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Best of Alan Krigman

Gaming Guru

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Was It Wrong to Buck the Odds If You Won?

7 December 1998

When a blackjack dealer starts a round showing 10-up and doesn't have an ace in the hole, you're the underdog with all but five of the 19 non-blackjack two-card player starting totals. You're favored slightly on a 10 by hitting, moderately on an 11 by doubling, slightly on a 19 and strongly on a 20 by standing, and moderately on an ace-ace by splitting. Since everything else is weak, some brazen blackjack buffs flout the fickle fancies of fate and split proscribed pairs under these conditions.

This phenomenon came to the fore the other day. Fellow players at two different tables ignored "the book." They split pairs against a 10 when Basic Strategy said "hit." And they emerged triumphant.

Tillie split 3-3. She drew an eight on the first, doubled (correctly), and pulled a 10 to total 21. She drew a seven on the second, doubled (incorrectly), and pulled a 10 for a total of 20. The dealer turned over a nine to total 19. Tillie won four units. Playing "properly," she would have hit the six with the seven and then the 10, busted, and lost one unit.

Billy split 7-7. He drew a six on the first, hit (correctly), and pulled a nine to bust. He drew a four on the second, doubled (correctly), and pulled a 10 to total 21. The dealer flopped a 10 for a total of 20. Billy lost one and won two -- a net one-unit gain. Playing "correctly," he would have hit the 14 for a push.

Both solid citizens had luck working for them on these hands. The odds were adverse even with the statistically optimum decisions. Defying the laws of probability further reduced the chances. But, I wondered at the time, since they were in a damage control mode anyway, how much tougher did they make it for themselves?

I checked when I got home. The following list gives what I found. It shows how expected loss per dollar bet increases against a 10-up, by splitting rather than hitting 2-2, 3-3, 4-4, 6-6, and 7-7 as well as splitting rather than standing on 9-9.

hand expected loss per $1 bet
hit (H) or stand (S) split
2-2 $0.29 (H) $0.47
3-3 0.34 (H) 0.52
4-4 0.25 (H) 0.57
6-6 0.38 (H) 0.66
7-7 0.47 (H) 0.63
9-9 0.17 (H) 0.29

Here's an example of how to interpret the table. Expected loss when hitting 3-3 against a 10 is $0.34 per dollar bet; splitting raises this to $0.52. None of the "incorrect" splits is anywhere close to Basic Strategy. The least theoretical sacrifice, on 9-9, is $0.12 per dollar bet. Billy worsened his woes by $0.16 per dollar when he split the 7-7. Tillie exacerbated her expectation by $0.18 per dollar when she split the 3-3. Despite the dimmer prospects, however, both did better than they would have with the optimum decisions in these particular instances.

Am I telling you to throw caution to the breeze? To a degree, of course, you're doing that by gambling at all. But, as anyone who knows me in person or through this column is aware, I ardently advocate those bets and decisions most apt to be profitable -- consistent with individual bankrolls, goals, and temperaments. I also urge players to think in terms of their chances beforehand, not the outcomes after the dust settles and the band packs up.

Still, it helps to recognize that if gambling is about nothing else, it's about uncertainty. You can give yourself the best chance the casino offers, and lose your lunch money. Or you can follow the most off-the-wall hunches or be governed by the most outrageous superstitions, and catch that limo ride to Easy Street. Over the long haul, playing the percentages should make a significant difference. On a single bet, the next card or roll or spin may have certain probabilities -- but, unless the chance is truly zero or 100 percent, any allowable result could occur.

Sumner A Ingmark, composer of cantos on kismet, counseled carefully contemplating this commentary on the human condition:

Those who go by the book will oft times take offense,
When the workings of fate with reward recompense,
Those who trust more to luck than to knowledge and sense.

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.