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Best of Alan Krigman

Gaming Guru

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What's the source of the house advantage in blackjack?

26 April 2010

Blackjack house advantage arises from double busts. Players who exceed 21 lose, even when the dealer subsequently also busts. In most casinos, dealers must hit totals 16 or below and stand on 17 or above, including those with ace valued at 11. Under this rule, dealers break an average of 28 percent of their hands. A bettor following the same strategy would have 28 percent chance of busting, too. Therefore, double busts would occur with an average frequency of 28 percent times 28 percent, roughly 7.8 percent.

Were this the whole sordid story, dealers would win 49.4 percent and players 41.6 percent of all rounds over the long haul, the other 9 percent being pushes. House advantage would be 49.4 - 41.6 or 7.8 percent. No sensible person betting at or over the usual table minima would play a 1-to-1 game with this much edge.

To temper the edge, the rules give players some concessions. The 3-to-2 blackjack bonus is a big factor, especially because you don't have to do anything to get it. Just be wary of games that offer all kinds of goodies but pay blackjacks less than 3-to-2. This feature doesn't alter the likelihood of winning a round. And the probabilities of dealers or players receiving blackjacks are the same, about 4.7 percent. But dealers only collect what's bet while players are paid half again as much. The extra half cuts the overall edge by (1/2) x 4.7 or 2.35 percent.

Proper doubling also pares the edge. Depending on the dealer's upcard, this either doesn't affect or actually shaves prospects for a winning round. An 11 versus a dealer's five illustrates the former; following Basic Strategy, whether players hit or double, they'd stop after receiving one card. A 10 versus a dealer's eight typifies the latter; a player who drew a four, for a total of 14, would take another card if allowed and would win this combination more often by doing so than stopping. The reduction in edge by doubling, overall about 1.6 percent, results from betting more money when you already know your position is strong.

Splitting pairs is helpful both offensively and defensively. Offensive in two modes. First, splitting pairs such as nines against weak upcards like fives can lead to more advantageous starts; second, splitting pairs such as eights against a seven convert an underdog 16 into two somewhat promising eights. Pairs of eights against a 10 represent the classic defensive situation. An eight is weak versus a 10, but less so than a 16. And even one side winning and the other losing, a net push, is preferable to complete defeat. Proper splitting cuts edge, overall, by approximately 0.4 percent. The effect is an amalgam of the greater amount bet under improved conditions and an increase in the frequency of pushes, more at the expense of losses than wins.

The option to hit or double on soft 17 and 18, as appropriate, is another concession. It raises the frequency of winning rounds and can boost the amount at stake under favorable conditions. The impact is a 0.3 percent overall decrease in edge.

Ability to stand on 12 through 16 against the upcards on which the dealer is most apt to bust trims overall edge by 3.2 percent. Solid citizens avoid going over 21 and win if the dealer crashes.

There's no reason to hit when Basic Strategy says stand, or conversely. Such a move dims the outlook for winning a round while not changing the amounts involved. Declining to split or double when appropriate may be warranted if a player's poke is down to the dregs. And taking either of these actions rather than hitting or standing may be justified if winning the extra money seems more critical at any specific juncture than losing it.

Figures for the overall impact of the various options reflect the chance the opportunity will arise as well as the projected gain on the cards at issue. In any particular instance, the effect on expectation may be substantial. For this, you'd want to know the splits and doubles that yield the most and least potential gains, which is another topic entirely. And, even here, the operative word is "potential." As the inkster, Sumner A Ingmark, intoned:

When you're thinking of lessening gambling's high edge,
Count a bird in the hand as worth two in the hedge.

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.