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Best of Alan Krigman

Gaming Guru

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In Blackjack Card Counting, You May Prefer Neatness to Accuracy

21 September 2005

Most blackjack players know that aces and 10s are good and low cards bad. In general, the more 10s and aces left in the shoe -- or, to be strictly correct -- the higher the ratio of these to low cards, the greater the bettor's expectation of profit.

This is the effect card counters try to use to gain an advantage. "Try" is the operative word because the idea is more elementary in principle than in practice. One hindrance is that casinos are adept at spotting counters, and can take preventive measures if a shoe becomes too favorable to folks they fear are milking the cash cow. Another obstacle is that standard counting techniques involve mental addition, subtraction, and division -- all prone to error in the distracting atmosphere of the blackjack pit.

Little can be done about spotters, notwithstanding attempts at "camouflage," except to note that they rarely bother players at low-limit tables who don't push their bets through the roof when the count zooms up. There's a partial solution to the problem of doing arithmetic accurately in your head while talking to the dealer, totaling your hand and remembering what action to take, ignoring noise around you, giving your order to the server, and so forth. This solution is a simpler counting scheme indicating when you have an edge. It's less potentially profitable than classical counting done correctly. But it's better than trying to run with the big dogs and stumbling, or cowering under the porch.

It's a two-stage process. First, keep a tally of how many 10s and aces have been dealt. It may help to create a stack of chips, for instance one for every 10 aces and 10s you see, to mark where you are. Second, when a round is about to start, estimate how many whole decks are in the discard rack, multiply this times 20, and subtract 10 from the product. After you've practiced a bit, you can refine the approach to eyeball the discards for half-decks. Either way, if your tally is below the result, you're in the catbird seat; if it's above, the house still has the advantage.

Here are some examples. Pretend you've tallied 36 10s and aces. A peek at the discards shows two decks. Multiplying 2 x 20 yields 40, minus 10 is 30. Your tally is 36, so too many high cards have been dealt and the house has an edge on what's left. Alternately, say your tally is 57 10s and aces. You peg the discards at three and a half decks. Multiply 3-1/2 x 20 to get 70, minus 10 is 60. Your tally shows a dearth of high cards dealt so you're flush.

The easiest way to use your knowledge of the advantage is to stay at the table minimum when your ace-10 tally exceeds the threshold you figure based on the discard pile, and to raise your bet when it's below this point. The wider the bet spread, the more effective the method. But during the course of a single session you'll generally have an overall advantage just by doubling up.

The procedure is approximate and forgives minor errors in tallying aces and 10s as well as in estimating the size of the discard pile. To avoid betting big when conditions are actually adverse, guess high when you're uncertain of the tally and low when you're unsure how many decks you see. Confidence also improves as more cards are dealt. So, if you're nervous moving out the moolah when your tally is below the threshold but not by much, stay at the minimum until three decks have been dealt.

For reference, consider an eight-deck game. At two decks out, the threshold of 30 aces and 10s gives you an edge of 0.9 percent. At three decks out, 50 aces and 10s gives you a 1.1 percent edge. And at six decks out, 110 aces and 10s gives you a 3.6 percent edge. Further, your advantage is higher when the tally is lower. With four decks out, the threshold value of 70 aces and 10s gives you a 1.6 percent edge while at 65 aces and 10s it's 2.6 percent.

Will this modus operandi make you rich? Will it guarantee a win every time? If the pit bosses know what you're doing and don't take countermeasures, will they still give you a comp? The poet, Sumner A Ingmark, addressed all these questions when he wrote:

In the world of probabilities success at best is tenuous,
Overcoming short-term setbacks calls for effort very strenuous.

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.