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Best of Alan Krigman

Gaming Guru

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Is Playing by the Book Better than by Experience?

5 November 1996

Some experienced blackjack buffs are punctilious about obeying the commandments of "basic strategy" in playing their hands. They've read, for instance, that 12 is an underdog versus a dealer's two-up but it's marginally more advantageous to draw than stand with these cards, so they hit.

Other experienced players know what's in the books and charts, but deviate slightly based on intuition gained at the table. They remember, for example, doubles often winning on hands like ace-five against a dealer's three-up even though the experts say hitting is a teensy bit better, so they slide out that extra bet.

How much do the fine points really matter?

To get an answer unbiased by my own hopes of just reward for study and/or practice, I set up my computer to play blackjack automatically and at warp speed. The computer simulated an eight-deck shoe, cut-off three decks from the end. House rules allowed "players" to double-down on any two cards and double after splitting, but not to resplit or surrender. Six spots were occupied at the table; the key player was in the fourth position, always betting a single unit on one spot.

The game ran in two modes. First, the key player stuck precisely to eight-deck double-after-split basic strategy. Second, the key player strayed from the straight and narrow with minor "errors" commonly committed by seasoned solid citizens: a) stand rather than hit 12 versus dealer's two- or three-up; b) double rather than hit 11 versus dealer's ace-up; c) double rather than hit ace-four and ace-five versus dealer's three-up; d) double rather than hit ace-two and ace-three versus dealer's three- or four-up.

One set of tests was designed to determine the house advantage for the two modes of play. The computer ran games in each mode for 25 million rounds. That's more than 1.5 million shoes.

I expected to find that drifting from basic strategy raised the casino's advantage. Surprise! The two modes of play yielded almost identical results. The house edge in both cases was roughly 0.57 percent of the initial bet per hand and 0.51 percent of the average total (including money for splits and doubles) per hand; that's 5.7 cents and 5.1 cents per $10 at risk, respectively.

A second set of tests was designed to investigate possible impacts of the two modes on individual players after single shoes. Here the computer ran 10,000 shoes in each mode.

Again, I expected to find that imperfect basic strategy imposed a small penalty on the player. It didn't. In both modes, the key player averaged close to one betting unit profit per shoe. Results in the two cases varied between a 12-unit win and a 10-unit loss per shoe, with characteristic fluctuations of over six betting units up or down. Likewise, either way, wins and losses were fairly well balanced with skewness approximately zero.

Here are what I consider the two most significant conclusions to be drawn from these tests.
o Common marginal departures from mathematically optimum play don't adversely affect a bettor's expectation over any practical playing period.
o For play close to optimum, the inherent fluctuation in the game more strongly influences the results of a session for an individual bettor than does the casino's edge.

You may form your own conclusions. Just be careful to recognize that the tests involved particular house rules and small departures from mathematically optimum play. Findings might differ considerably for alternate playing conditions - say, six-deck shoes with resplitting - and if deviations from basic strategy involved gross shifts such as doubling rather than standing on 16 verses five-up or splitting fours against a dealer's nine. As the punter's poet, Sumner A Ingmark, astutely admonished:

Extrapolation leads to dangers:
Results that hold in minor ranges,
May not pertain to major changes.

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.