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# Ace Is the Most Dangerous Up-Card, Blackjack or Not

25 June 1998

Rogue theories of gambling are based other than on the math and logic of probability and utility. You can usually spot rogue theories, even if you're uncertain about the statistical engine driving a game. The clue is that players vehemently defend oddball strategies with arguments starting: "Here's my theory..."

A rogue theory that's recently been ravaging blackjack bankrolls involves splitting and doubling against a dealer's ace-up. Two players at my table were doing it last week. One of these solid citizens, a \$25 bettor, took insurance then split a pair of threes. He pulled eight on the first, doubled down, and drew another eight - total of 19. He got seven on the second, doubled, and drew nine - also, total of 19. The dealer turned over four and drew five - total of 20. The player lost \$112.50.

"That was risky," I politely noted. "Not really," the player shot back. "It didn't work that time. But I've made more than I've lost by doing it. Here's my theory..." He then proceeded to elaborate. "If the dealer had blackjack it wouldn't matter. I'd have pushed - lost one bet, won it back on the insurance. With no blackjack, aces are just low cards - and anyone would split threes and double on 10 or 11 if the dealer had two-up."

"I'm not sure that's right," I replied. "Aces are dangerous up-cards, blackjack or not." But I could see a hassle coming. So I sidestepped, saying I'd think about it, and dropped the subject.

You can picture the problem with this rogue theory two ways.

First, consider the following table. Entries give probabilities a dealer will bust or get various final results with ace-, deuce-, or 10-up, assuming no blackjack. Values are for six decks, dealer stands on soft 17; other common variations yield similar chances. The key percentages for splitting pairs and doubling involve the dealer busting, because players may well find themselves drawing to stiffs or stopping with low point totals. The figures show, from this perspective, aces are not only about twice as tough as deuces, they're also one and a half times worse than 10s.

 final point total dealer upcard ace 2 10 bust 16.6% 35.4% 23.0% 17 18.8 14.0 12.1 18 19.0 13.4 12.1 19 18.8 13.0 12.1 20 19.0 12.4 36.9 21 7.8 11.8 3.8

The second way to judge the pros and cons of different actions when the dealer is showing an ace is to compare expected long-term gains or losses associated with alternate choices, again when the dealer doesn't have blackjack.

Detailed analysis shows that absent a dealer blackjack, splitting pairs of aces against ace-up yields expected profit of about \$13 per \$100 bet, while hitting or doubling are projected losers. Splitting eights against ace is also statistically correct; it cuts expected loss from \$56 per \$100 initial bet for hitting and \$50 for surrender to \$39 for splitting. Splits of other pairs all anticipate worse results than hitting or standing.

Doubling never has higher expectation than hitting against an ace in a six-deck game. For instance, doubling 11 in this situation yields an expected profit of about \$12 per \$100 initial bet; hitting raises this to nearly \$15 per \$100 bet. A point total of 10 shows an expected gain of \$8 per \$100 initial bet by hitting; 10 becomes an expected loss when the hand is doubled.

Basic strategy follows from the laws of probability. Certain deviations from "the book" are sanctioned for individual gambling goals by utility theory. Rogue theories, however, bespeak technical naivete of the type that leads to belief in abductions by aliens from outer space, extrasensory perception, and the power of intoning the numerological sequence 9-1-1 to summon help when in need. But, I'd better stop here, or we'll soon be wondering if gamblers are superstitious. Instead, I'll conjure up the heretofore lost mumblings of the mystic muse, Sumner A Ingmark:

Conclusions reached wrongly,
Are argued most strongly.

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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.