Hope and Science in Dollar Stores, Used Car Lots, and Casinos

Everybody occasionally runs into something that seems too good to be true. Strange how often it's at 99-cent or dollar stores, used car lots, or casinos. Experience ought to prepare people to know better. But Alexander Pope had it nailed in 1733 when he wrote, in An Essay on Man, "Hope springs eternal in the human breast" and also lamented, "His soul proud Science never taught to sway."

Video poker variations with wild cards and machines offering "more ways to win" or secondary bonus rounds nurture such hope. And while table snobs may scoff at slot low-brows who don't believe bosses give with one paw and grab with the other, the green felt is no less apt to engender similar spurious optimism.

You may spot a new version of blackjack fitting this paradigm at your friendly neighborhood gambling den. At first glance, it looks like the answer to the prayers of players who've wished they could swap their top cards with the folks beside them.

Say you start with a 10 and a yokemate begins with a six; the dealer shows an eight-up. You top off with a five and watch your comrade get a nine. So you're each weak with totals of 15. Your expectations are to lose $0.42 on the dollar apiece. If you could exchange top cards without cheating, you'd both be strong. Per dollar bet, your 19 would be worth a theoretical profit of $0.59 and your new best pal's 11 -- on a double -- $0.35.

"Blackjack Switch" lets you do just this. Only you play two spots yourself on every round and make the substitution on your own hands. But if, in "discovering" this game, hope springs in your breast, you've neglected what science ought to have taught.

That science lesson is to ascertain all the news, not just the part you want to hear (and they to tell). Blackjack Switch has several possible implementations. The form you're most likely to encounter pays 1-to-1 instead of 1.5-to-1 on a blackjack, gives ties on 17 through 19 to the house as opposed to pushing, makes the dealer hit rather than stand on soft 17, disallows pair splitting, and prohibits switching top cards when they're aces.

The 1-to-1 payout on a blackjack, alone, adds about 2.25 percent to the house's edge in the game. Inability to split pairs costs another 0.4 percent. These considerations, combined with the soft 17 rule and the dealer winning ties on 17 through 19, essentially balance the benefit provided by the ability to interchange top cards. An individual who memorizes the optimum switching strategy is therefore pretty much in the same boat, vis-a-vis house advantage, as a solid citizen who plays the traditional game in an otherwise identical manner.

Of course, you realize that you've got to make two bets instead of one. So you're risking $20 in what's nominally a $10 game.

What's more, the "correct" decision whether to trade cards isn't necessarily as simple as it might appear. Good players know that intuition doesn't always anticipate what the laws of probability prove is the optimum strategy. For instance, who'd "guess" that hitting beats standing on 12 against two-up, and doubling is "right" on A-4 versus four but not against three? Similar factors apply to permuting top cards on sets of hands. Say you have three-nine and four-10 with a dealer's 10-up. You should switch because three-10 and four-nine gain you 0.002 percent in an eight-deck game. How about six-nine and four-10 against the 10? Here, it's better by 0.011 percent to keep the hands as-is. Sure, these differences are small. But small differences, enough of them anyway, are the engines that pay the casinos' mortgages.

This doesn't mean you might not enjoy the challenge of the extra decisions in Switch Blackjack. Or the excitement of the chance to make two great hands out of a set of dogs. The game may be good. But not too good to be true. It's designed to attract players with action that gives the house an edge on which it can earn a profit. Sumner A Ingmark, who until now has never been mentioned in the same sentence as Alexander Pope, issued this caveat:

Know then thy cards, presume not hunch to play,
But proper maxims of the game obey.