Playing it smart - Why six decks are better than eight

Most experienced blackjack buffs are aware that the fewer the decks from which cards are drawn, the better the game in theory for players. That is, six decks are preferable to eight, four to six, and so on. All else being equal, of course.

Not many solid citizens know why this is the case. In fact, it's commonly believed that the difference involves either the ease or beneficial effect of counting cards in smaller shoes. So they think no advantage accrues to folks who merely follow Basic Strategy or worse don't.

Reducing the number of decks does improve the prospects for card counters. However, it also lowers the house advantage for other players. The reasons involve the way probabilities of drawing various cards are affected by the size of the residual shoe.

The likelihood of pulling a blackjack offers one illustration.

Suppose the dealer gives you a 10 on the first pass around the table. Ignoring other cards exposed on that pass or in previous rounds, what's the chance this'll happen? And, assuming it does, how apt are you to be blessed with an ace on the second pass?

A six-deck shoe has 6 x 16 = 96 10-values and 6 x 52 = 312 total cards. The chance of an initial 10 is therefore 96 out of 312 or 30.769 percent. Considering only the 10 to be gone, the shoe then would have 6 x 4 = 24 aces in 311 remaining cards. So the chance of topping the 10 with an ace is 24/311 or 7.717 percent.

An eight-deck shoe has 8 x 16 = 128 10-values and 8 x 52 = 416 total cards. The chance of an initial 10 is therefore 128 out of 416, which is 30.769 percent as in the six-deck game. But the shoe now has 415 unknowns, of which 8 x 4 = 32 are aces. So the chance of topping your 10 with an ace is 32/415 or 7.711 percent.

Having started with a 10, your chance of finishing with a blackjack is accordingly slightly better in a six- than an eight-deck game, 7.717 as opposed to 7.711 percent. Including the inverse ace first and 10 next and combining the chances associated with both cards, the probability of a blackjack works out to 4.749 percent with six decks and 4.745 percent with eight.

More frequent blackjacks favor players. Dealers have the same chance of these hands as bettors. But dealers only take one unit when their blackjacks win, while bettors normally get 1.5 units for theirs. This 50 percent bonus trims what's otherwise the edge in the game. Accounting for the chance of a push simultaneous player and dealer blackjacks this factor alone cuts edge by 0.0029 percent more in a six- than an eight-deck game. All of which explains, incidentally, why a one-deck game with a 6-to-5 blackjack payoff a paltry 20 percent bonus is a bum deal.

Similar arithmetic shows doubles to be stronger in six- than eight-deck games. Calculations are more complicated because every situation must be evaluated for every imaginable draw and for all the ways the dealer's hand could be resolved. A few examples suggest the magnitude of the effect. Say you bet $10 and receive 5-5 versus 4-up. In a six-deck game, your expected profit by doubling averages out to $4.81. With eight decks, it's $4.76. Likewise, 8-2 versus nine-up gives the player an expectation of earning $1.49 and $1.48 with six and eight decks, respectively.

The differences, pennies on $10 bets, may seem minor. But they're not inconsequential. This, because the edge in blackjack and other of the more sophisticated casino games is a only a small fraction of the money in action per round to begin with. So the best anyone can hope to do is to shave a bit here and a bit there. Not that edge is the only element working against you in a casino. Still, the more you can tame it without introducing adverse consequences on other fronts like getting into a pickle by overbetting your bankroll or setting yourself up for killer downswings -- the better the gambler you are. As the enigmatic inkster, Sumner A Ingmark, eruditely intoned:

Avoid being sorry a day or so after,
And masking your anguish with counterfeit laughter,
For giving casinos more edge than you hav'ter.