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# Playing It Smart: How much better are six decks than eight in blackjack?

13 May 2008

Blackjack is a game of fine distinctions. Sure, standing with 10-10 versus 10 is a no-brainer compared to splitting or hitting. Both intuitively and statistically. For reference, the math says standing wins 55.80 cents/dollar while hitting or splitting lose 44.02 or 84.76 cents/dollar, respectively. But many hands are close calls. Take 9-7 versus 10. It's a dog no matter what you do. With eight decks, loss averages 53.77 cents/dollar standing and 53.65 cents/dollar hitting. Surrender saves 3.77 cents/dollar over hitting, and hitting saves 0.12 cents/dollar over standing.

Six decks have lower edge than eight, although the effect is also marginal. With identical rules (this may not be the case; eight-deck games often have weaker options), including resplitting non-aces, Basic Strategy edge is 0.40 percent with six decks and 0.43 percent with eight. Savings are only \$0.03/\$100. Fewer decks mean more to card counters than Basic Strategy buffs. The reason is that probabilities change faster and fluctuate more widely with draws from smaller sets, opening more and better windows of opportunity. Picture it for one or two decks. Prospects of any rank are four out of 52 with one fresh deck and eight out of 104 with two. These both equal 7.69 percent. If the first card is a five, what's the chance the next will pair it? With one deck, three out of 51 or 5.88 percent. With two decks, seven out of 103 or 6.80 percent. Fewer decks yield greater probability changes.

Variations in probability with shoe size underlie the other differences as well. For instance, blackjacks pop more often in games with fewer decks. Likelihoods are equal on either side of the table, but blackjacks impact edge since dealers collect only the amount at risk when theirs win, while players pick up 1.5-to-1 when they luck out. The chance of a blackjack in a six-deck game when no discards are known is that of an ace then a 10 or a 10 then an ace. That's [(6x4)/(6x52)]x[(6x16)/(6x52 1)] + [(6x16)/(6/52)]x[(6x4)/(6x52 1)] or 4.7489 percent. For eight decks, it's slightly less substitute 8 for 6 in the formula and you get 4.7451 percent. The probabilities differ by 0.0038 percent. The edge reduction is half as much, 0.0019 percent (\$0.19/\$10,000) owing to the half-unit imbalance between what solid citizens and dealers get for their respective blackjacks.

Probabilities of occurrence similarly account for the remaining edge difference between six and eight deck games. Blackjack has 550 starting combinations. Of these, six-deck shoes theoretically win more or lose less in 346, eight-deck shoes are projected do better in 190, and the configurations are equal in 14. Of course, combinations aren't uniformly apt to be dealt or yield wins. Six decks are better in 58.1 percent of all hands, eight in 36.5 percent, and the shoes are equal in 5.4 percent.

Proficient blackjack players relish hands on which they can double down. Done properly, these represent auxiliary wagers made when bettors are at an advantage. Basic Strategy doubles account for 98 of the 550 combinations, 9.64 percent of all hands, with shoes of both sizes. The benefit in edge arises because 87 of the 98 doubles have higher profit expectation with six decks. The 11 where eight decks are better are 9-2 versus seven, 6-5 versus 10, and 9-2, 8-3, and 7-4 versus eight, nine, or 10.

Occasions to split pairs differ slightly between shoe sizes. Both involve 52 out of the 550 hand combinations. But six-deck splits have a probability of 2.53 percent while it's 2.56 percent with eight decks. For offensive splits, when expectation goes from negative to positive or gets increasingly favorable, six decks account for 37 combinations with a probability of 1.75 percent while for eight decks it's 36 combinations and 1.73 percent. Defensive splits, which reduce but don't reverse the house's advantage, include 15 combinations for six decks at 0.77 percent, and 16 combinations for eight decks at 0.83 percent.

Given a choice, when conditions are equal or superior at six-deck tables, go for these over eight=deck games. But if you must bet more to play, dwell on the definition of "equal" and ponder this pithy proverb from the parsimonious poet, Sumner A Ingmark:

Overbet your pocketbook and run the risk that you'll wish,

You weren't quite as penny-wise while being so pound-foolish.

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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.