The Bad, the Good, and the Beautiful at Blackjack

4 October 2006

By Alan Krigman

Gamblers are naturally pleased to win wagers and disappointed to lose them. In most games, the odds associated with the ecstasy or agony are ordained before bets are made, or are established when players pick the propositions on which they put their pennies. Slots typify the first situation, since the probabilities and payouts governing all possible results are inherent in the machines. Roulette and craps epitomize the second, with opportunities for aficionados to make trade-offs on a scale from high probability of small wins to longshots at large returns.

Games like blackjack differ. Chances and payoffs at the outset of a round are one element, and determine overall edge, volatility, and skewness. At this stage of a game, the uncertainty of who gets which cards is a factor. However, once a player's starting hand and dealer's upcard are known, conditions change. Some combinations favor players while others leave them at a disadvantage. Victory then is especially sweet when achieved by an underdog and defeat particularly bitter when delivered to the occupant of the catbird seat.

Blackjack players who don't know the wheat from the chaff often overestimate the prowess they're showing when winning strong starters. And, conversely, tend to become overly frustrated about the bad breaks befalling them when they lose hands that begin as bummers. Either attitude can lead to specious action.

Here's the skinny when neither the player nor the dealer has a blackjack. Players are favored regardless of the dealer's upcard when starting with totals of 10, 11, 19, and 20. Expectation is also positive with nine or 18 versus two- through eight-up, eight versus three though seven-up, and 17, seven, and four versus six-up. All other two-card totals represent uphill battles. Of the combinations, eight versus three-up, seven versus seven-up, and five versus six-up, are so marginal as to be essentially neutral.

In all, there are 170 "playable" two-card total and dealer upcard combinations: the 17 hands from four through 20 times the 10 upcards. This discounts starting with 21 and recognizes that no starting hands total two or three because at least one ace would be involved and these would be figured as 12 or 13 respectively. Of the 170, 62 are promising and the remaining 108 pernicious.

The outlook isn't as bleak as the 108-to-62 scorecard might imply. One reason is that 20 is not only especially potent, but also is the most common two-card total. It's formed by two 10-values of which there are four times as many as any other rank as well as ace-nine. To illustrate, a player should average only about three 16s for every four two-card 20s.

A second reason why simply tallying projected winners and losers doesn't tell the whole story is that the good hands tend to be more robust than the poor are frail. Here are some examples, per dollar bet at the start of a round. Totals of 20 are projected to earn between $0.56 against a 10 and $0.79 against an eight, 19s peak at $0.62 against sevens, and 11s get as high as $0.67 against sixes. On the bleaker prospects, the worst is 16 versus 10 where average loss is $0.54 per dollar, followed by 16 against ace at $0.52 per dollar, 15 against nine at $0.51 per dollar, and 15 against 10 at $0.50 per dollar.

These insights aren't meant to affect the way you play particular hands. But they can help you understand why you're winning or losing. Are you getting a decent share of strong starting hands? Are you winning enough of the propitious and at least some of the inauspicious? Are you being dealt projected losers in round after round and not pulling at least some of them off, or are you getting what should be winners and watching them get trounced?

Of course, there's still the matter of how knowing the answers to these questions can make you a better bettor. It has to do with the way attitude affects your ability to act rationally, like the mature adult you think you are. And for this, you may want to go for guidance to the gamblers' doer of doggerel, Sumner A Ingmark:

Counting your profit before you receive it,
Leads you to make up a myth and believe it.