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# Why "the Book" Says What It Does for Aces, Eights, and 11s vs Aces

27 May 2003

Every blackjack buff has heard the hortation: "always split aces and eights regardless of the dealer up-card; always double on totals of 11 except against aces." Yet many bettors question it. Realizing that a 10 in the hole renders any choices moot, they wonder about wasting twice as much money in tight spots with the weak splits, or giving up the premium with the strong double.

The bottom line, for beavers eager to skip the dull details, is that Basic Strategy optimizes statistical expectation in each situation. You can forfeit twice as much on aces and eights or gain only half as much on 11s. But that's not why "the Book" says what it does. The rules minimize losses and maximize profits in terms of long-run averages. Where the laws of probability prophesy bankrolls will tend to be after extended play.

The ace-up is the sticky wicket. It's the greatest threat a dealer can issue. Principally because it leads to busts less often than any other card -- 11.5 percent of the time. Overall, against an ace, players have worse than 34 percent disadvantage.

Look at the aces, eights, and 11s separately against the ace to see how the prospects for these hands work out in practice.

With the pair of aces, splitting has positive expectation while the alternatives yields negative results. Per dollar bet at the outset of a round, splitting anticipates a gain of almost \$0.13. Hitting forecasts a loss of about \$0.02. Doubling ranks only slightly less disastrous than standing, \$0.62 versus \$0.67.

A 16, per se, is junk no matter what it faces. But a split pair of eights, when doubling is allowed after splitting, favors the player against seven and below. On a dealer's eight and above, splitting is also mathematically correct. However, it's a "defensive" tactic that doesn't turn the tide from adverse to advantageous, but reduces the presumptive damage. Per dollar bet when the round starts, splitting eights against ace projects a loss of \$0.38 -- hardly happy, although it beats hitting and standing with expected losses of \$0.51 and \$0.66, respectively.

Doubling on 11 against an ace, despite the wallet-size crib sheets dictating a hit, is the opposite case. Players are in the catbird seat either way. Again, use a dollar bet at the beginning of the round as a reference. Hitting is forecast to average nearly \$0.15 profit. Doubling, the predicted gain is between \$0.12 and \$0.13 depending on the cards comprising the 11.

Going strictly by expectation, the choices against an ace-up are therefore unambiguous. Split pairs of aces and eights. Hit 11s. But, is expectation the be-all and end-all of gambling?

With pairs of aces, the high penalties make hitting tough to defend and doubling is demented. Maybe, if you'd just bet your last buck, hitting might outweigh buying-in for more money.

With eights, you may hesitate to put twice as much at risk and still be the underdog. And while a theoretical loss per dollar of \$0.51 by hitting is worse than \$0.38 by splitting, you may deem the difference a fair price to pay when the reality is a good chance of sending \$2 rather than \$1 down the proverbial tubes.

On the 11, the sacrifice of a theoretical \$0.02 or \$0.03 may not seem like a serious detriment when the upside is to earn twice as much by doubling. To make an informed choice, though, consider how the profit is derived. To average \$0.15 gain with \$1 at risk, a little high school algebra shows you winning 57.5 percent of all decisions (meaning wins or losses, ignoring pushes). To average \$0.13 gain with \$2 at risk, the same arithmetic has you winning 53.25 percent of all decisions. So the lower expectation is accompanied by a 4.25 percentage point drop in the likelihood of winning the hand at all, with twice as much money at risk. Still worth taking a shot? You may think so if you try it and succeed. Give it a go and fail? Well, as the Tennyson of 20-20 hindsight at the tables, Sumner A Ingmark, attested:

Gamblers confident, resilient,
Know they win because they're brilliant.
Losing never steals their thunder,
'Cause it's someone else's blunder.

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Best of Alan Krigman
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.