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Best of Alan Krigman

Gaming Guru

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How Often Can You Expect to Split or Double in Blackjack

8 March 1999

House advantage in blackjack results because the player's hand is decided after the dealer's. Players therefore lose by going over 21, even if the dealer later busts. The standard casino rule, hit below 17 and stand thereafter, leads to about 28 percent chance of breaking. If players also adhered to this practice and all wins paid 1-to-1, edge would be roughly 8 percent -- equivalent to the (0.28)x(0.28) chance of simultaneous breaks.

The casino automatically reduces this advantage to about 5.5 percent by paying 3-to-2 for winning blackjacks. Bettors can trim the edge further, to about 2 percent, merely by being smart and standing with totals under 17 against certain dealer upcards and hitting soft 17 (A-6) and soft 18 (A-7) against others. They can shave the edge more, to a fraction of a percent, by exploiting opportunities to split pairs and double down. However, the old Bezonian adage, "ya gotta risk woe if ya wanna win dough," applies because these options require making additional wagers.

Solid citizens, in sizing bets, should therefore consider the possibility they may want to slide out extra money during a round to split or double. What's the sense of rationally or otherwise pressing aggressively prior to the deal, then because big bucks are at stake, spurning an opening to increase expectation by splitting or doubling? Sure, it's a here-and-now thing when it happens -- you pull six-five against a dealer's four and decide whether you can afford to double or must simply hit. But say the cards haven't been dealt yet. You're thinking about pumping your bet. You know the butterflies would go on a rampage in your stomach if get into a position where basic strategy says to split or double. Before going hog wild, weigh the odds you'll have a hand the gurus tell you demand those additional dollars.

The probability you'll receive a hard nine, 10, or 11 against an upcard appropriate for doubling is 8 percent. The chance you'll have a soft hand against an upcard favorable for doubling is 1.6 percent. The total -- 9.6 percent -- means you can anticipate the opportunity to enhance your stance by doubling on an average of one out of every 10 or 11 hands. Likewise, the probability that you'll be dealt a pair against an upcard fit for a split is 2.55 percent. This is approximately one out of every 40 hands.

Combined, the chance you may want to place twice your initial wager at risk during a round to go for a propitious double or split is 12.15 percent. This exceeds once in every eight hands. It's frequent enough to be seriously contemplated in sizing your normal bet, or when the hunch fairy urges you to impress the pit boss and raise your wager during a game.

Situations also arise in which even greater multiples of your original wager come into play. For instance, some casinos allow resplits to three hands; the probability you'll draw cards where your illusions of grandeur are supported by the statistics of this strategy is 0.4 percent -- one out of every 250 times. Similarly, a triple bet is needed to double on one side of a split pair; the chance of doing so under promising conditions is 0.7 percent -- once per 140 hands. Together, the likelihood a player following basic strategy will want to bet three times the starting amount is 1.1 percent or about once in every 90 hands.

Even higher multiples are possible, although the prospects are low enough not to be a major factor in sizing bets. As an example, following basic strategy, the chance you'll split then get a shot at doubling on both sides -- quadrupling your original wager -- is roughly 0.08 percent or once in every 1,250 hands.

Players who sweat over multiple units can always forego a split or double and take the next best option. In general, you forfeit the least expectation by skipping soft doubles, then by hitting rather than splitting low pairs against low upcards. Still, it's wisest to anticipate the auxiliary bet before starting each round, so you're comfortable risking more when conditions warrant. As the rhymer of risk, Sumner A Ingmark, wrote:

If you wince when the chance comes to double or split,
Then the size of your bet and your bankroll
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.