Blackjack Dealers Break Less Often Than You May Think

Sometimes I wonder. Do we analytical wonks focus on the trees andforget the forest? Spray for fleas when the grizzly is charging?

Take this reception for a company boasting about its digitaltelevision research. Formalities over, we were milling aroundmunching canapés. A reporter buttonholed the firm's whiz kid,saying, "Tell me again how these new TV sets'll work." The guylaunched into the information superhighway, error-correctingcodes, data compression, store-and-forward logic, sampling andaliasing, and so on. The reporter finally broke in, "I mean, willyou turn the sets on and off or change channels with a regularremote, or will it be like using a computer?"

A few Sundays later, the parallel clicked between the scientist'smisdirected emphasis and my own modest efforts to coach casino-goers. As I was finishing brunch, a couple whom I'd seen beforebut didn't know took the next table and began burbling aboutblackjack. "I'm gonna try a new system I just thought of. Neverhit anything over 11," he stated. "That's not what the bookssay," she scolded. "Yeah, but think of this," he went on. "If Ihit, I might go over. If I stand, I'm still in the game in casethe dealer busts."

I'm growing grey over decimal point differences between splittingpairs of fours, doubling down, or just hitting when the dealershows a six. And, this solid citizen stands on things like 13against 10s so's not to bust in case the dealer does.

Once, I would have interrupted with more math than these folkscared about. And articulated so eloquently that even I couldn'thave comprehended what I was saying. Instead, I politely signalled for another cup of coffee and pondered predicating my nextcolumn on the nub of what this chap, and abler blackjack playerstoo, did and didn't know.

They know that much of the house advantage in blackjackcomes from the dealer's going last. If the player and thedealer both bust, the house wins.

They don't know that the dealer busts much less than halfthe time, regardless of upcard. The average is 28 percent ofall hands. Even showing a stiff, two through six, thedealer's chance of breaking only averages 39 percent. Sitting pretty, seven through ace, dealers average a 21 percentbreak rate.

The accompanying table gives fractions of hands on which dealerscan be expected to exceed 21 for different upcards. The figuresindicate how vulnerability to breaking rises as upcards go fromtwo to six, drops sharply at seven and continues to fall through10, then plummets at ace.

The table shows that on normal shoes, the dealer should make 17through 21 on almost two-thirds of the stiffs and four-fifths ofthe stronger upcards. Waiting for the dealer to break obviouslyisn't playing it smart. Rather, optimum decisions are embodied inbasic strategy . No abstract theory, these rules maximize expectedreturn based on the likelihood of drawing various cards from theshoe. They weigh the chances dealers will bust as well as consequences of standing and the risks and rewards of drawing to tieor beat hands dealers make.

Is there a miracle "system" that, by some twist of fate, countless casino patrons and computer buffs have missed? Is there atooth fairy? Those who seek such serendipity argue that nobody'shaving found them yet doesn't mean nobody ever will. But I'dbetter stop here or we'll soon be meditating on whether it'spossible to prove that something's impossible (it isn't). Anyway,Sumner A Ingmark, poet of probabilities, gave as good a responseas any to this objection when he wrote:

They scoffed at Thomas Edison,
For incandescent light,
But just because they scoff at you,
Don't think your system's right.