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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Veering away from "the book"

21 September 2009

Playing blackjack "by the book" minimizes house advantage or edge in the game. For any given bettor's hand and dealer's upcard, Basic Strategy uses this criterion to decree when to hit, stand, double, split a pair, or surrender. The rule yields the highest long-term average or statistically expected gain for propitious combinations, and the lowest such loss in adverse situations.

The data show that, for 6-3 versus 7, players are favored whether they hit or double. Basic Strategy is to hit because this action returns an average profit equal to 17.5 percent of the initial bet, while doubling is projected to be worth only 11.3 percent of the opening wager. This would be $1.75 and $1.13 for hitting and doubling, respectively, with a $10 bet prior to the deal.

Nobody who bets $10 actually gets paid $1.75 for hitting or $1.13 for doubling, however. In practice, a player can win $10, push, or lose $10 by hitting, and win $20, push, or lose $20 by doubling. In either case, chances are greater of winning than losing, as shown by expectation being positive for both options.

Now that you know expectation is positive for doubling as well as hitting 6-3 versus 7, would you be tempted to go for the former with these cards, Basic Strategy aside. The incentive would be a better than even chance to grab a quick $20 rather than $10. Over the long term, say 10,000 instances of this combination, hitting would bring in approximately $17,500 while doubling would net roughly $11,300. But, what about the short term of a single hand?

One way to answer this question would be to weigh the chances of winning or losing with one or the other alternative. Ignoring pushes and considering only wins or losses, players who hit have 58.75 percent prospect of joy and the complimentary 41.25 percent of sorrow. The corresponding values for doubling are 52.83 percent likelihood of ecstasy and 47.17 percent of agony. That's a 5.93 percent decrease in probability of success by doubling.

Here are the chances of triumph for some other situations in which doubling has positive expectation, but hitting is ordained by Basic Strategy.

* 5-3 vs 6: 56.04 percent by hitting and 52.48 percent by doubling, a decrease of 3.56 percent by doubling;

* A-2 vs 4: 55.17 percent by hitting and 51.64 percent by doubling, a decrease of 3.53 percent by doubling;

* 6-2 vs 5: 53.89 percent by hitting and 50.45 percent by doubling, a decrease of 3.43 percent by doubling;

* A-3 vs 4: 54.07 percent by hitting and 51.62 percent by doubling, a decrease of 2.45 percent by doubling;

* 7-2 vs 2: 53.78 percent by hitting and 51.70 percent by doubling, a decrease of 2.09 percent by doubling.

Should you take a shot? Unless you're one of those solid citizens who believes that violating Basic Strategy is punished by a change in the proverbial "flow of the cards" that ruins the table for everyone, it's a point to ponder. Raising the stakes when you know you have a positive expectation is certainly appealing. But will you accept the reduced odds of being successful?

Whether you're amenable to making the tradeoff is a matter of personal preference and gambling style. There's no absolute right or wrong. You can sink or swim either way depending on the next card that happens to fall. The figures, though, afford a basis for a decision that works for you. The renown rhymer, Sumner A Ingmark, composed this couplet about just such a conundrum:

Is it wise to be bold and go for the gold,
Or to lower the stress and settle for less?

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.