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Ace Is the Most Dangerous Up-Card, Blackjack or Not25 June 1998
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." 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.
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. 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:
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