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Best of Alan Krigman

Gaming Guru

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Distinctions between Right and Wrong in Blackjack Are Often Slender

4 March 2003

Blackjack buffs rarely make grossly outrageous decisions, like hitting hard 19 or standing on soft 14 regardless of the dealer's upcard. And some doubt, but few flout, edicts such as stand on 10-10 rather than split the pair against a dealer's stiff. This, despite passing fancies that doing so might actually be wise.

Of course, you can lose by playing strong hands perfectly, and win by starting weakly and picking the worst available option. But, mainly, situations that separate proficient players from duffers entail fine distinctions. It's worth knowing what the laws of probability proclaim as proper on the close calls, but also rewarding to recognize how narrow the leeway may be.

Pairs of eights against a 10-up are among the hands most hotly debated by solid citizens who toe the line precisely, and those who can't believe the gurus got it right. You're the underdog no matter what. Statistically, the least of the evils is to split the pair, so this is Basic Strategy. On the average, splitting is projected to lose $6.02 and $6.06 less per $100 bet than hitting with eight- and six-deck shoes, respectively. It beats standing by $6.15 and $6.20 in the corresponding games. Not much, when you realize you have to risk at least $100 more to split the pair.

Contention aside, pairs of eights aren't the most tenuous entries on the wallet-sized charts. Consider a two-card 12 against a dealer's 4-up. Neither standing nor hitting is promising, as is sadly evident from the accompanying "expectation" table. The data show theoretical losses ranging between $20.249 and $21.539 per $100 bet. Almost everybody stands, and it's a better choice -- albeit marginal at under $1 per $100 bet for any particular situation. Better, except for one little irregularity.

Expected loss per $100 bet playing two-card 12 against
4-up in six- and eight-deck blackjack

eight decks
six decks
hand
standing
hitting
standing
hitting
10-2
$21.110
$21.116
$21.112
$21.036
9-3
20.881
21.492
20.804
21.539
8-4
20.787
21.364
20.679
21.368
7-5
20.466
21.111
20.249
21.028

 

In all but one instance, standing is predicted to average less of a loss than hitting and is therefore recommended. The exception, which you surely spotted, is on 10-2 in a six-deck game where hitting beats standing by $0.076 per $100. Most Basic Strategy charts don't even point out this anomaly, chiefly because it's such a small amount and involves the composition of a hand rather than just its total. But there it is, and hitting is "correct."

You can picture intuitively why 10-2 might be unique. Starting with 9-3 or 8-4, one nine or one eight -- ranks that could complete strong hands -- are already gone from the shoe; this cuts prospects of success. Beginning with 7-5, one seven and one five, two ranks that could complete moderately good hands, are unavailable; this also trims chances of triumph. The desirable fives through nines are all still available when you have 10-2, and one 10 -- which you don't want -- is removed from the supply.

The six- versus eight-deck difference is more obscure. Chances of finishing with various totals, shown in accompanying probability table, suggest the effect. You're slightly more apt to end up with a 17, 18, 19, 20, or 21 and less under 17 or over 21 with six than eight decks. This, plus a minor shift in the likelihoods of the dealer's ending hand, account for the disparity.

Probabilities of alternate finishes after
hitting a two-card 12 against a dealer's 4-up

Final tally
six-deck
eight-deck
under 17
30.4207%
30.5085%
17
7.7670%
7.7482%
18
7.7670%
7.7482%
19
7.7670%
7.7482%
20
7.7670%
7.7482%
21
7.7670%
7.7482%
bust
30.7443%
30.7506%

 

So, next time you're tempted to grumble at someone for "playing wrong and ruining the table for everyone else," remember: 1) Basic Strategy involves expectations and not some mystical flow of the cards; 2) the difference between right and wrong is often minuscule; 3) a decision you think is stupid may actually be astute. Or, as the rhymer of fine lines, Sumner A Ingmark, said:

Accomplishment's the best rebuttal,
When dealing with distinctions subtle,
And lines 'tween what won't work and what'll.

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.