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Best of Alan Krigman

Gaming Guru

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When the Odds Say It's Best to Breach Basic Strategy

5 February 1996

Bona fide blackjack believers sometimes backslide. They deviate from, or at least deeply doubt, the dogma of basic strategy. Maybe they can't get themselves to split eights when the dealer has nine-up. Or are uneasy surrendering 15 to a dealer's 10. Or hesitate to hit 12 versus a dealer's two or three. Or lack the faith to double down on soft 18 against a dealer's four.

The problem? Basic strategy accounts for the probabilities of all the cards in the shoe and yields the best statistical choice for each situation. But most questionable hands are underdogs one way or another, so "best" may just be the pick of a poor litter. Solid citizens therefore remember taking a bath more often than not when "going by the book," and are tempted to try a different path. While flouting the laws of math may work on any given hand, it boosts house advantage and hurts players over the long haul.

Now and then, breaching basic strategy turns out to be technically correct and cuts the house's edge. This happens when the proportions of what's in the "bank" -- the unknown set from which the next card will come -- differ enough from the original distribution to affect the odds. Bettors who "count" the cards withdrawn from the shoe know when such conditions occur.

Card counting can get complicated. And the benefits are often minor even with sophisticated systems where tallies are used to fine-tune decisions. One counting trick, though, is worthwhile because it's simple yet yields a small improvement over basic strategy in specialized but not uncommon circumstances.

Say a player receives a two-card "hard" 16 versus a dealer's 10. In descending order of preference, basic strategy indicates:

1)if the 16 is a pair of eights, split it into two hands;

2)if the 16 is not a pair of eights, surrender when this option is available;

3)if neither of the above apply, draw an additional card.

What happens as the relative proportion of high cards in the bank increases? There is a correspondingly greater chance that a hit will put the hand over 21. Some counting systems consider this phenomenon and make standing the third choice when the likelihood of drawing a high card is known to be enough above normal.

Assume you have no idea what's been dealt previously, and look only at your own hand and the dealer's upcard. The bank will be rich at the high end when an excess of low cards is exposed.

The percentages and probabilities have been precisely calculated. For practical purposes, the mathematical mumbo-jumbo reduces to an easy rule. Think of low cards as those which will improve a 16 -- ace through five; high cards are the rest -- the breakers. Ignore basic strategy and stand when your multi-card hard 16 and the dealer's 10-up, combined, show an excess of low cards.

Hard 16 starting hands always comprise two breakers -- six-10, seven-nine, or eight-eight. With the dealer's 10, this exposes three excess high cards; the bank is low-end rich so you follow basic strategy. What if you start with four-five and pull a seven, or ace-five and draw a 10? Including the dealer's 10, you'd see equal numbers of low and high cards; this case is marginal -- purists would stand but hitting is OK. Now imagine you're dealt a two-three then draw another three followed by a four, an ace, and a three; including the dealer's 10, you now see five excess low cards. Stand because the bank is high-end heavy.

The laws of probability also indicate when to stand on 16 versus nine and 15 versus 10. In six- and eight-deck games, however, the corresponding required excesses of low cards are so large they can't occur in a single hand, so these criteria require full-blown card counting.

Relief from the rules of basic strategy recalls the rhyme of Sumner A Ingmark, lovingly lauded as the law-and-order lyricist:

I know and use the time-worn rules,
'Cause doing so seems smart.
Picasso used not rules but tools.

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.