity a bit over once every 10 hands -- a frequency around 9.6 percent. True, they must win a fair share of these doubles, given the extra money at risk. This doesn't always happen. And a string of doubles gone awry can be ruinous. Still, prospects are positive – players have an edge – on 100 percent of all proper doubles.
Split pairs are another matter. They're expected to occur roughly once every 39 hands, a frequency just under 2.6 percent. Of Basic Strategy splits, slightly over two-thirds – 67.5 percent -- have positive expectation. The remaining third are projected to break even or lose more money than they win on the average. Enquiring minds may want to know why anyone should match the money already up for grabs by splitting pairs that are projected to lose a third of the time. It's because the average loss in these adverse instances is less by splitting than by the other alternatives. So, while the house's edge isn't overcome, it's reduced.
Together, doubles and splits account for roughly one in every eight hands – 12.2 percent. Blackjacks, contested as well as uncontested, are another 4.7 percent. This leaves Basic Strategy mandating standing on one out of 2.5 hands – 40.6 percent, and hitting one out of 2.4 – 42.4 percent.
It's comforting, while not necessarily rewarding, to stand with a 20 when facing a weak dealer upcard. But not all hands designated for standing are this promising. A player may be glad to be able to stop with 16 against three, yet is more apt to lose than win.
Some hits are weak. A 16 against seven or higher may win with a hit, but it's an underdog. Even apparently strong hits are not without anxiety. Hitting nine versus seven has a solid positive expectation of $0.17 per dollar bet. But it's hardly a lock.
Overall, situations calling for players to stand are stronger than those in which "the book" decrees a hit. Of non-blackjack Basic Strategy stands, 48.9 percent have positive expectation. Of Basic Strategy hits, 13.1 percent have positive expectation.
Which counts for more, luck or skill? Louis Pasteur reputedly said, "luck favors the well-prepared." The punter's poet, Sumner A Ingmark, thusly disparaged depending on the fortuity of fate:
'Though a few may be successful, the many just go bust.
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