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Best of Alan Krigman

Gaming Guru

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Which Blackjack Hands Put You in the Catbird Seat?

23 June 2003

Some combinations of player totals and dealer upcards at blackjack are favorable, at least when handled properly. Others are adverse regardless of how executed.

The junk outnumbers the jems by 11-to-10 based on probabilities of losing and winning. However, the 3-to-2 bonus on uncontested bettor blackjacks and the extra money wagered under propitious conditions by doubling down narrow the gap. These features give the game a low edge, notwithstanding proficient players averaging only 10 winning rounds for every 11 they lose.

Basic Strategy helps with a set of rules telling gamblers which decisions yield the optimal statistical return relative to what's wagered prior to each deal. Depending on circumstances, this may be the largest profit or the smallest loss. Doubling on 11 versus six-up exemplifies the former; in an eight-deck game, it's projected to win $0.670 per dollar opening bet, as opposed to $0.335 by hitting. Splitting eights against a 10 illustrates the latter; the associated theoretical loss is $0.476 per initial dollar, contrasted with $0.536 by hitting and $0.538 by standing.

Few bettors are fully aware of the situations where they have an advantage or are underdogs. The usual tendency is to overvalue certain hands, such as totals of 17 or pairs like six-six against low dealer upcards, and to assume they're in the catbird seat regardless of their own total when the dealer begins with six or less. Conversely, solid citizens tend to underrate low soft totals, especially when they call for hits and not doubles.

Players have an edge with 10, 11, 19, 20, 21, and A-A against all dealer upcards. The accompanying list gives the other hands for which punters are favored in each instance. This assumes eight decks, adherence to Basic Strategy, and no dealer blackjack on 10- or ace-up.


Hands in addition to 10, 11, 19, 20, 21, and A-A
on which players are favored to win
for various dealer upcards

Dealer
Upcard
  Player
Totals
Ace
  --
10
  --
9
  --
8
  9, 18, A-2, A-3, 9-9
7
  8, 9, 18, A-2, A-3, A-4, A-6, 2-2, 8-8
6
  5, 7, 8, 9, 17, 18, A-2, A-3, A-4, A-5, A-6, A-7, 2-2, 3-3, 4-4, 6-6, 7-7, 8-8, 9-9
5
  8, 9, 18, A-2, A-3, A-4, A-5, A-6, A-7, 2-2, 3-3, 4-4, 6-6, 7-7, 8-8, 9-9
4
  8, 9, 18, A-2, A-3, A-4, A-5, A-6, A-7, 2-2, 3-3, 7-7, 8-8, 9-9
3
  8, 9, 18, A-2, A-3, A-4, A-5, A-6, A-7, 8-8, 9-9
2
  9, 18, A-2, A-3, A-6, 8-8, 9-9
     

Soft hands and pairs are only shown when treated differently from their nominal totals. So A-8 and A-9 don't appear because they're invariably played as 19 or 20, respectively. A-7 is given for dealer three through six, when it's a double; it's not listed for two, seven, and eight, despite being advantageous as a total of 18 on which a player would stand. Ditto for 9-9 versus seven.

The always-strong 10, 11, 19, 20, 21, and A-A are the only favorites facing nines and above. The field expands markedly for dealers' eights and below. Hands that then become promising include hard nines, pairs of nines -- considered to be an 18 with seven-up and split otherwise, and soft 18 -- shown for three through six where it's a double and treated as hard 18 otherwise. Blackjack buffs are often also surprised to discover that A-2 and A-3 have positive expectations against upcards as high as eight.

Combinations other than those indicated have players swimming against the current. Hard 17, for instance, is only favorable against a six. And six-six only against dealer fives and sixes.

How good or bad does it get? The most profitable non-blackjack total prior to the dealer's draw is 21; this can't lose, but because of pushes expects to earn less than even-money -- $0.96 on the dollar. Next best are 20 versus eight and seven, respectively anticipating gains of $0.79 and $0.77 per dollar. The worst are hard totals of 16 against 9, 10, and ace and 15 against 10, all projecting to lose over half the initial bet. Which is why enlightened enthusiasts exercise the "late surrender" option when the bosses are kindly enough to offer it. And it's why the beloved bard, Sumner A Ingmark, volunteered this venerated verse:

Those who think a situation's without hope,
Haven't sought enough for strategies to cope.

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.