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# Why blackjacks are more significant than most bettors realize

18 October 2010

Blackjack buffs all know the joy attending an ace-10 duo showing at their spot on the table. Ask bettors why blackjacks are important, though. You're almost sure to hear it's mainly because they can't lose -- they win, or they push against dealers' blackjacks unless you buy insurance and "take even money." Secondarily, it's because they pay a nice little bonus.

Few gamblers realize how much the no-lose and bonus features pull the house edge in the game down as low as it is. The probability of a blackjack "off the top of a shoe" is 4.75 percent. Players and dealers have equal chance of getting such a hand, of course.

Solid citizens collect 1.5 times the bet for theirs, however, while the bosses earn only the money wagered. Ignoring "contested blackjacks" that result in pushes, the bonus, multiplied by the probability it will be won, amounts to 0.5 x 4.75 or 2.375 percent of the average bet. This is subtracted from the edge the casino would have by winning double-busts were the game balanced.

The chance of a blackjack and consequent reduction in edge vary as aces, 10s, and other cards are removed from the shoe between shuffles. Enquiring minds will obviously want to know whether a simplified card counting scheme based entirely on aces and 10s can indicate when advantage shifts to the player, or gets so high for the establishment that it might be prudent to quit the shoe.

Say you're at an eight-deck table. More, you've become proficient at keeping track separately of the aces and 10s being placed in the discard rack. And you've learned to estimate closely when the discard pile contains half a shoe -- four decks.

If half the aces (16) and 10s (64) are missing from the shoe when four decks have been retired, the chance of a blackjack has risen from the full-shoe value of 4.745 to 4.757 percent. Neglecting other consequences of rank depletion, the corresponding edge reduction is 0.5 x (4.757 - 4.745) or 0.006 percent. Not enough to warrant altering your modus operandi.

Make believe, instead, that after four decks, half the aces but only 58 10s have been withdrawn. The probability of a blackjack increases to 5.203 percent; solely by this criterion, the house edge decreases by 0.5 x (5.203 - 4.754) or 0.224 percent. It's less adverse than usual, but not enough to give you an advantage.

Similarly, pretend that only 12 aces but half the 10s have been taken away. The probability of a blackjack is then 5.946 percent. This equates to cutting the house edge by 0.5 x (5.946 - 4.745) or 0.600 percent and makes you the favorite by over 0.1 percent.

When the remaining half-shoe is rich in both 10s and aces, you're in better shape yet. For instance if only 12 aces and 58 10s have become unavailable, the probability of a blackjack is 6.503 percent. This is worth 0.5 x (6.503 - 4.754) or 0.874 percent in edge. You'd then have a leg up on the casino exceeding 0.4 percent, about the same edge the joints normally have over players who follow perfect Basic Strategy.

The converse, an excess of desirable ranks relegated to the compost bin, is deleterious. Continuing to disregard other results of card removal, with 16 aces and 70 10s out of action, the likelihood of a blackjack is 4.311 percent and the house edge is half again as high as the nominal value. At 20 aces and 64 10s already dealt, the chance of a blackjack drops to 3.567 percent and the house edge jumps over 1 percent. Together, when 20 aces and 70 10s are missing from the remaining half shoe, the likelihood of a blackjack is only 3.233 percent, firmly belting the bosses into the catbird seats with roughly 1.2 percent edge.

Are such changes enough to justify raising your bets or concocting an excuse to take a break until the dealer shuffles? That's your call, predicated on the data at your disposal.

For, as the punters' poet, Sumner A Ingmark, pithily put it:
'Though facts are facts their implications,
Are subject to interpretations,
To meet each person's aspirations.